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Astronomy, NASA, Physics

Webb Spies Uranus Rings

Webb image of the rings of Uranus. Credit SCIENCE: NASA, ESA, CSA, STScI
IMAGE PROCESSING: Joseph DePasquale (STScI); Source: https://tinyurl.com/mukddzcm

This zoomed-in image of Uranus, captured by Webb’s Near-Infrared Camera (NIRCam) Feb. 6, 2023, reveals stunning views of the planet’s rings. The planet displays a blue hue in this representative-color image, made by combining data from two filters (F140M, F300M) at 1.4 and 3.0 microns, which are shown here as blue and orange, respectively.

What a typical Press Release might tell you.

        Uranus has eleven known rings that contain dark, boulder-sized particles. Although the rings are nearly-perfect circles, they look like ellipses in some pictures because the planet is tilted as we are viewing it and so the rings appear distorted. They appear compressed in the side-to-side direction but are their normal undistorted distance from Uranus in the top-down direction in this image.

The outermost ‘epsilon’ ring is made up of ice boulders several meters across. The other rings are made up mainly of icy chunks darkened by rocks. The rings are thin ( less than 200 meters), narrow (less than 100 km), and dark compared to the rings of other planets. They are actually so dark they reflect about as much light as charcoal. The rings have a temperature of about 77 Kelvin according to U.C. Berkeley astronomers.

Read More!

NASA Press Release: Webb Scores Another Ringed World

Mashable.com. Surprise! Uranus has rings!

Research paper. Thermal emission from uranian ring system

Press Releases and textbook entries depend on scientists interpreting the data they gather to create a better picture of what they are seeing. I am going to show you in this Blog just how some of those numbers and properties are derived from the data astronomers gather. I have created three levels of interpretation and information extraction that pretty nearly match three different education levels and the knowledge about math that goes along with them.

I. Space Cadet (Grades 3-6)

This is the easiest step, and the first one that astronomers use to get a perspective on the sizes of the things they are seeing. In education, it relies on working with simple proportions. The scale bar in the picture tells you how the size of the picture relates to actual physical sizes.

1) Use a millimeter ruler to calculate the diameter of Uranus in kilometers.

2) Place your ruler vertically across the disk of Uranus. Measure the vertical (undistorted) distance from the center of Uranus to the center of the outer ‘Epsilon’ ring. How many kilometers is this ring from the center of Uranus?

3) Compare the size of the Uranus ring system to the orbit of our moon of 385,000 km. Would the moon’s orbit fit inside the ring system or is it bigger?

II. Space Commander (Grades 7-9)

This level of interpretation is a bit more advanced. If you are in Middle School, it works with concepts such as volume, mass, speed and time to extract more information from the data in the image, now that you have completed the previous-level extraction.

1) What is the circumference of the Epsilon ring in kilometers?

2) The rings of Uranus are only about 200 meters thick and no more then 100 km wide, which means their cross-section is that of a skinny rectangle. What is the cross sectional of the area of the Epsilon ring in square-kilometers assuming it is a rectangle with these dimensions?

3) What is the volume of the ring in cubic-kilometers if Volume = Area x Circumference?

4) If the volume of Earth is 1 trillion cubic kilometers, how much volume does the Epsilon ring occupy in units where Earth = 1?

5) With sizes of about 7-meters in diameter, what is the average mass of a single boulder if it is made from ‘dirty ice’ with a density of 2000 kg/m^3?

6) Scientists estimate that there could be as many as 25 billion boulders in the Epsilon ring. From your answer to the previous question, what is the total mass of this ring?

7) [Speed and time] The particles in the Epsilon ring travel at a speed of 10.7 km/s in their orbit around Uranus. How many hours does it take for a boulder to complete one orbit?

III. Junior Scientist (College, Graduate school)

This is a very hard level that requires that you understand how to work with algebraic equations, evaluate them for specific values of their constants and variables, and in physics understand Planck’s Black Body formula. You also need to understand how radiation works as you calculate various properties of a body radiating electromagnetic radiation. Undergraduate physics majors work with this formula as Juniors, and by graduate school it is simply assumed that you know how to apply it in the many different guises in which bodies emit radiation.

The Planck black body formula is given in the frequency domain by

where E is the spectral energy density of the surface in units of Watts/meter^2/Steradians/Hertz and the constants are h = 6.63×10^43 Joules Sec; c = 3.0×10^8 meters/sec and k = 1.38 x 10^-23 Joules/k.

  1. If the temperature of the Epsilon ring material is T=77 k, what is E in the 1.4-micron band of the Webb (F140M) and in the 1.3- millimeter band of the Atacama Large Millimeter Array (ALMA) for a single ring particle?
  2. What does your answer to Question 1 tell you about the visibility of the rings seen by the Webb at 1.4-microns?
  3. If the 1.3-millimeter total flux in the Epsilon ring was measured by ALMA to be 112milliJanskies (Table 3), about how many particles are contained in the Epsilon ring if it consists of dirty ice boulders with a 7-meter diameter? Note: 1 Jansky = 10^-26 watts/m^2/Hz. Assume a distance to Uranus of 1 trillion meters.
  4. If the volume of the Epsilon ring is about 6.4×10^6 cubic kilometers, about how far apart are the boulders in the ring?
  5. From your answer to Question 4, if the relative speeds of the ring boulders are about 1 millimeter/sec (see Henrik Latter), how often will these boulders collide?

So, how did you do?

You may not have gotten all of the answers correct, but the important thing is to appreciate just how astronomers extract valuable information about an object from its image at different wavelengths. Other than visiting the object in person, there is no other way to learn about distant objects than to gather data and follow many different series of steps to extract information about them. Some of these series of steps are pretty simple as you experienced at the Space Cadet-level. Others can be very difficult as you saw at the Junior Scientist-level. What is interesting is that, as our theoretical knowledge improves, we can create new series of steps to extract even more information from the data. Comparing the ring brightness at two or more wavelengths, we can deduce if the boulders are made of pure ice or dark rocks. By studying how the thickness of the ring changes along its circumference relative to the locations of nearby moons, we can study gravity and tidal waves in the ring bodies that tell us about how the density of the ring particles change. Astronomy is just another name for Detective Work but where the ‘crime scene’ is out of reach!

Answers

I.1 Close to 50,700 km.

I.2 Close to 51,000 km radius 102,000 km diameter.

I.3 The moons orbit radius is 385,000 km. The outer Epsilon ring could easily fit inside our Moon’s orbit.

II.1 Circumference is about 2(pi)R, so with R = 51,000 km, the circumference is 320,000 km.

II.2 The cross-section is 100 km long and 200 meters tall so its area is just A = 0.2 km x 100 km = 20 square km.

II.3 Volume = Area x Circumference = (20 km^2)x (3.2×10^5 km) = 6.4 x 10^6 km^3.

II.4 Volume = 6.4 x 10^6 km^3 / 1 trillion km^3 = 0.0000064 Earths.

II.5 Mass = volume x density. A single boulder with a radius of 3.5 meters has a volume of 4/3 pi (3.5)^3 = 179 m^3. Then its mass is 179 m^3 x 2000 kg/m^3 = 359000 kg or 359 tons.

II.6 There are 25 billion of these boulders so their total mass is 25 billion x 359 tons = 9.0×10^15 kg or 9 trillion tons. According to calculations in 1989, the mass of the Epsilon ring is estimated to be closer to 1016 kg or 10 trillion tons [Nature].

II.7 51,000 km/(10.7 km/s) = 8.3 hours.

III.1 Working with the Planck equation is always a bit tricky. The units for B will be Watts/m^2/Str/Hertz. First lets evaluate the equation for its constants h, c and k.

For the Webb infrared band of 1.4-microns, its frequency is 3×10^8/1.4×10^-6 or 7.1×10^13 Hertz. For ALMA the frequency is 231 GHz or 2.31×10^11 Hertz. For a temperature of 77 k, we get B(Webb) = (5.26×10^-9)(5.8×10^-20) = 3.0×10^-28 watts/m^2/Hz/str. For ALMA it will be B(ALMA) = (1.8×10^-16)(6.46) = 1.2×10^-15 Watts/m^2/Hz/str.

III.2 The visibility of the ring by its thermal emission cannot be the cause of its brightness in the Webb F140M band because its black body emission at 1.4 microns is vanishingly small due to the huge exponential factor. It must be caused by reflected visible light from the sun.

III.3 In the ALMA 1.3-millimeter band, the flux density from a black body at a temperature of 77 k is 1.2×10^-15 watts/m^2/Hertz/str. One Jansky unit equals 10^-26 watts/m^2/Hz, so the black body emission in the ALMA band can be re-written as 1.2×10^11 Janskies/str. The angular radius of the boulder at the distance of Uranus ( 1 trillion meters) is given in radians by Q = 3.5 meter/1 trillion meters = 3.5×10^-12 radians. The angular area is then AQ = pi Q^2 = 3.9×10^-23 steradians. Then the black body flux density from this boulder is about S=1.2×10^11 Jy/str x 3.9×10^-23 str so S=4.5×10^-12 Janskies. But ALMA detects a total emission from this ring of about 0.112 Janskies, so the number of emitters is just 0.112 Jy/4.5×10^-12 Jy/boulder = 2.5×10^10 boulders or 25 billion boulders.

III.4 The ring volume is 6.4 x 10^6 cubic kilometers, so each boulder occupies a volume in the ring of about 6.4×10^6 km^3/25×10^9 boulders= 256,000 cubic meters/boulder. The average distance between them is L = V^0.333 = 63 meters.

III.5 Time = distance/speed so 63m/0.001 m/sec = 17.5- hours. The Epsilon particle orbit speed is about 8.3 hours (see II.7), so the particles collide about twice every orbit.

Brain Research, Education

Your Brain..On Math!

Credit: SciTechDaily https://scitechdaily.com/researchers-discover-how-the-human-brain-separates-stores-and-retrieves-memories/

In my earlier blogs, I talked about Math Anxiety, about how the brain creates a sense of Now, and various other fun issues in brain research too. Branching off of my long, professional interest in math education, I thought I would look into how ‘doing’ math actually changes your brain in many important ways, especially for children and adolescents. Brain research has come a long way in the last 15 years with the advent of fMRI and sensors that can listen-in to individual neutrons [1]. For a detailed glimpse of modern research have a look at my reference list at the end of this blog.

Here is what we know about how math affects brain structure and maturation. My previous blog on Math Anxiety covered this topic but here are some additional points.

The Basic Anatomy of Math

First of all, let’s put to rest a popular misconception. Its a complete fallacy that we only use 10% of our brain. The misconception probably arose because glial cells that support neurons account for 90% of the cellular matter in the brain, so neurons account for 10% [9,11,10]. The truth is, by the end of each day, your brain has used nearly all of its neurons to facilitate movement, sensory processing, advanced planning, and even day-dreaming!

The architecture of our brains is controlled by about 86 million neurons and the trillions of synaptic connections between them. At the lowest level, our brains are composed of numerous modules that are specialized for specific tasks. Each has its own local knowledge system and ‘data cache’ and can act much faster than the whole-brain, which is the way evolution designed this system to help us respond quickly and not get eaten. We benefit from this ancient architecture because craftsmen, musicians and dancers cannot tell you how they perform their tasks because it is largely unconscious and controlled by specific modules. [6:p45, 198].

Before the age of 2, children use a general knowledge ‘program’ that takes up all of their working memory [2:p151] to interact with the environment. Children require more working memory to do math than adults. Number facts and basic opeations are not yet in long-term memory so they use more of their prefronal cortex (PFC) to keep math in working memory so that they can solve problems [2:p155]. But through training they develope a growing multitude of specialized modules and automatic ‘subroutines’ for specific tasks and skills. [6:p56]. Consciousness occurs when these non-communicating modules begin to share their knowledge across many communities of modules spanning the entire cerebral network. Some of these global communication pathways are highlighted by the so-called brain connectome map. This sharing of multiple representations of similar knowledge leads to problem solving and creativity which now draw inspiration from the experiences of many different modules [6:p58] spanning the entire cortex.

The wiring diagram of a human brain revealing connections. Courtesy of the consortium of The Human Connectome Project

Development of the Brain

At birth, the average baby’s brain is about a quarter of the size of the average adult brain. Incredibly, it doubles in size in the first year. It keeps growing to about 80% of adult size by age 3 and 90% – nearly full grown – by age 5 [12]. Over 1 million new neural connections are created every second among the synapses of the growing population of neurons and dendrites [13]. What then ensues is a process of pruning as seldome-used connections wither and dissappear while others are strengthened [20].

The growing brain does not start out as a tabla rasa but through genetics and evolution there are already features in place that anticipate the growth of mathematical knowledge.

Number Line Maps

At the most elementary level, neurons already exist at birth that are active for specific numbers. These ‘number neurons’ have been found in both monkeys and in humans. In humans they are mostly found in the lateral prefrontal cortex (l-PFC) and the intraparietal sulcus (IPS). [2:p129], but also the mediotemporal lobe (MTL) [2:p98]

Our brain’s hippocampous has place and grid cells that form a direct map written on its cortex that represents the location of objects in space [7p219]. The posterior cingulate region has neurons tuned to the location of objects in the outside world, and is connected to the parahippocampal gyrus where “place cells’ are found. These neurons fire whenever an animal occupies a specific location in space like the northwest corner of your room. These place cells are so advanced that readout of individual nerve cell firings can be used to tell a researcher where the object is in the subjects visual field of view. This even works when the subject closes their eyes and imagines an animal located there. [4:p149].

A curious feature of how the young brain processes quantities is that it perceives quantities as being located on a mental number line. Called the SNARC Effect, even three-day-old infants will look-right for large quantities and look-left for smaller quantities.[2:236]. That calculation-related activity is being processed like mental movement on a number line was also tested in older subjects by studying neuron activation in the superior parietal lobule (SPL) where information is being manipulated in working memory. They found that eye motion alone predicted the answers to simple addition and subtraction problems [2:239]. So just as the brain uses an internal map in the hippocampus to locate objects in space, it also uses an internal map to locate numbers in space along a line! The number line however is not uniform.

Kindergarten students with no math knowledge see number intervals as quantities mapped out in logarithmic intervals just as many animals do, so that quantities are perceived almost the same way as light brightness or sound volume [2:87]. Large numbers with smaller intervals are crowded together in the right-hand of the mental number line while smaller numbers are more spread out in the left-side of the line.

Meanwhile, the concepts of addition and subtraction are already known to infants as young as nine months[2:196]. Thinking about quantity as symbolic numerals like 1,2,3 etc instead of dots like [.], [..], […] etc at first occupies children up to age 7 who have to use their working memory to keep track of this, but within a few years the relationship between number symbols and dots becomes automatic and unconscious [2:185]. By the way, although algebra looks like a language, algebra is not processed in the brain’s language centers [2:p222] You can think and reason logically without language. In fact, when professional mathematicians are studied and asked to solve advanced problems, their language centers are not activated. Instead, the bilateral frontal, intraparietal and ventrolateral temporal regions were active, which are connected to the regions associated with processing numbers [2:232].

Math Remodels the Brain.

For mathematicians, an interesting recycling of brain areas occurs in order to accommodate advanced mathematics. Afterall, the brain volume is fixed by the volume of the skull, so the only way that new skills are learned and mastered is by appropriating cerebral real estate from other adjacent functions. The inferior temporal gyrus (ITG) is an area where face recognition occurs. For mathematicians, part of this region is invaded by adjacent regions used in number processing [2:191], in some cases making it harder for mathematicians to recognize faces!

Admittedly, this is an extreme result of brain reorganization, but there are other examples that are more relevant to children and young adults and the answer to the question ‘Why do I need to know math?’

Researchers have proposed that math training not only makes us better at math, but also strengthens our ability to moderate our feelings and our social interactions because of the brains proclivity in  sharing brain regions for other purposes.

Example 1: In my previous blog on Math Anxiety, I mentioned that the sub-region called the dorsolateral prefrontal cortex helps us keep relevant  problem-solving information ‘fresh’ in our working memory. In math it is activated when the individual is keeping track of more than one concept at a time. As it also turns out, this region is also activated as we regulate our emotions. For example, most children learn how to tone-down their glee at winning a game when they see their friends are mortified at  having lost.  It is also important in suppressing selfish behavior, fostering commitment in relationships, and most importantly inferring the intentions of others, which is called a Theory of Mind.

Example 2: The long-term effect of not continuing math education and problem-solving in adolescents has also been documented. A recent study of adolescents in the UK shows that a lack of math education affects adolescent brain development. In the UK, students can elect to end their math education at age 16.  The neurotransmitter called gamma-Aminobutyric acid (GABA) is present in the middle front gyrus (MFG), which is a region involved in reasoning and cognitive learning. GABA levels are a predictor of changes in mathematical reasoning as much as 19 months later.  What was found among the older adolescents was that GABA showed a marked reduction[14]. This neurotransmitter is also correlated with brain plasticity and its ability to reconfigure itself by growing new synapses as it learns new skills or knowledge having npothing to do with math [16].

Example 3: The mediotemporal lobe (MTL)  includes the hippocampus, amygdala and parahippocampal regions, and is crucial for episodic and spatial memory. The MTL memory function consists of distinct processes such as encoding, consolidation and retrieval, and supports many functions including emotion, affect, motivation and long-term memory. The MTL also has numerous number neurons [2:p98] and is involved in processing mathematical concepts. Activity in this region represents a short-term memory of the arithmetic rule, whereas the hippocampus may ‘do the math’ and process numbers according to the arithmetic rule at hand.”[15].

Example 4: Memory-based math problems stimulate a region of the brain called the dorsolateral prefrontal cortex, which has already been linked to depression and anxiety. Studies have found, for example, that higher activity in this area is associated with fewer symptoms of anxiety and depression. A well-established psychological treatment called cognitive behavioral therapy, which teaches individuals how to re-think negative situations, has also been seen to boost activity in the dorsolateral prefrontal cortex. The ability to do more complex math problems might allow you to more readily learn how to think about complex emotional situations in different ways. Greater activity in the dorsolateral prefrontal cortex was also associated with fewer depression and anxiety symptoms. The difference was especially obvious in people who had been through recent life stressors, such as failing a class. Participants with higher dorsolateral prefrontal activity were also less likely to have a mental illness diagnosis.[17]

The bottom line for much of the research on how the brain functions with and without mathematics stimulation is that low numeracy is a bigger problem for the brain than low literacy [2:p307] It affects your economic opportunities in life, handeling personal finances, operating as a savvy consumer, and it even connects with your ability to logically process complex social situations and predict what your best course of action might be in many different circumstances.

Many of the brain regions needed for math performance are still under development between ages of 16 and 26 including most importantly the frontal cortex essential for judgment and anticipating future consequances of actions.

So when a student asks what is math good for, take a step back and walk them through the Big Picture!

Books that are definitely worth the time to read!

[1] The Tell-Tale Brain, V.S. Ramachandran, 2011, W.W. Norton and Co.

[2] A Brain for Numbers, Andreas Nieder, 2019, MIT Press

[3] The Consciousness Instinct, Michael Gazzangia, 2018, Farrar, Straus and Giroux

[4] Consciousness and the Brain, Stanislaus Dehaene, 2014, Penguin Books.

[5] Being You: A new science of consciousness, Anil Seth, 2021, Dutton Press

[6] The Prehistory of the Mind, Stevem Mithen, 1996, Thames and Hudson Publishers.

[7] The Idea of the Brain, Matthew Cobb, 2020, Basic Books

[8] The River of Consciousness, Oliver Sacks, 2017, Vintage Books

[9] Myth: We only use 10% of our brains. Stephen Chew ,2018, https://www.psychologicalscience.org/uncategorized/myth-we-only-use-10-of-our-brains.html

[10] Neurological glial cells – https://www.ncbi.nlm.nih.gov/books/NBK10869/

[11] Unsung brain cells play key role in neurons’ development, 2009, Bruce Goldman, https://med.stanford.edu/news/all-news/2009/09/unsung-brain-cells-play-key-role-in-neurons-development.html#:~:text=Ben%20Barres’%20research%20has%20led,90%20percent%20of%20the%20brain.

[12] https://www.firstthingsfirst.org/early-childhood-matters/brain-development/

[13] https://developingchild.harvard.edu/science/key-concepts/brain-architecture/

[14] www.sciencedaily.com/releases/2021/06/210607161149.htm and DOI:10.1073/pnas.2013155118

[15] Math Neurons” Fire Differently Depending On Whether You Add Or Subtract, 2022, https://www.iflscience.com/math-neurons-fire-differently-depending-on-whether-you-add-or-subtract-62658

[16] https://www.theguardian.com/education/2021/jun/07/studying-maths-beyond-gcses-helps-brain-development-say-scientists

[17] https://today.duke.edu/2016/10/could-mental-math-boost-emotional-health

[20] https://coverthree.com/blogs/research/kids-brain-development

Astronomy, Big Bang, Education, Physics

The Big Bang: Explained at the reading level of Genesis.

The universe began with a bang. Can we explain it all as simply as in many religious stories. (Image credit: Shutterstock)

I have often wondered how the modern description of the Big Bang could be written as a story that people at different reading levels would be able to understand, so here are some progressively more complete descriptions beginning with Genesis and their reading level determined by Reliability Formulas.

Genesis (from MIT Bible Gateway)

“In the beginning God created the heavens and the earth. Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters. And God said, “Let there be light,” and there was light. God saw that the light was good, and he separated the light from the darkness. God called the light “day,” and the darkness he called “night.” And there was evening, and there was morning–the first day. And God said, “Let there be an expanse between the waters to separate water from water.” So God made the expanse and separated the water under the expanse from the water above it. And it was so. God called the expanse “sky.” And there was evening, and there was morning–the second day. And God said, “Let the water under the sky be gathered to one place, and let dry ground appear.” And it was so. God called the dry ground “land,” and the gathered waters he called “seas.” And God saw that it was good. Then God said, “Let the land produce vegetation: seed-bearing plants and trees on the land that bear fruit with seed in it, according to their various kinds.” And it was so. The land produced vegetation: plants bearing seed according to their kinds and trees bearing fruit with seed in it according to their kinds. And God saw that it was good. And there was evening, and there was morning–the third day. And God said, “Let there be lights in the expanse of the sky to separate the day from the night, and let them serve as signs to mark seasons and days and years, and let them be lights in the expanse of the sky to give light on the earth.” And it was so. God made two great lights–the greater light to govern the day and the lesser light to govern the night. He also made the stars. God set them in the expanse of the sky to give light on the earth, to govern the day and the night, and to separate light from darkness. And God saw that it was good.”

The Flesch Reading ease Score gives this an 87.9 ‘easy to read‘ score. Flesch-Kincaid gives this a grade level of 4.5. The Automated Readability Index gives it an index of 4 which is 8-9 year olds in grades 4-5. Amazingly, the scientific content in this story is completely absent and in fact promotes many known misconceptions appropriate to what children under age-5 know about the world.

Can we do at least as well as this story in a 365-word summary that describes the origin of the universe, the origin of the sun, moon and earth, and the appearance of life? Because the reading level of Genesis is only at most Grade-5, can we describe a scientific treatment using only concepts known by the average Fifth-Grader? According to the Next Generation Science Standards, students know about gravity, and scales of time but ideas about atoms and other forces are for Grade 6 and above. The average adult reader can fully comprehend a text with a reading grade level of eight. So if the text has an eighth grade Flesch Kincaid level, its text should be easy to read and accessible by the average US adult. But according to Wylie Communications, half of all US adults read at or below 8th-grade level. The American Academy of Arts and Sciences survey also shows that US adults know about atoms (51%), that the universe began with a Big Bang (41%) and that Earth orbits the sun (76%) so that US adults rank between 5th and 9th internationally in our basic scientific knowledge.

The genesis story splits itself into three distinct parts: The origin of the universe;The origin of stars and planets; and The origin of life and humanity. Only the middle story has detailed observational evidence at every stage. The first and last stories were one-of events for which exact replication and experimentation is impossible.

Because we are 3000 years beyond the writing of Genesis, let’s allow a 400-word limit for each of these three parts and aim at a reading level and science concept level not higher than 7th grade.

First try (497 words):

Origin of the Universe. Our universe emerged from a timeless and spaceless void. We don’t know what this Void is, only that it had none of the properties we can easily imagine. It had no dimension, or space or time; energy or mass; color or absence of color. Scientists use their mathematics to imagine it as a Pure Nothingness. Not even the known laws of nature existed.

Part of this Void exploded in a burst of light and energy that expanded and created both time and space as it evolved in time. This event also locked into existence what we call the Laws of Nature that describe how many dimensions exist in space, the existence of four fundamental forces, and how these forces operate through space and time.

At first this energy was purely in the form of gravity, but as the universe cooled, some of this energy crystalized into particles of matter. Eventually, the familiar elementary particles such as electrons and quarks emerged and this matter became cold enough that basic elements like hydrogen and helium could form.

But the speed at which the universe was expanding wasn’t steady in time. Instead this expansion doubled in speed so quickly that within a fraction of a second, the space in our universe inflated from a size smaller than a baseball to something many billions of miles across. Today, after 14 billion years of further expansion we see only a small fraction of this expanded space today, and we call it the Observable Universe. But compared to all the space that came out of the Big Bang, our entire Observable Universe is as big as a grain of sand compared to the size of our Earth. The Universe is truly an enormous collection of matter, radiation and energy in its many forms.

Meanwhile, the brilliant ‘fireball’ light from the Big Bang also cooled as the universe expanded so that by one million years after the Big Bang, it was cooler than the light we get from the surface of our own sun. Once this light became this cool, familiar atoms could start to form. As the universe continued to expand and cool, eventually the light from the Big Bang became so cool that it could only be seen as a dull glow of infrared light every where in space. The atoms no longer felt the buffeting forces of this fireball light and had started to congregate under the force of gravity into emmence clouds throughout space. It is from these dark clouds that the first stars would begin to form.

Mixed in with the ordinary matter of hydrogen and helium atoms was a mysterious new kind of matter. Scientists call this dark matter because it is invisible but it still affects normal matter by its gravity. Dark matter in the universe is five times more common than ordinary matter. It prevents galaxies like the Milky Way from flying apart, and clusters of galaxies from dissolving into individual galaxies.

Flesch Reading Ease 60. (Average difficulty); Flesch-Kincaid Grade: 10.2; Automated Readability Index: 11

Second Try (538 words):

Origin of the Universe. Our universe emerged from a timeless and spaceless void. We don’t know what this Void was. We think it had none of the properties we can easily imagine. It had no dimension, or space or time. It had no energy or mass. There was no color to it either blackness or pure white. Scientists use their mathematics to imagine it as a Pure Nothingness. They are pretty sure that not even the known laws of nature existed within this Void.

Part of this Void exploded in a burst of light and energy. Astronomers call this the Big Bang. It  expanded and created both time and space as it evolved in time. This event also locked into existence what we call the Laws of Nature. These Laws describe how many dimensions exist in space. The Laws define the four fundamental forces, and how they operate through space and time.

At first the energy in the Big bang was purely in the form of gravity. But as the universe expanded and cooled, some of this energy crystalized into particles of matter. Eventually, the familiar elementary particles such as electrons and quarks emerged. This matter became cold enough that basic elements like hydrogen and helium could form.

But the speed at which the universe was expanding wasn’t steady in time. Instead this expansion doubled in speed very quickly. Within a fraction of a second, the space in our universe grew from a size smaller than a baseball to something many billions of miles across. After 14 billion years of further expansion we see only a small fraction of this expanded space today. We call it the Observable Universe. But compared to all the space that came out of the Big Bang, our entire Observable Universe is as big as a grain of sand compared to the size of our Earth. The Universe is truly an enormous collection of matter, radiation and energy in its many forms.

Meanwhile, the brilliant ‘fireball’ light from the Big Bang also cooled as
the universe expanded. By one million years after the Big Bang, it was cooler than the light we get from the surface of our own sun. Once this light became this cool, familiar atoms could start to form. As the universe continued to expand and cool, eventually the blinding light from the Big Bang faded into a dull glow of infrared light. At this time, a human would see the universe as completely dark. The atoms no longer felt the buffeting forces of this fireball light. They began to congregate under the force of gravity. Within millions of years, immense clouds began to form throughout space. It is from these dark clouds that the first stars would begin to form.

Mixed in with the ordinary matter of hydrogen and helium atoms was a mysterious new kind of matter. Scientists call this dark matter.  It is invisible to the most powerful telescopes, but it still affects normal matter by its gravity. Dark matter in the universe is five times more common than the ordinary matter we see in stars. It prevents galaxies like the Milky Way from flying apart. It also prevents clusters of galaxies from dissolving into individual galaxies.

Flesch Reading Ease 66.7. (Average difficulty); Flesch-Kincaid Grade: 7.2; Automated Readability Index: 6.6 (11-13 year olds).

Third Try ( 410 words )

Origin of the Universe. Our universe appeared out of a timeless and spaceless void. We don’t know what this Void was. We can’t describe it by its size, its mass or its color.  It wasn’t even ‘dark’  because dark (black) is a color.  Scientists think of it as a Pure Nothing.

Part of this Void exploded in a burst of light and energy. We don’t know why.  Astronomers call this event the rather funny name of the ‘Big Bang’. It  was the birth of our universe. But it wasn’t like a fireworks explosion. Fireworks expand into the sky, which is space that already exists. The Big Bang created space as it went along.  There was nothing for it to expand into. The Big Bang also created  what we call the Laws of Nature. These Laws describe how forces like gravity and matter affect each other.

As the universe expanded and cooled, some of its energy became particles of matter. This is like raindrops condensing from a cloud when the cloud gets cool enough. Over time, these basic particles  formed  elements like hydrogen and helium.

The universe continued to expand. Within the blink of an eye, it grew from a size smaller than a baseball to something many billions of miles across. Today, after 14 billion years  we see only a small piece of this expanded space today. Compared to all the space that came out of the Big Bang, what we see around us is as big as a grain of sand compared to the size of our Earth. The Universe is truly enormous!

After about one million years  the fireball light from the Big Bang became very dim. At this time, a human would see the universe as completely dark. There were, as yet, no stars to light up the sky and the darkness of space. Atoms  began to congregate under the force of gravity. Within millions of years, huge clouds the size of  our entire Milky Way galaxy began to form throughout space. From these dark clouds, the first stars started to appear.

Mixed in with  ordinary matter  was a mysterious new kind of matter. Scientists call this dark matter.  It is invisible to the most powerful telescopes. But it still affects normal matter by its gravity, and that’s a very good thing! Without dark matter,  galaxies like our Milky Way and its billions of stars would fly apart, sending their stars into the dark depths of intergalactic space.

Flesch Reading Ease 73.3. (Fairly easy to read); Flesch-Kincaid Grade: 5.9 (Sixth grade) ; Automated Readability Index: 5.1 (8 – 9 year olds) Fourth to Fifth grade.

Summary.

The Third Try is about as simple and readable a story as I can conjure up, and it comes in at a reading level close to Fourth grade. Scientifically, it works with terms like energy, space, expansion, matter  and gravity, and scales like millions and billions of years. All in all, it is not a bad attempt that reads pretty well, scientifically, and does not mangle some basic ideas. It also has a few ‘gee whiz’ ideas like Nothing, space expansion and dark matter. 

So, what do you think? Leave me a note at my Facebook page!

Next time I will tackle the middle essay about the formation of  stars and planets!

Astronomy, aurora, Space weather, sunspot cycle

Sunspot Cycle Update!

Aurora over South Dakota on April 23, 2023 taken by Evan Ludes. https://spaceweathergallery2.com/indiv_upload.php?upload_id=195462

The spectacular solar storm we had on April 23, 2023 reminds us that, as the current sunspot cycle continues to progress, we will have many more of these spectacular aurora to look forward to in the next few years. So where are we in the current sunspot cycle?

Sunspot cycles average about 9 to 12 years, with the stronger cycles on the shorter end of this range and weaker cycles on the longer end of this range. The current cycle, Number 25, seems to be exceeding all forecasts for a weaker cycle and may in fact resemble previous ones like Cycle 22 or 23.

Solar Cycle Progression (Solar Cycle 24 – 25) – March 2023. Credit: NOAA/SWPX https://www.swpc.noaa.gov/products/solar-cycle-progression

The current cycle began in December 2019 and some predictions at that time suggested that it would probably be a very weak cycle perhaps not even exceeding Cycle 24. This is shown by the grey band in the above figure. Some even thought based on solar magnetic field data that we could be heading into another Maunder Minimum with no recognizble sunspots for the next 50 years. Instead, the rapid rise of activity and solar flares since 2020 has demonstrated that we still do not really understand what drives sunspot cycles.

This is rather embarrasing. The sunspot cycle is one of the most glaring features of the sun whose nearly constant period of 11 years begs to be explained. This is like meteorologists still not being able to explain why Earth has its four seasons.

The current sunspot cycle was born with the first spots sighted around April 2018 with spots that had the opposite polarity of those in Cycle 24. It is common for such spots to start appearing several years before the actual cycle commences. But by November 2019 this number had increased to two spots. In May 2020 the first M-class flare erupted, followed by the first X-class flare in July 2020.

Since 2020, the sunsppot counts and flare activity have consistently placed Cycle 25 on the upper tracks of the strong cycle forecasts being nearly 50% more active than the initial predictions year-by-year. Already by January and March 2023 we are seeing 143 and 122 sunspots which compares with the peak of 146 seen for Cycle 24. The red band in the figure below shows the current range of curves based on the most recent data. This places the trend for the maximum somewhere between Cycle 23 and Cycle 24. But the current year 2023 trends will probably give us the definitive predictions. So far, it looks like Cycle 25 will peak around early-2024.

This chart shows from lft to right the sunspot cycles 21,22,23 and 24. The last one on the right is the current cycle 25, with the original predicted number of sunspots, represented as the blue line. The green lines show the observed sunspots, which are trending toward the red line – the McIntosh et al. study – which predicts a higher number of sunspots. https://blogs.nasa.gov/solarcycle25/

So far, Cycle 25 is 40 months old. During this time we have already experienced 8 X-class flares on (X1) October 2, 2022, (X1.2) January 5, 2023, (X1.3) January 9, 2023, (X1) January 10, 2023, (X1.1) February 11, 2023, (X2.2) February 17, 2023, (X2.1) March 3, 2023, and (X1.2) March 29, 2023. Most of these appeared in 2023 so the pace of these major events is quickening.

Why is this important?

The sunspot cycle is a barometer of what we call space weather. Space weather is a term analogous to Earth weather with a number of parallels. Strong terrestrial winds are equivalent to the solar wind. Solar flares are equivalent to severe lightning storms, and coronal mass ejections are analogous to hurricanes and tornados. Just as severe Earth weather can cause billions of dollars of damage, severe space weather can damage satellites in Earth orbit, produce harmful radiation for astronauts working in space, and cause electric power grid outages. They also produce dramatic aurora!

The most recent examples of what space weather can do is the loss of 40 Starlink satellites on February 3, 2022 costing SpaceX over $100 million. The cause was a space weather event that heated up Earth’s outer atmosphere causing it to expand into space and provide extra drag to the satellites in Low Earth Orbit. The satellites tried to compensate by firing their thrusters but quickly used up all their propellant and burned up in the atmosphere.

Meanwhile, the European Space Agency’s Swarm satellites are having their own problems. Launched in 2013, these satellites measure and map Earth’s magnetic field. By July 2022 the satellites in the three-satellite constellation have been falling by up to 20 km per year from their initial orbit of 450-530 km.

How stormy can it get?

Frequency of geomagnetic events stronger than Kp=6 (blue) Kp=7 (red) and Kp=8 (black) averaged over the recent ‘strong’ sunspot cycles by the year of the cycle. Sunspot Maximum occurs near Years 5-6.

The graph shows how disturbed Earth’s magnetic field is during various years throughout the sunspot cycle. It is based on the average activity from the past three cycles. The black line gives the average number of extreme storms with Kp > 8 that produce aurora seen as far south as southern California or Florida like the recent one on April 23, 2023. The red line is storms stronger tha Kp = 7, and the blue line is storms stronger then Kp=6. These still produce brilliant aurora, but generally only seen in the northern-tier states of the United States and in New England and Alaska.

We are now in Year 4 of the current sunspot cycle with a maximum that may be between Year 5-6 in 2024-2025, so we should expect that most of the aurora activity is still in our future, peaking sometime between Year 7 and 9, which is about 2026-2028. It all depends on how the sunspot numbers play out this year and in 2024, but for aurora lovers, the best is yet to come!

Climage Change

Climate Change Tools

Over the years I have collected a number of online tools that help me keep climate change in perspective. Here are some of my favorites!

Flooding risk areas. Dark blue and black are extreme risk areas with more than 5% risk increase in next 30 years.

Riskfactor.com – Just enter your address and it will use a database from FEMA to give you a forecast of the possible risks your home and property face in the next 30 years. I was not surprised that my Kensington, Maryland has a low risk for fire and heat, but startled that even at my elevation of 200 feet my risk for flooding in the next 30 years was pretty high, mostly from ordinary rain runoff. This is likely because Climate Change predicts more frequent and more severe rain storms that dump more water on my property than what it has faced in the last 50 years. I was also surprised that my Heat risk is elevated from 5 days over 100-degrees F to 20 days over 100-degrees F. This could have health implications for my wife!

Risk by county. What kind of a county do you live in by income or community group? Are you Urban? Rural? Military? How will your county be affected by future hurricanes, tornadoes and floods? The above risk for sea level rise shows the expected risk distribution. My county, Montgomery County, MD has no risk….how about yours??? Other interactive maps at this site give hurricane, tornado, rainfall risks too. The map below shows counties expected to have the greatest heat stress.

Natural Disasters. The map below shows the cumulative federal FEMA payouts for all 50 states due to climate disasters between 1980 and 2020, with most of the expensive ones at more than a billion dollars each, happening since 2010.

“The South, Central and Southeast regions of the U.S., including the Caribbean U.S. territories, have suffered the highest cumulative damage costs, reflecting the severity and widespread vulnerability of those regions to a variety of weather and climate events. In addition to the highest number of billion-dollar disasters experienced, Texas also leads the U.S. in total cumulative costs (~$290 billion) from billion-dollar disasters since 1980. Florida is the second-leading state in total costs since 1980 (~$230 billion), largely the result of destructive hurricane impacts. Louisiana has the 3rd highest total costs (~$205 billion) from billion-dollar disasters, but has a much smaller population and economy than either Texas or Florida. Therefore, the relative cost and impact from extremes in Louisiana is more severe and difficult to recover. ” 

Earthquake Risk! – Yeah I know, earthquakes are not climate change events but I thought this was a neat graphic to include. If you want to see a realtime display of earthquakes in your area, go to the USGA website or the UC Berkeley Seismic Lab.

Getting back to climate change-related resources…..The practical consequences of increased disasters is your Home Owner’s Insurance. The website HowMuch.net gives the map below of the average annual policy costs by state. My state, Maryland, is half the cost of Texas, but Texas is where everyone wants to live thanks to their excellent marketing over the last 150 years! Everything certainly is BIGGER in Texas!!

Homeowners insurance rates by 2020. The number is the average annual policy rates and the color is the rate relative to a national average of $2,300.
Astronomy

Exoplanet Update!!

An artist’s impression of an exoplanetary system as seen from the surface of an exomoon. Image credit: IAU/L. Calçada.

The last time I discussed exoplanets in this blog was in 2017 with my essay ‘Exoplanets Galore‘, but I think we can all agree that a lot has happened since then!

Here’s the bottom line by March 2023 if you don’t want to read further.

Total exoplanets: 5,312 confirmed out of 9,343 candidates

Total in Habitable Zone: 214 exoplanets of all sizes

Total Earth Analogs: 23 the size of Earth in their Habitable Zones

Number of directly imaged exoplanets: About 30.

Number of atmospheres detected: 11 so far: Water, carbon dioxide, methane, hydrogen, helium and no biosignatures like oxygen, nitrogen.

Planets with magnetospheres: 1 so far: HAT-P-11b

Closest Earth Analog: Proxima Centauri b at 4.2 light years. (probably lifeless due to frequent flares from star). Gliese 1061 b, c,d at 12 light years. A planetary system with multiple Earth-sized candidates in HZ.

Closest Earth Analog around sun-like star: Kepler 452b, 1,400 light years from Earth orbiting G-type star. It is 5 times the mass of Earth and has twice the surface gravity. Probably between a terrestrial and Neptune-type surface with large ocean.

Searches in Progress: TESS was launched in 2018 and will operate until 2025. It will search the 200,000 brightest stars in the sky and hopefully find ‘thousands’ of new exoplanets using the transit method. So far it has found 6,386 candidates and 326 confirmed exoplanets. Gaia was launched in 2013 and will also last until 2025. So far, Gaia has found 18,383 candidates and has verified 73 exoplanets. Meanwhile there are over 43 ground-based major observatories with exoplanet detection programs mostly designed to verify candidates spotted by satellite studies.

Now let’s dig into the details!

According to NASA, by March 30, 2023 there are now 5,312 confirmed exoplanets, among 9,343 candidates, including 3,981 multiple-exoplanet ‘solar systems’. These confirmed exoplanets include 195 that are ‘terrestrial’ or Earth-sized, and 1,605 that are ‘super-Earths’ up to 5 times bigger than Earth. According to the European, Extrasolar Planet Encyclopedia (EPE) as of March 31, 2023 lists 5,346 exoplanets in 3,943 planetary systems, and 855 multi-planet systems.

The NASA catalog is searchable but very bare-bones. It only gives name, size and distance. The Extrasolar Planet Encyclopedia ( EPE), however is also searchable but in many more fields including the exoplanet’s radius, period and distance from its star.

First a bit of terminology.

Habitable Zone (HZ), also called the Goldilocks Zone, means the region surrounding a star where the temperature of an exposed surface with no atmosphere, is between the freezing point of water and the boiling point of water where life could supposedly exist. Of course you can’t have liquid water on a planet with no atmosphere, so these distances are lower limits. If the planet has a warming Greenhouse atmosphere dense enough for water to exist it can be farther from the star than these limits because the surface is warmed to a higher temperature. But it is a good first guess for the size of this zone without making any assumptions about atmospheric composition. By the way, Earth is right in the middle of our Sun’s HZ. Care has to be used in using this in the seach for life because even exoplanets that seem too cold to sustain liquid water could have liquid oceans under a thick icy crust like the moons of Jupiter.

Earth-sized means that the exoplanet is very close to our Earth in SIZE, meaning diameter, which means a radius of about 6,300 km. It also means that it can be found anywhere both inside and outside the HZ. Care has to be taken in using this as a search for life indicator because the moons of Jupiter-sized exoplanets can be Earth-sized like Titan in our own solar system, and tidal energy could keep their interiors warm enough for liquid water.

Earth-like means that the exoplanet is not only Earth-sized but inside its star’s HZ. These are also called Earth Analogs or Potentially Habitable Exoplanets.

Habitable Zone exoplanets

The very first thing that you or I would want to know is, how many of the 5,300+ exoplanets are in their HZs? Although a good estimate is about a few hundred, the exact answer is not as straight-forward as you might think.

Exoplanets are often found in elliptical orbits so some of these may only spend part of their ‘year’ in the HZ and most of their time too hot or too cold to support liquid water. To make matters worse, because stars evolve over time and become brighter, the HZs around every star start out close to the star when the star is young but slowly drift further away from the star as it ages. A planet formed inside the HZ may find itself outside the HZ as it gets older. In our solar system, Venus started out inside the HZ of the sun when it was formed 4.5 billion years ago, but now finds itself just inside the HZ today as a much hotter and inhospitable Earth-sized world. The range of distance during the entire lifetime of the star where HZ conditions exist is now called the Continuously Habitable Zone. Our Earth will leave this zone in another 7 billion years, while Mars will find itself in the comfortable middle of this zone by then.

Neither the NASA nor the EPE catalogs explicitly give statistics on this sub-category because the exact location of the HZ for each star depends on some assumptions including orbit shape, age of star, surface reflectivity, and Greenhous gas content. None of these ‘official’ catalogs wants to offer an official count because it could be ‘incorrect’ or worse-still, meaningless.

According to the Habitable Zone Gallery maintained by astronomers Stephen Kane and Dawn Gelino, their March 2023 catalog includes 4,628 exoplanets with known orbits. The figure below shows in green that only a total of 214 spend more than half their ‘year’ inside their star’s HZ. These include all types of exoplanets not just Earth-sized ones.

Image credit : HZGallery.org.

The Search for Earth Analogs.

How many exoplanets are both Earth-sized and in their star’s HZ? Depending on the details there are up to a few dozen that seem very promissing.

Encyclopedia Britanica says 40 as of March 2023. The searchable Habitable Exoplanets Catalog gives 23 Earth-sized and 39 super-Earths (3-10 times Earth mass) for a total of 62 habitable worlds by January 5, 2023. One graphical summary by Chester Harman gives 13 potentially habitable exoplanets as of March 2022 when stellar evolution is factored-in. So, lets take the charitable view and use the Habitable Exoplanets Catalog tally of 23 Earth-sized and 39 super-Earths.

The habitable zone for a range of stellar temperatures, showing Venus, Earth, Mars, and a selection of potentially habitable exoplanets. (image credit: Chester Harman)

Well first of all, the super-Earth exoplanets are problemtical because they are larger and more massive than Earth. They have a lower density so many astronomers suspect that these are Water Worlds. If you had placed Neptune in the sun’s HZ at the time of formation, instead of being a planet with a thick icy mantle on top of a rocky core the size of Earth, it would have had a thousand-kilometer-deep water ocean on top of a rocky Earth-sized core. You could have life in a deep ocean, of course, but with no solid surface on which life could emerge and evolve. It is hard to understand how ‘fish’ would have created telescopes or even known that the rest of the universe exists at all.

Some of these super-Earths closer to the size of our planet could have enormous oceans covering their surface but with diminishing land areas. For future explorers, these exoplanets would still be massive enough that we would never be able to visit the small islands on their surfaces and return to space because their escape velocities are so high.

The closest Earth Analogs.

We are obsessed with finding the closest because these would be the easiest targets for future interstellar probes to visit within a human lifespan of travel. The current catalog lists quite a few of these but they all orbit red dwarf stars. TheTRAPPIST-1 system contains TRAPPIST-1e, f and g — all located in the habitable zone of the star. The M8V red dwarf star is 39 light years from Earth. Unfortunately, different studies have come to different conclusions on whether any TRAPPIST-1 planet can retain substantial amounts of water. Because the planets are most-likely synchronized to their host star, water could become trapped on the planets’ night sides and would be unavailable to support life.

Meanwhile, Kepler 442b located 1,200light years from Earth is only 2-3 times the mass of Earth and is in the HZ around a K-type sun-like star. It has a temperature of 233 K (−40 °C; −40 °F) and a radius of 1.34 REarth. Because of its radius, it is likely to be a rocky planet with a solid surface. The mass of the exoplanet is estimated to be 2.36 MEarth. The surface gravity on Kepler-442b would be 30% stronger than Earth, assuming a rocky composition similar to that of Earth.

Based on the observations available by 2013, statistically, there should be nearly 9 billion habitable Earth-sized planets in our Milky Way. A 2020 estimate places this at about 6 billion exoplanets orbiting sun-like stars. A 2019 study places this at 10 billion habitable exoplanets orbiting the stars in the Milky Way of which one in every four G-type stars have habitable planets. A bit of math tells us that the volume of the Milky Way is about 17 trillion cubic light years. If you scatter 10 billion habitable exoplanets throughout this volume, you get 17 trillion cubic light years/10 billion exos = 1,700 cubic light years/exoplanet. That means the average distance between them is about 12 light years, which is very promissing!

Within 100 light years of the Sun there are 512 of these sun-like stars so there could be as many as 128 habitable Earth-like exoplanets yet to be discovered! These would be close enough to Earth to consider sending fast, unmanned spacecraft to visit them and check for lifesigns first-hand.

Astronomy, Space Travel

Welcome to the 22nd Century!

(Excerpt from my upcoming ebook ‘The Next Billion Years’)

A not unlikely interplanetary spacecraft design using known technology. Image Credit.

Thinking ahead to the 22nd seems no more of a challenge than what we had in the 1960s when we considered the mythical 21st century. But one thing is for certain, we had no idea that the socially transformative impacts of computers, smartphones and the internet would be on the horizon. We also had no idea that Stanly Kubrick’s 2001: A Space Odyssey would be way too imaginative even after Neil Armstrong walked on the moon. In the 1950s, we thought we would be driving atomic-powered cars by the 1960s. And of course, we had no idea that global warming was going to be such a problem only 40 years after the first Earth Day. One thing we do know for sure is that on April 27, 2109 Rutgers University will be opening a Time Capsule! 

This essay covers some ideas in space exploration and travel. A future essay will cover climate change and other issues.

Space Travel

Historically before 2025 CE, NASA’s budget was locked at about 0.5% of the federal discretionary budget and human spaceflight was allotted from this $10 billion (0.17% of federal budget). At this sustained pace,  there should be an accumulated minimum of $770 billion invested in manned activities in space by 2100 CE – the lions share going to lunar and Martian bases.  You can buy a lot of infrastructure for that amount of money even with expensive billion-dollar launch vehicles!

A stable population of over 50  researchers and engineers would be a conservative estimate. This requires only an annual off-world population growth rate of 2% by 2100 CE. They would be operating inside habitats protected from radiation exposure, have sophisticated medical and surgical facilities, and the low gravity of the moon (0.2 g’s), would not be an issue impacting astronaut (Lunites?) health. The location of this base would be near the shadowed craters in the South Pole where water ice would be mined for fuel and atmosphere. The buildings would be robotically built using 3D printing techniques developed in the 2020s. They would also be covered by radiation-proof lunar regolith. Better yet, find a lava tube and seal off its ends, then erect a pair of pressurized bulkheads and build ordinary habitats at low cost. Using 3D printing, this process can be automated.

By the start of the 22nd century, if the first human expedition to Mars occurred in 2050 CE, then 50 years have now elapsed. While a lunar base at this time may have 50-100 people, the level of difficulty in transporting material and people to Mars may not allow a Martian base with more than a dozen ‘Martians’ on a  2-year rotation back to Earth. The Planetary Society thinks there could be over 1,000 people living in a sustained way on Mars by 2070, but the devil is in the details as they say. At an off-world sustained growth rate of 2% per year, we only get to about 200 people by then including the lunar base. Of course, the  rapid commercialization of space may well create its own demand for people to visit the moon and Mars, and so extra capacity will have to be built by private companies.

Aside from billionaires, it is not known how much a trip will cost and if ordinary people being chased by climate change issues, will have the spare cash. The truth of the matter is that on Mars, there is simply nothing for a non-scientist to do to occupy their time. You will always live inside a cramped ‘dome’ and only venture outside in a spacesuit. You could hike or drive to a new destination, but you would always see essentially the same rust-red landscape unless you visited the ice-covered poles, which would be hazardous.  Psychologists say that we have limited coping skills to deal with this kind of monotony,

However, if any traces of life are discovered either as fossils or as living systems, this will entirely change the game. It is not unlikely that with indigenous Martian life, Mars will be under extreme quarantine to prevent humans from contaminating the Martian biosphere with terrestrial DNA, or coming into contact with potentially lethal viruses. 

As for the rest of the solar system, we have had tremendous success deploying robotic explorers to the moon and Mars. This technology will continue to be used with even more advanced systems that have sophisticated artificial intelligence and can operate autonomously for long periods. By the end of the 22nd century, these systems will have been placed on the surfaces of Mercury, Venus, the large moons of Jupiter and Saturn, and even a few of the distant moons of Uranus, Neptune and some asteroids too. The Curiosity rover cost $2.5 billion and has lasted over 10 years, so this technology is extremely cost-effective for the science returned. Making them fully autonomous using AI will eliminate the need for long time delays to Earth to operate them telerobotically. These systems will return to Earth high-def video that will be immediately incorporated into fully immersive Virtual Reality experiences for the general public not just a few lucky scientists.

 Astronomy

Meanwhile, astronomers will continue to have no problems forecasting eclipses and unusual planetary alignments with enormous accuracy to the day, hour and minute across the centuries.  We are still going to have two or three solar eclipses every year, but the one on June 25, 2150 will be the longest one since 1973 at 7 minutes and 14 seconds. It will be followed on July 16, 2186 by the longest total solar eclipse in 10,000 years at 7 minutes and 29 seconds. Most eclipses last only 2-5 minutes so these will be truly exceptional. 

The first transit of Venus across the face of the sun since 2012 will occur on December 11, 2117. The previous one was a major media event observed by billons of people.  Its companion event will occur 8 years later on December 8, 2125. 

Then on September 14, 2123 from Earth, Venus transits across the disk of Jupiter. The last time this happened was on November 22, 2065 and it will no doubt still be a public spectacle of some interest. 

Venus transit of Jupiter

Mars gets into the act three years later as it ducks behind the planet Mercury on July 29, 2126. Then on November 15, 2163 Mars colonists will see Earth pass across the face of the sun. This Earth transit will be repeated on May 10, 2189. Some lucky ‘Martians’ may actually get to see both events.

From Neptune, there will also be a transit of Jupiter across the sun on August 8, 2188, so if you were clever you could see the Jupiter transit first and then travel to Mars to see the Earth transit a few years later.

And among the other astronomical events, the nerds among us will wait patiently for the astronomical ‘Julian Day’ calendar to roll over to 2500000 on August 18, 2132. We also get to  celebrate the return of Halley’s Comet on March 27, 2134. Forty years later in 2178, Pluto returns to the same place in its orbit where it was discovered in 1930. But one astronomical activity will continue its essential work. 

Killer Asteroids

Earth orbits the sun in a veritable shooting gallery of asteroids that share nearly the same orbit, and comets that arrive unexpectedly from the far reaches of the solar system. 

Chelyabinsk Meteor….20-meters….1,000 people injured. Image credit.

By 2023 CE, the orbits of 20,000 ‘Near Earth Objects’ had been calculated. Hundreds of these  NEOs have been placed on a Potentially Hazardous Object watch list  because they are larger than 100 meters and could be ‘City Killers’ or worse if they impacted a populated area. The highest risk of impact for a known asteroid is a 1 in 714 chance by an asteroid designated 2009 FD in 2185, meaning that the possibility that it could impact then is less than 0.2 percent. The Sentry Risk Table only lists 2017WT28,  about 8 meters in diameter, as an impact risk for the year 2104. Its odds are about one-in-100. A 2021 survey estimates that there are over 4 million NEOs larger than 10 meters yet to be found.  However, current surveys are estimated to be more than 95% complete for objects bigger than 200 meters. This means that there are no Dinosaur Killer events of the 6km-class anytime soon.

The DART spacecraft impact with the 5-million-ton asteroid Dimorphos was a success and demonstrated we can alter the orbits of asteroids to avoid collision with Earth. (Image credit: NASA)

By the end of the 22nd century, we will have had at least one if not two more events like Tunguska in 2009 and Chelyabinsk in 2013. If we are unlucky, a city or town may be obliterated, but chances are we will be able to divert its orbit to avoid impacts using the DART technology from 2021.

New Physics

Among physicists and astronomers, the search for the nature of dark matter and clues on how to go beyond the so-called Standard Model will inevitably be helped by new instruments. Current designs already have 100 TeV available by the end of the 21st Century, and likely 1,000 TeV by the 22nd century. Along the way, we may even discover new approaches to achieving these high energies, perhaps by harnessing free cosmic ray protons. These are known to have energies above 300,000,000 TeV, but they are unfortunately few and far between. You get one or two of these during the lifetime of a typical physicist.

Although no ‘new physics’ has been detected by 2023 CE, it is almost certain that the Standard Model will start to show its incompleteness somewhere above 20 TeV. Hopefully, the missing ingredients we discover will explain both the nature of dark matter and the origin of dark energy, which were discovered by astronomers in the 20th century.

Dark matter (blue) in the Bullet galaxy cluster. Still a mystery after 100 years?

The really good news is that even with these mysterious ‘dark’ ingredients to the universe, there are almost no examples in history where some new scientific observation did not have a complete explanation within a century of its discovery.  

Exoplanets and the Search for Life

Astronomers will also be very busy studying exoplanets and discovering ones with signs of a biosphere, leading to a surge of innovative techniques for trying to actually image the surfaces of these worlds and detect artificial illumination on their dark hemispheres or signs of industrial pollution. Beyond the ‘baked-in’ mysteries of our dark universe, the search for extraterrestrial life will have matured in some fascinating directions by now. In our solar system, we will have explored the deep oceans of Europa, Titan, probed the crust of Mars, and settled the question of whether in our solar system any other abode than Earth ever  experienced life. 

 Beyond our solar system, our catalog of over 500,000 exoplanets by then, and a thousand nearby habitable worlds discovered, will have been followed by an equally intense period of searching for biomarkers in their atmospheres, or illumination on their nighttime hemispheres. This isn’t to say that it is a certainty we will find extraterrestrial life by the 22nd century, but we will have certainly studied all the ‘low hanging fruit’ exoplanets for signs of it. Within 500 light years of the sun, we will know what planetary systems to avoid if we chose to visit them with AI-enabled spacecraft. If we don’t find any exoplanets with biosignatures in the solar neighborhood by this time, humans may never take the next step and conduct interstellar travel, at a cost of trillions of dollars per mission. What would be the point?

Meanwhile, another search-for-life pursuit will have started to mature so that it can inform us about an even bigger picture. 

Intelligent Life in the Universe

Since the late-20th century, a small cadre of intrepid and patient astronomers have been using radio telescopes to search for signs of intelligent life. On Earth, a biosphere in existence for 3.8 billion years led to beings with radio technology only in the last 100 years. The goal of these radio searches is to detect the ‘spillover’ radiation from other civilizations across the Milky Way, far outside the 1,000 light year limits we are searching for viable biospheres. Every year that goes by, and every negative result that turns up, only reinforces the statistical assessment that intelligent life capable of, or interested in, radio technology are dismally few and far between in our Milky Way.

Science fiction author Arthur C Clarke  once remarked, “Two possibilities exist: either we are alone in the Universe or we are not. Both are equally terrifying.” I don’t find the prospects of extraterrestrial life ‘ terrifying’  and am more inclined to agree with what Ted Arroway said in the movie Contact, “I don’t know Sparks. But I guess I’d say if it was just us…seems like an awful waste of space”.

 Gravity Astronomy

The discovery of gravity waves in 2015 will lead to far more sensitive instruments by the 22nd century that will lay-bare the details of the Big Bang event itself along with actual hard data on the origin of time and space. Cosmology should largely become a closed textbook with all of the essential physical details worked out and covered by newer Big Bang theories. This, of course, depends on whether the issue of dark matter and dark energy are also resolved. Stay tuned!

 Science Fiction

Recognizing the futility of creating interesting science fiction stories that begin only a few decades out, some writers have moved their stories to 2050 and beyond. Only a few Old School stories written in the mid to late-20th century still find the first decades of the 21st century interesting, and with the right technology twists to make entertaining reading. None of them were very good at predicting what the end of the 20th century would look like, so we take any fictional prognostication with  grain (ton?) of salt. Still…

2100   The Ring of Charon. Earth accidentally destroyed by a Graduate Student(Allen)

2101   Babylon 5. First Martian base established (TV).

2115   Childhood’s End. Adult humans extinct. Killed by their own mutated children(Clark)                    

 2119   Orphans of the Sky. The first Centauri expedition (Heinlein)            

 2123   Starwings. Earth Holocaust;  Interstellar travel begins. (Proctor) 

2125   Methusela’s Children – Interstellar colonies (Heinlein)  

2125  Childhood’s End. The Earth is destroyed by its evolved children (Clark)

2130   Rama Revealed. Alien artifact found(Clark)   

2140   New York 2140. Major flooding (Robinson)  

2144   Aliens.  Movie events. Need I say more?

2149   The Seeds of Aril.  Interstellar Expeditions in 1-person pods(Robertson)

2150   Dr Who.  Earth overrun by the Daleks. (TV)

2150   The Expanse – Mars population 100 million (TV)

2156   Babylon 5 – The Centauri civilization contacts Earth.

2171   Moving Mars – Major Mars colony established (Bear)

2190   Seetee Ship – Story events (Williamson)

2195   Ender’s Game –  Interstellar war with aliens (Card)

Astronomy, NASA

Desciphering Webb Telescope Images

Astronomers can look at images of celestial objects like planets, nebulae and galaxies and immediately see their significance, but for the average person seeing them on the Evening News the pictures are, of course, beautiful but at the same time, generally mysterious. My recent book The Hidden Universe takes 68 images you might have encountered, shows you how they were created, and what interesting story lurks beneith their gorgeous countenences. This blog will describe one of these.

By now you have seen the spectacular images provided by the Webb Space Telescope (JWST), and boy are they breath-taking even for an astronomer! I have been waiting all my professional life for HD-quality images of objects in the mid-infrared spectrum (wavelength: 1 to 28 microns), and JWST has not dissappointed. NASA’s Spitzer Space Telescope also produced high-quality infrared images to be sure (wavelength: 3 to 160 microns), but JWST is a much-larger telescope (50-times larger than Spitzer) with decades-more-modern sensors!

For a full array of Webb’s first images and spectra, please visit: https://esawebb.org/initiatives/webbs-first-images/

Selecting Your Color Pallet

The first thing to remember when looking at JWST images at wavelengths between 0.6 and 28-microns is that they are not colorized the way your eye would see the light. Human eyes end their color sensitivity to visible light at around 0.6-microns, so the idea that something seen by JWST would ‘look green or red’ is completely incorrect. JWST, in fact many astronomical images used in research, are colorized to help the astronomer detect differences in how objects emit light at different wavelengths.

Our brain has evolved our color vision to be a sophisticated pattern-recognizer, so all you have to do is put your data into ‘RGB’ form, and BANG! you can use the image processing power of the wet-ware in your brain to quickly survey a new subject.

The particular color pallet an astronomer uses is all about their artistic sensibility and what they want to emphasize, so it is not unreasonable for a bright red color to be used to represent hot dust and bright blue colors for cooler dust, etc. Ironically, in the electromagnetic spectrum, red wavelengths are cooler objects and blue wavelengths are hotter objects, but humans feel that blue is a cooler color than red, so our interpretation of color is backwards! For astronomers, you can even colorize the speeds of gas clouds (ie Doppler shift) so that blue colors represent clouds moving towards you and red clouds are clouds moving away from you, irrespective of the wavelength being used.

Image Analysis 101.

To analyze JWST images, let’s start with an image that has become an astronomical and even world-wide ‘classic’: The Pillars of Creation.

Vital Statistics: The ‘Pillars’ are actually a small part of the Eagle Nebula, also called Messier 16. This is a beautiful star-forming region in the constellation  Serpens located 7,000 light years from Earth. With a size of about 60 light years, the region contains 8,000 stars  of which the brightest of these, HD-168076, is 80 times the mass of our sun and only a few million years old. Its intense ultraviolet light illuminates the nebular gas and causes the atoms to emit the colorful patina of light that we see in optical photographs. Here is what the entire nebula looks like with ‘true color’ RGB filters in the visible spectrum:

        This three-color composite optical image was obtained with the Wide-Field Imager camera on the MPG/ESO 2.2-meter telescope at the La Silla Observatory. At the center of the nebula you can see the Pillars silhouetted against the bright nebular gases, which makes these ‘dark nebulae’ really stand out. The cluster of bright stars to the upper right is called NGC 6611, which the Pillars are pointing at, and are the home to the massive and hot stars that illuminate the Pillars.

Ionizing Radiation: The intense ultraviolet radiation from the massive stars in the cluster at the upper-right is actively eating away at the dense interstellar cloud that gave birth to them at the lower-left. These are what astronomers classify as O and B-type stars or just ‘OB’ stars. Each is more than 5 times as massive as our sun, and with surface temperatures above 20,000o C they emit most of their light at ultraviolet wavelengths. Astronomers can detect this ionized gas at radio-wavelengths too. They are called ‘HII’ (H-two) regions because HI is the symbol for ordinary ‘neutral’ hydrogen and ‘II’ means that the neutral hydrogen atoms have lost one electron to make them ionized, hence ‘HII’. This ultraviolet radiation streaming through the hydrogen HI gas to ionize it into HII results in many unusual wind-swept shapes including what astronomers call ‘elephant trunks’ such as the Pillars. Their shapes act like ‘wind socks’ and point towards the main source of the ionizing gas flow, which is expanding outwards from the OB star cluster at speeds up to 10 km/s….. that’s about 22,000 mph. At this pace, the ionzation front can travel 4 light years in 100,000 years, which is enough to cross the space of most star-forming regions.

What you also notice is that the optical image shows the Pillars as dark and obscurring the background nebula which we call ‘dark nebulae’, while the JWST image shows the Pillars being very bright as ’emission nebulae’. The bright emission nebula produced by the stars is also missing in the JWST image, and instead you see thousands of stars in the background. The reason this happens is your first exposure to astrophysics!


Here is a side-by-side comparison of the Hubble (left) and Webb images (right).

Interstellar Dust: Interstellar gas clouds would be entirely invisible were it not for the fact that for about every trillion atoms of gas you have one dust grain. These dust grains are about 1-micron in diameter and were formed in the cool atmospheres of ancient red super giant stars like rain condensing out of a storm cloud on Earth. The dust grains do two things. First they scatter light at optical wavelengths, just like the dust in our atmosphere does, making the sky (or a nebula) appear blue. Secondly, they are very cold, but even so they emit their own ‘heat radiation’ in the infrared spectrum. If a cloud contains lots of dust grains, it will obscure the light from background stars, but at the same time emit infrared radiation making them appear bright at infrared wavelengths. This is what we see in the Pillars.

These linear Pillar clouds are about 2 to 4 light years in length and are rich in dust grains, so they block optical light in the famous Hubble images making them look dark, but emit their own radiation making them look bright at infrared wavelengths in the JWST images. For the first time, astronomers can study just how lumpy the surfaces of these interstellar clouds are by looking at the infrared light they are emitting directly. Taking a closer look at the Pillars gives even more information.

Close up of the Pillars dust cloud showing stars being born – red dots and color near center of image.

Star-forming regions: Zoom in a little more, until you see red dots springing into view. There are dozens of them. Each of those red dots covers an area larger than our solar system. The finger-like protrusions are also larger than our solar system, and are made visible by the shadows of evaporating gaseous globules (EGGs), which shield the gas behind them from intense UV flux. EGGs are themselves incubators of new stars. The stars then emerge from the EGGs, which then are evaporated.

So there you have it! One picture rendered into ‘a thousand words’. To be sure, this one image will easily form the basis for someone’s PhD thesis because it is so rich in detail missing from even the best Hubble images. When combined with spectroscopic data from JWST and data from radio astronomy, we will have a detailed understanding of just ONE star-forming region in our Milky Way. We are definitely living in exciting times for astronomical research!

If you want to see more astronomical images analyzed this way, have a look at my new book ‘The Hidden Universe’ available at Amazon.

Check back here for my next blog!

Astronomy, Eclipse

The Last Total Solar Eclipse…Ever!

Credit  Luc Viatour  https://Lucnix.be….An email to Viatour Luc would be appreciated too.

Well…The answer is 700 million years from now, but the details are interesting!

Since the dawn of recorded history, humans have had a love-hate relationship with total solar eclipses. For most of human history, these events were feared and taken as omens of the downfall of empires or the end of the world. Only in the last thousand years or so have people settled down and viewed them as the beautiful and bizarre events that they are. By the 19th Century, scientists and artists traveled the world over to capture them with sketches at the telescope eyepiece. Among the first images taken by primitive cameras were those of total solar eclipses.

Predicting total solar eclipses

Today, the physics and mathematics of these events are known with such detail that they can be predicted to within minutes from 2000 BCE to 3000 CE [1]. They can even be used to track the slowing down of earth’s rotation by comparing the predicted time and place with historical observations [2]. But total solar eclipses require a precise geometric circumstance to exist. Our moon has a diameter of 3,475 km at a perigee distance of 363,300 km, while the sun has a diameter of 1.4 million km at a distance of 150 million km. This means that, although the sun has a diameter that is 403 times the moon, it is 412 times farther away so that the apparent size of the dark lunar disk completely covers the blinding disk of the sun in the sky. Depending on the exact timing of the moon in its orbit, this ratio of 403/412 can be made to be exactly equal to 1.00 so that the disk of the moon exactly covers the sun to give the classic total solar eclipse shown in the picture above. But this precise geometric circumstance is not written in stone. In fact, to get a proper prediction far into the fiuture you need a supercomputer!

Earth orbit evolution

Currently the distance from earth to the sun has an average value of 150 million km, but because Earth’s orbit is an ellipse, it varies from 152 million km in July to 147 million km in January. This leads to the ironic circumstance that in the Northern Hemisphere, the sun is actually farthest away from the sun in the summer and closest in the winter! Only the Southern Hemisphere with its reversed seasons gets it right!

For many decades, researchers have modeled the evolution of the orbit of the Moon and Earth with supercomputers and pretty much nailed down what we can expect to happen for the next few billion years. As it turns out, this is a fiendishly difficult calculation because it depends on an exact knowledge of the interiors of the moon and earth, the location of the continents, and the influences of the other planets. The inner solar system is dynamically unstable and displays a chaotic behavior over times of 100 million years or longer. A consequence of this is that even changing the location of Mercury in its orbit by 1 meter today causes a variety of different outcomes in a billion years including its collision with Venus and ejection from the solar system. Earth, however, seems to exist in a remarkably stable gravitational balance such that its orbit changes only insignificantly from what we see today. [3] It will drift outwards from the sun by a few thousand kilometers due to the sun itself losing mass. The sun converts 4 million tons of mass into radiant energy every second and added up over millions of years, this causes the sun’s gravitational hold on Earth to weaken and its orbit to drift outwards by 1.5 cm/year [4].

The outward drift of Earth in its orbit is entirely negligable so we won’t bother including it. We will assume that the average perihelion and aphelion distances will still remain close to 147 and 152 million km. This means that from Earth the angular diameter of the sun from the surface will vary between 1,964 seconds of arc at perihelion to 1,900 seconds of arc at aphelion, where 3600 seconds of arc equals 1 angular degree.

Lunar orbit evolution.

The moon raises ocean and solid-body tides in Earth. The tidal bulge accelerates the moon in its orbit and the orbit of the moon increases over time. The tidal bulge also slows down Earth’s rotation and lengthens the length of its ‘day’.

We know from geologic data that our moon was formed some 4.4 billion years ago and orbited Earth at a distance of only about 30 Earth Radii ( 190,000 km) causing Earth to have a rotation period of about 12 hours in a ‘day’. [5]. Since its formation, it has drifted out to its present distance at a current rate of about 3.8 cm/year based on lunar laser metrology [6]. But this outward drift continues today so that in the future the moon will be even farther from Earth. This means that at some time in the future, the ratio of lunar:solar size and lunar:solar distance will fall below the magic 1.000 needed for a total solar eclipse. The moon will simply be too small in apparent size to perfectly cover the disk of the sun. We can’t predict the exact date when we will see the very, very, very last total solar eclipse from Earths surface, but we can get a pretty good idea what timescales are involved.

Simple Linear Model

Suppose we just used the current perihelion and aphelion distances and then assumed that the moon is moving away from Earth at a constant rate of 3.8 cm/year. If we calculate the angular sizes of the moon and sun from Earth we get the following figure.

Explanation: The orange line is the angular size of the sun viewed from Earth when Earth is closest to the sun (perihelion) and the yellow line is the same calculation from when Earth is farthest from the sun (aphelion). The black line is the angular diameter of the moon at its farthest distance from Earth (apogee) and the green line is for its closest distance to Earth (perigee). What you see is that the lunar curves cross the solar curves and indicate when these two diameters are equal, allowing a total solar eclipse to be viewed. So long as the solar lines are between the two lunar lines, you will have a total solar eclipse.

What this graph says is that 1044 million years ago, the sun at perihelion matched the moons size at apogee when it had the smallest angular size. After this ‘year’ the moons size at apogee was too small to cover the sun at perihelion and so total solar eclipses at lunar apogee ceased to happen when the solar disk was largest at perihelion. Notice that before 1044 million years the lunar lines were above the solar lines. This means that the disk of the moon was always much greater than the disk of the sun at any time in the lunar orbit. In fact, the lunar disk was so big that not only was the disk of the sun covered by the moon but much of the inner corona too. You would still have total solar eclipses before 1044 million years ago, but they would look dramatically different than the ones we see today.

By the time we get to 710 million years ago, the moon at apogee was also too small to cover the sun at aphelion when the solar disk is smallest. Between 1044 and 710 million years ago, the small apogee moon could still cover the sun when the sun was between aphelion and perihelion, but after 710 million years ago, there would never again be a total solar eclipse of the sun when the moon was at apogee. This was before the emergence of multi-cellular life on Earth during the Cambrian Explosion. Only annular eclipses will be viewed from then on during lunar apogee.

Now the second lunar curve in green is more interesting. It shows the angular size of the perigee moon, and it is pretty clear that today (Time-0) the size of the perigee moon is larger that the sun at both perihelion and aphelion. So we get total solar eclipses no matter if Earth is at perihelion or aphelion. However, by 280 million years from now, the moon will start to become smaller than the solar disk at perihelion and so eclipses will stop being total solar eclipses when the sun is closest to earth and the moon is also closest to earth. After 613 million years from now, you will no longer have total solar eclipses for the perigee moon and the smaller aphelion sun. After 613 million years the lunar disk will never again be big enough to completely cover the solar disk. This is the estimate you are likely to find in many popularizations of this Final Event such as a SpaceMath problem at NASA, and NASAs lunar scientst Dr. Richard von Drak.

A More Accurate Calculation.

The previous linear calculation was based on the moon maintaining its outward 3.8 cm/yr motion for the next 600 million years, but detailed supercomputer calculations of the evolution of the Earth-Moon system give a more accurate result. I used the model published in 2021 by Prof. Houraa Daher and her team at the University of Michigan [7], and specifically used their Figure 5a, which gave the past value for the lunar orbit semi-major axis. I also used the 2020 data from the published work by Dr. Bijay Sharma [8] at the National Institute of Technology in India, specifically Figure 7, which gave the recession speed (cm/yr) with lunar semi-major axis. Ideally, both of these data should be derived from the same calculations but unfortunately this was not possible to obtain at the time of this writing. However, if they are both faithful to the same underlying physics, then the results should be consistent.

The application of these detailed models to the lunar size evolution is shown in the next figure.

The straight, linear extrapolations have now been replaced by more realistic curved predctions. Here we see along the black line that at 700 million years ago, the lunar size at apogee matched the solar disk size at perihelion (1952 arc-seconds) , some 300 million years later than the linear model. By 500 million years ago the apogee lunar disk no longer covered the disk of the sun at aphelion, so from this time forward there were no longer any total solar eclipses when the moon was at its farthest apogee distance. This happened around the time of the Cambrian Explosion.

Meanwhile, the green line for the perigee moon shows that it has a disk size greater then the size of the large perihelion sun (1952 arcseconds) disk until 300 million years from today. At this time, the lunar diameter varies from 1718 arcseconds (black line) to 1952 arcseconds (green line) so we can still have total solar eclipses so long as the moon is close to its perigee when the sun passes through one of the lunar ‘nodes’ during the equinoxes. At about 700 million years from now the large perigee moon with a diameter of 1952 arcseconds covers the sun at perihelion, but after this time, its diameter continues to decrease until from this time forward all we ever see are annular eclipses. So this critical ‘date’ is about 80 million years later than the linear model.

By 700 million years from now, the moon will continue to drift away from Earth, but at a slower rate of 3.0 cm/year. Its distance from Earth will have grown from 60.2 Re (384,400 km) to 63.8 Re (407,155 km). The moon will then take 28.4 days to orbit Earth having gained about 26.4 hours since today. This means that the time between one full moon and the next will be 30.7 days instead of the current 29.5 days. Meanwhile, the Earth’s rotation has changed from its current 23h 56m to about 26h 25m as the lunar tides continue to do their work. What this means is that an Earth Year at 700 million years from today will only about 330 days long!

Will there be anyone there to care? Probably not.

Our sun continues to evolve and grow in luminosity so by then it will be about 10% more luminous than it is today.  This means the average global temperature will be 117o F and not the 57o F we enjoy today. By this time, the level of carbon dioxide will have fallen below the level needed to sustain C3 carbon fixation photosynthesis used by trees.  Some plants use the C4 carbon fixation method to persist at carbon dioxide concentrations as low as ten parts per million. However, the long-term trend is for surface plant life to die off altogether. The extinction of plants  will be the demise of almost all animal life since plants are the base of much of the animal food chain on Earth. Climate models suggest that by about this time Earth will be hot enough to cause the slow evaporation of the oceans into the atmosphere. This will be the start of what is called the “moist greenhouse” phase, resulting in a runaway evaporation of the oceans and Earth becoming Venus.  Meanwhile, the current continents will have merged and separated and merged again into yet another supercontinent with its own lethal contribution to global heating and weather [9].

So basically by about 700 million years from now, Earth will be a humid, desert world with no complex living organisms to appreciate total solar eclipses except perhaps extremophile bacteria…and cockroaches?

Have a nice day!

[1] Five Millennium Catalog of Solar eclipses https://eclipse.gsfc.nasa.gov/SEcat5/catkey.html

[2] Ancient eclipses Reveal How Earths Rotation has Changed https://www.space.com/ancient-eclipse-records-earth-rotation-history

[3] Highly Stable Evolution of Earths Future Orbit Despite Chaotic Behaavior of Solar System https://iopscience.iop.org/article/10.1088/0004-637X/811/1/9

[4] https://www.forbes.com/sites/startswithabang/2020/04/09/earth-is-spiraling-away-from-the-sun-for-now-but-will-eventually-crash-into-it/?sh=863220238580

[5] Long-Term Earth-Moon Evolution With High-Level Orbit and Ocean Tide Models https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JE006875 figure 6

[6] The moon has been drifting away from Earth for 4.5 billion years. A stunning animation shows how far it has gone. https://www.businessinsider.com/video-moon-drifts-away-earth-4-billion-years-2019-9

[7] Long‐Term Earth‐Moon Evolution With High‐Level Orbit and Ocean Tide Models, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9285098/

[8] The Past, Present and the Futuristic Earth-Moon Orbital-Global Dynamics – and its habitability – https://www.proquest.com/openview/c945a68d9b4a2354aaea7cf859b776ba/1?pq-origsite=gscholar&cbl=4882998

[9] What if You Traveled One Billion Years into the Future? https://whatifshow.com/what-if-you-traveled-one-billion-years-into-the-future/

Brain Research

Math Anxiety: Origins and Cures

Portrait Of Student With Head Down On Stack Of Books

Someone asks you to perform a simple arithmetic calculation, or perhaps you encounter these while doing your income tax. As a consumer you might want to compare the cost of two products with different sales prices. Or perhaps the tags give  you the same product by two different manufactures who tell you the unit cost, but the products are  in either 12-count or 18-count packages. The odds are very good that along with millions of other adults you will have some trepidation in ‘doing the math’. That’s because math anxiety (MA) is endemic not only among US adults but around the world. It crosses ethnic groups, cultures and continents. According to a recent study of MA[1] 93% of all adults in the US suffer from some level of this condition; internationally and across many cultures, this incidence can be over 40%.  It is reinforced by parents, the news media, and even by teachers using outdated pedagogy– all with devastating consequences, long-term. Like ADHD, you can find yourself somewhere on the Math Anxiety Spectrum. Your location might even change as you advance from childhood to adulthood.

Your Brain on Math

The evolution of our brains over millions of years has prepared it to do many kinds of math but often at an unconscious level. We, along with thousands of other species, have an innate ability to compare quantities and figure which is larger. Some species can even count including chimpanzees, crows, bees and frogs[2]. Our brains come hard-wired at birth to understand addition and subtraction. There are actual brain neurons in the parahippocampal cortex that are only active during addition while others are only active during subtraction[3].They also respond when the instruction is written down symbolically as a word or a symbol (five and three  or 5+3).

Credit: https://anthonybonato.com/2016/04/20/this-is-your-brain-on-mathematics/

The number of brain regions involved in mathematics performance reads like a catalog of nearly half of the cerebral cortex itself. This means that many of these math-activated regions are also used for other purposes in the brain. This is a common feature of brain architecture in that regions are recycled to form other neuronal networks depending on the task at hand.

  • Dorsolateral prefrontal cortex
  • Left inferior parietal lobe
  • Left precentral gyrus
  • Left superior parietal lobe
  • Left supramarginal gyrus
  • Left middle temporal gyrus
  • Insula
  • Middle cingulate cortex
  • Middle frontal gyrus
  • Superior temporal gyrus
  • Inferior frontal gyrus
  • Thalamus
  • Bilateral intraparietal region
  • Dorsal prefrontal region
  • Inferior temporal region

As a brain matures, these regions respond to external experiences but are always influenced by innate survival instincts provided by the limbic system composed of the thalamus and the amygdala. When no previous  negative experiences trigger a limbic response for fight-or-flight, all is well.  Even by the age of 7, children still have an enthusiastic and playful attitude towards math. This attitude unfortunately starts to wane in direct proportion to the number of negative performance tests they experience, which is why MA arises.

A common view shared by many MA students is that, unless I can do math quickly, I must not be very good at it. This is also a pervasive attitude among adults who, despite performing well in grade-school math may still not see themselves ‘good’ at math. Math skills are unlike reading skills because there has evolved over time a massive social permissiveness to being a poor math performer that simply  isn’t found in other academic topics.

Thanks to advances in brain research and mapping, we have a ring-side seat into what brain regions and neuronal circuitries are responsible, not only for handling mathematical problem-solving of increased sophistication, but how this process maps into generating anxiety. There is even a specific brain protein called MAOA that correlates with MA and can be used to spy on your emotional state as you are confronted with different problems.

Math comprehension and execution, like our language centers (Broca and Wernicke Regions) are activated primarily in two main regions: The parietal lobe is involved with calculating and processing numbers; The frontal lobe is involved in recalling numerical knowledge and working memory[3].

The sub-region called the dorsolateral prefrontal cortex is most curious because it is also activated as we regulate our emotions. For example, most children learn how to tone-down their glee at winning a game when they see their friends are mortified at  having lost. In math this region seems to be activated when the individual is keeping track of more than one concept at a time[2]. This region, which in math helps us keep relevant  problem-solving information ‘fresh’ in our working memory,  is also shared by circuits that allow us to suppress selfish behavior, foster commitment in relationships, and inferring the intentions of others, which is called a Theory of Mind. Researchers have proposed that math training not only makes us better at math, but also strengthens our ability to moderate our feelings and our social interactions because of the brains proclivity in  sharing brain regions for other purposes.

The Amygdala Hijack

Brain imaging studies[3] show that individuals with MA, not unexpectedly, activate circuits associated with negative emotional processing (amygdala, prefrontal cortex), the experience of pain (insula), but also areas involved with inhibiting irrelevant information, and conflict processing. The emotional control network is activated even before mathematical performance occurs. MA does its dirty work by literally robbing the individual of resources in its working memory so that they no longer have access to recalling how similar problems were previously solved. In fact, actual physical changes to the brains of MA students were found in the amygdala, the anterior corpus callosum, the right inferior frontal sulcus and the pericallosal sulcus. In particular the right amygdala volume is smaller and more reactive in students with MA[4]. Chronic hyperactivity of the amygdala in response to stress results in cellular atrophy and a decreased ability to regulate negative emotions. This effect continues into adulthood, so repeated negative math experiences in childhood alters the way that adults handle MA in a way that is both cumulative and apparently not easily mitigated in adulthood because it involves physical changes (atrophy) to specific brain regions.

One of the most troubling features of exercising a math skill is that the regions used are also connected via neuronal synapses to  the prefrontal cortex and to the amygdala. The PFC is a vital executive brain region used for synthesizing data symbolically, keeping information present in a ‘working memory’ and forecasting what happens next. This means that getting better at math allows your PFC to be trained to make better decisions about the future. But here is the BIG PROBLEM. The amygdala also watches over this process and stamps it with an emotional context. Under conditions were the stress hormone cortisol is elevated, the amygdala sees your current condition as a fight-or-flight situation and ‘hijacks’ your brain. [5]This immediately shuts down your PFC and flavors your conscious thinking with the survival instinct of wanting to flee the situation. Forget about logic and planning – it’s time to run! Of course this is not possible when working on a difficult math problem, plus the hijack has now robbed you of clear executive thinking, planning and working memory, which only increases the cortisol.

Defeating MA

This cycle of increasing stress can be defeated by first recognizing it is happening   (sweaty palms, rapid heartbeat), using deep slow breathing, and especially clearing your mind of intrusive thoughts. It only takes 90 seconds to defeat this progression. But sometimes, putting yourself in a state where MA cannot get a toe-hold is ‘simply’ a matter of not triggering the Amygdala Hijack in the first place. Here are some recommendations for teachers from researchers who have studied this triggering process.

  • Incorporate math into real-world concepts that students understand.
  • Focus on the fun elements of math like pattern making and a curiosity about numbers, not on rote memorization and theory.
  • Have them see how numbers and data literacy surround them in life from supermarket shopping to predicting future trends.
  • Avoid negative self-talk. Train yourself to have a positive attitude.
  • Consider math as a foreign language that takes practice.
  • Break the vicious downward cycle  of a bad test grade leading to lower self-esteem leading to another bad test grade leading to still-lower self-esteem.
  • Never scold a student for being wrong or having failed to perform a ‘simple’ math task.
  • Never tell your child ‘I was never good at math either’. This tells the child they can succeed in life without knowing math, which is demonstrably false in the 21st century.
  • Find ways to provide alternate student assessments rather than timed tests. This is a major source of stress and a key factor in MA.
  • Investigate ‘mixed-ability’ groupings to avoid placing MA student together, which only reinforces and normalizes  MA through peer-pressure.
  • Make math fun with lots of positive reinforcement. This reduces stress and heart rates and mitigates MA.
  • Have parents read math-related bedtime stories.
  • Encourage understanding not rote memorization. STEM professionals are those who think slowly, creatively and deeply..not necessarily quickly.
  • Display ‘anchor charts’ with examples of work, previous problems or formulas as visual clues to recall previous material.
  • Draw or write down facts or relevant equations before working on a math problem
  • Have students describe the problem to a partner to help articulate their thinking
  • Start the class with a ‘diffuser’ such as sharing a joke, or asking ‘who can tell me something we did in class yesterday?”
  • Focus on how a student got their answer and not on it whether it is right or wrong. If incorrect the student may realize this as they explain the process they used.
  • Allow students to post pictures or written explanations of their methods of solving a problem.
  • Pay attention to the words you use. Instead of ‘this is easy’ say ‘this is like the problem we did yesterday”.
  • Always project a positive, confident attitude to support modeling MA-free behavior and attitudes.

Genetic Predispositions

Here’s some bad news. MA might be genetically inheritable. The epigenetic genome controls how genes are expressed. It represents an additional way that traits and tendencies can be passed on. It is well known that traumas to parents can be passed to children, especially starvation and malnutrition. If the starving mother is pregnant, the epigenome she gives to her fetus can cause childhood difficulties in expressing proteins needed for proper digestion. Epigenetics also seems to explain how stress-related disorders can be inherited. According to a review article by TruDiagnostic published in 2020[6], the amount of cortisol in the brain can be regulated by the inherited epigenetic genome and predispose a child to stress-related behavior. It is not impossible that the same transfer of tendencies might happen that predispose the child to MA.  MA seems to result from an interaction of genetic vulnerability with negative experiences learning math. Only an unkind word from a teacher, parent or social group would be enough to set MA in motion, full-blown.

Researchers have also found that a molecular genetic marker called the monoamine oxidase A gene (MAOA) when not expressed at high enough levels correlates with increased MA especially in girls who are known from other studies to be especially susceptible to MA[7]. However, Zhe Wang at Ohio State finds that genetic factors may only account for about 40% of the individual differences in math performance based on a study of 216 twins “If you have these genetic risk factors for math anxiety and then you have negative experiences in math class, it may make learning that much harder.”[8]

MA causes millions of children, especially girls, to not consider STEM careers. This can relegate them to lower-paying jobs that are less quantitative in skill-set. With manual cash registers, some arithmetic acumen was always required even in low-paying sales jobs. Today, change is made with computerized terminals so low-paying jobs require virtually no math and are free of MA triggers.  However, the consequences of not continuing  math education in adolescence can be potentially disastrous not only reducing their career options but in the actual development of their brains.

A recent study of adolescents in the UK shows that a lack of math education affects adolescent brain development. In the UK, students can elect to end their math education at age 16.  The chemical called gamma-Aminobutyric acid (GABA) is present in the middle front gyrus (MFG), which is a region involved in reasoning and cognitive learning. GABA levels are a predictor of changes in mathematical reasoning as much as 19 months later.  What was found among the older adolescents was that GABA showed a marked reduction[9]. Because this chemical is also involved in brain plasticity and the ability to learn new skills and thinking, this reduction at this critical stage in brain development can have far-reaching impacts into adulthood.

Don’t worry…Be happy

But the good news is the brain is not a static thing. It is very ‘plastic’ when it comes to learning and dealing with new experiences. With patience and a more-supportive classroom environment, students can be shown how to make other associations between math and emotions, but this time ones that mitigate MA.

References

[1] Brain areas associated with numbers and math, 2018, doi.org/10.1016/j.dcn.2017.08.002 

[2] Mental math and the fine-tuning of emotions. Sandra Ackerman, 2017, Dana Foundation Blog, dana.org/article/mental-math-and-the-fine-tuning-of-emotions/

[3] Dorsolateral Prefrontal Cortex, 2013, Simmon Moss,  and Wikipedia [ref 8]

[4] Neurostructural correlate of math anxiety in the brains of children. Karin Kucian et al,   Translational Psychiatry, 2018; 8:273. Doi: 10.1038/s41398-018-0320-6. And www.ncbi.nlm.gov/pmc/articles/PMC6288142/

[5] The stress-learning connection: Manage an Amygdala Hijack in three steps. The Brain Health Magazine, 2022, thebrainhealthmagzine.com/hormones/the-stress-learning-connection-manage-an-amygdala-hijack-in-three-steps/

[6] Epigenetics and Anxiety – The relationship between genes and stress-related disorders, 2020, blog.trudiagnostic.com/epigenetics-and-anxiety/

[7] MAOA-LPR polymorphism and math anxiety: A marker of genetic susceptibility to social influences in girls, 2022, Annals of the New York Academy of Sciences 1516(1), DOI:10.1111/nyas.14814.

[8] Who’s afraid of math? Genetics plays a role but researchers say environment still key, 2014, geneticliteracyproject.org/2014/03/19/genetics-plays-a-role-in-math-anxiety/

[9] www.sciencedaily.com/releases/2021/06/210607161149.htm and DOI:10.1073/pnas.2013155118