Category Archives: Astronomy

The Last Total Solar Eclipse…Ever-Updated

One year ago, I posted a fun problem of predicting when we will have the very last total solar eclipse viewable from Earth. It was a fun calculation to do, and the answer seemed to be 700 million years from now, but I have decided to revisit it with an important new feature added: The slow but steady evolution of the sun’s diameter. For educators, you can visit the Desmos module that Luke Henke and I put together for his students.

The apparent lunar diameter during a total solar eclipse depends on whether the moon is at perigee or apogee, or at some intermediate distance from Earth. This is represented by the two red curved lines and the red area in between them. The upper red line is the angular diameter viewed from Earth when the moon is at perigee (closest to Earth) and will have the largest possible diameter. The lower red curve is the moon’s angular diameter at apogee (farthest from Earth) when its apparent diameter will be the smallest possible. As I mentioned in the previous posting, these two curves will slowly drift to smaller values because the Moon is moving away from Earth at about 3cm per year. Using the best current models for lunar orbit evolution, these curves will have the shapes shown in the above graph and can be approxmately modeled by the quadratic equations:

Perigee: Diameter = T2 – 27T +2010 arcseconds

Apogee: Diameter = T2 -23T +1765 arcseconds.

where T is the time since the present in multiples of 100 million years, so a time 300 million years ago is T=-3, and a time 500 million years in the future is T=+5.

The blue region in the graph shows the change in the diameter of the Sun and is bounded above by its apparent diameter at perihelion (Earth closest to Sun) and below by its farthest distance called aphelion. This is a rather narrow band of possible angular sizes, and the one of interest will depend on where Earth is in its orbit around the Sun AND the fact that the elliptical orbit of Earth is slowly rotating within the plane of its orbit so that at the equinoxes when eclipses can occur, the Sun will vary in distance between its perihelion and aphelion distances over the course of 100,000 years or so. We can’t really predict exactly where the Earth will be between these limits so our prediction will be uncertain by at least 100,000 years. With any luck, however, we can estimate the ‘date’ to within a few million years.

Now in previous calculations it was assumed that the physical diameter of the Sun remained constant and only the Earth-Sun distance affected the angular diameter of the Sun. In fact, our Sun is an evolving star whose physical diameter is slowly increasing due to its evolution ‘off the Main Sequence’. Stellar evolution models can determine how the Sun’s radius changes. The figure below comes from the Yonsei-Yale theoretical models by Kim et al. 2002; (Astrophysical Journal Supplement, v.143, p.499) and Yi et al. 2003 (Astrophysical Journal Supplement, v.144, p.259).

The blue line shows that between 1 billion years ago and today, the solar radius has increased by about 5%. We can approximate this angular diameter change using the two linear equations:

Perihelion: Diameter = 18T + 1973 arcseconds.

Aphelion: Diameter = 17T + 1908 arrcseconds.

where T is the time since the present in multiples of 100 million years, so a time 300 million years ago is T=-3, and a time 500 million years in the future is T=+5. When we plot these four equations we get

There are four intersection points of interest. They can be found by setting the lunar and solar equations equal to each other and using the Quadratic Formula to solve for T in each of the four possible cases.:

Case A : T= 456 million years ago. The angular diameter of the Sun and Moon are 1890 arcseconds. At apogee, this is the smallest angular diameter the Moon can have at the time when the Sun has its largest diameter at perihelion. Before this time, you could have total solar eclipses when the Moon is at apogee. After this time the Moon’s diameter is too small for it to block out the large perihelion Sun disk and from this time forward you only have annular eclipses at apogee.

Case B : T = 330 million years ago and the angular diameters are 1852 arcseconds. At this time, the apogee disk of the Moon when the Sun disk is smallest at aphelion just covers the solar disk. Before this time, you could have total solar eclipses even when the Moon was at apogee and the Sun was between its aphelion and perihelion distance. After this time, the lunar disk at apogee was too small to cover even the small aphelion solar disk and you only get annular eclipses from this time forward.

Case C : T = 86 million years from now and the angular diameters are both 1988 arcseconds. At this time the large disk of the perigee Moon covers the large disk of the perihelion Sun and we get a total solar eclipse. However before this time, the perigee lunar disk is much larger than the Sun and although this allows a total solar eclipese to occur, more and more of the corona is covered by the lunar disk until the brightest portions can no longer be seen. After this time, the lunar disk at perigee is smaller than the solar disk between perihelion and aphelion and we get a mixture of total solar eclipses and annular eclipses.

Case D : T = 246 million years from now and the angular diameters are 1950 arcseconds. The largest lunar disk size at perigee is now as big as the solar disk at aphelion, but after this time, the maximum perigee lunar disk becomes smaller than the solar disk and we only get annular eclipses. This is approximately the last epoc when we can get total solar eclipses regardless of whether the Sun is at aphelion or perihelion, or the Moon is at apogee or perigee. The sun has evolved so that its disk is always too large for the moon to ever cover it again even when the Sun is at its farthest distance from Earth.

The answer to our initial question is that the last total solar eclipse is likely to occur about 246 million years from now when we include the slow increase in the solar diameter due to its evolution as a star.

Once again, if you want to use the Desmos interactive math module to exolore this problem, just visit the Solar Eclipses – The Last Total Eclipse? The graphical answers in Desmos will differ from the four above cases due to rounding errors in the Desmos lab, but the results are in close accord with the above analysis solved using quadratic roots.

Landscape Dimming During a Total Solar Eclipse

During a solar eclipse, the lansdcape will slowly dim until it is nearly complete darkness along the path of totality. other observers wil see te landscape dim a bit but then brighten to normal intensity. If you didn;t know that an eclipse was going on you might not even notice the dimming, mistaking it for a cloud passing across the sun. The geometric condition for this dimming have to do with the area of exposed solar surface and how this changes as the disk of the moon passes across it. Below is a simple mathematical model for ambient light dimming that you can put to the test the next time a solar eclipse passes over your geographic location.

I have reanalyzed the geometry and defined it in terms of the center-to-center distance, L, between the sun and moon, and their respective radii Rs and Rm as the figure of the upper half-plane of the intersection shows, with the yellow area on the left representing the disk of the sun and the white area on the right the disk of the moon. This problem was previously considered in 2000 by British astronomer David Hughes who used the distance defined by the segment FE, which he called alpha, but L = 1+M-a. The figure shows the moon overlapping the disk of the sun in a lens-shaped zone whose upper half is represented by the area AFDE.


The basic idea is that we want to compute the area of the lunar arc cap AFD by computing the area of the sector BAF and subtracting the triangle BAE from the sector area. That leaves the area of the cap as the left-over area. We perform the same calculation for the solar sector CAE and subtract the triangle CAD from this.  The resulting area of the full lens-shaped overlap region is then

Occulting Area = 2x(AreaAFD + AreaAED).

Because of the geometry, the resulting area should only depend on the center-to-center separation and the radii of the sun and moon. You should not have to specify any angles as part of the final calculation. In the following we will use degree measure for all angles.

The area of the sector of a circle is just A = (Theta/360)piR2 so that gives us the first two relationships:

To simplify the problem, we are only interested in the fraction of the full sun disk that is illuminated. The full sun has an area of pi Rs2, so we divide Am and As by pi Rs2 , and if we define Rs=1.0 and M = Rm/Rs we get:

Although M is fixed by the solar-lunar ratio, we seem to have two angular variables alpha and theta that we also have to specify. We can reduce the number of variables because the geometry gives a relationship between these two angles because they share a common segment length given by h.

so that the EQ-1 for A can be written entirely in terms of the center-to-center distance, L,  and moon-to-sun disk ratio M = Rm/Rs. This is different than the equation used by Hughes, which uses the width of the lens (the distance between the lunar and solar limbs) segment FDE=a as the parameter, which is defined as L = 1+M-a.

During a typical total solar eclipse lasting 4 minutes, we can define L as

L = 1900 – 900*(T/240) arcseconds where T is the elapsed time from First Contact in seconds. Since L is in units of the current solar diameter (1900 asec) we have

EQ 3)          L = 1 – T/480.  

If we program EQ 1, 2, and 3 into an excel spreadsheet we get the following plot for the April 8, 2024 eclipse.

First Contact occurs at 16:40 UT and Fourth Contact occurs at 19:57 UT so the full duration is 197 minutes. During this time L varies from  -(1+M) to +(1+M). For the April 8, 2024 eclipse we have the magnitude M = 1.0566,  so  L varies from -2.0566 (t=0) to +2.0566 (t=197m). As the moon approaches the full 4-minute overlap of the solar disk between L=-0.05 and L=+0.05 (t =97m to t=102m), we reach full eclipse.

We can re-express this in terms of the landscape lighting. The human eye is sensitive to a logarithmic variation in brightness, which astronomers have developed into a ‘scale of magnitudes’. Each magnitude represents the minimum change in brightness that the human eye can discern and is equivalent to a factor change by 2.51-times. The full-disk solar brightness is equal to -26.5m, full moon illumination is  -18.0m on this scale. The disk brightness, S, is proportional to the exposed solar disk area, where E is the solar surface emission in watts/m2 due to the Planck distribution for the solar temperature of T=5770 k.  This results in the formula:

m = -26.5 – 2.5log10(F)

where F is the fraction of the full disk exposed and is equal to Equation 1.  For a sun disk where 90% has been eclipsed, f=0.10 and the dimming is only 2.5log(1/10) = 2.5m. How this translates into how humans perceive ambient lighting is complicated.

The concept of a Just Noticeable Difference is an active research area in psychophysics. In assessing heaviness, for example, the difference between two stimuli of 10 and 11 grams could be detected, but we would not be able to detect the difference between 100 and 101 grams. As the magnitude of the stimuli grow, we need a larger actual difference for detection. The percentage of change remains constant in general. To detect the difference in heaviness, one stimulus would have to be approximately 2 percent heavier than the other; otherwise, we will not be able to spot the difference. Psychologists refer to the percentages that describe the JND as Weber fractions, named after Ernst Weber (1795-1878), a German physiologist whose pioneering research on sensation had a great impact on psychological studies. For example, humans require a 4.8% change in loudness to detect a change; a 7.9% change in brightness is necessary. These values will differ from one person to the next, and from one occasion to the next. However, they do represent generally accurate values.

The minimum perceivable light intensity change is sometimes stated to be 1%, corresponding to +5.0m, but for the Weber Fraction a 7.8% change is required in brightness corresponding to only -2.5log(0.078) = +2.7m. This is compounded by whether the observer is told beforehand that a change is about to happen. If they are not informed, this threshold magnitude dimming could be several magnitudes higher and perhaps closer to the +5.0m value.


The Heliophysics Big Year

Heliophysics is an area of space science, named by NASA, which focuses on the matter and energy of our Sun and its effects on the solar system. It also studies how the Sun varies and how those changes pose a hazard to humans on Earth and in space.

The Heliophysics Big Year is a global celebration of solar science and the Sun’s influence on Earth and the entire solar system.During the Heliophysics Big Year, you will have the opportunity to participate in many solar science events such as watching solar eclipses, experiencing an aurora, participating in citizen science projects, and other fun Sun-related activities. For details, have a look at the NASA video that describes it in more detail [HERE].

This 14-month series for science and math educators focuses on heliophysics topics with related math problems at three levels: elementary, middle, and high school. It is sponsored by NASA’s Heliophysics Education Activation Team.

Each month, I will be hosting a webinar on the theme-of-the-month and also providing some math-oriented activities that go along with he theme. Here is a list of the Webinar viewing dates. When each webinar is completed, you can view a recorded version of it at the link provided. Visit this blog page a day before the scheduled program to register.

HBY Webinar programs:

December 19, 2023 – Citizen Science Projects – Do Auroras Ever Touch Ground?

January 16, 2024 – The Sun Touches Everything – Solar Panel Math and Sunlight Energy.

February 20, 2024 – Fashion – How do color filters work?

March 19, 2024 – Experiencing the Sun – Predicting Solar Storms.

April 16, 2024 – Total Solar Eclipse – The Last Total Solar Eclipse!

May 21, 2024 – Visual Art – Is the Sun Really Yellow?

June 18, 2024 – Performance Art – Do Songs About the Sun Follow the Sunspot Cycle?

July 16, 2024 – Physical and Mental Health – How Old is Sunlight?

August 20, 2024 – Back to School – Can You Accurately Draw the Solar Corona in Under 5 Minutes?

September 17, 2024 – Environment and Sustainability – Interplanetary solar electricity for spacecraft.

October 15, 2024 – Solar Cycle and Solar Max – Predicting the Next Sunspot Cycles and Travel to Mars.

November 19, 2024 – Bonus Science – TBD

December 17, 2024 – Parker’s Perihelion – TBD

To participate in a webinar, held at 7:00pm Eastern Time, you first need to register for it by clicking on the appropriate link below and filling out the registration form. You will then receive via email the link to the live program.

2/20/24 Fashion, Color, and Light https://us02web.zoom.us/webinar/register/WN_4w9xTzxHTO-fcOMJpSjWvA

3/19/24       Experiencing the Sun

https://us02web.zoom.us/j/82743230881

4/16/24       Total Solar Eclipse

https://us02web.zoom.us/webinar/register/WN_MJt-5gG-S-SskTPmYFb25g

5/21/24       Visual Art

https://us02web.zoom.us/webinar/register/WN_XqFErgloQECPkTn_uNEreA

6/18/24       Performance Art

https://us02web.zoom.us/webinar/register/WN_Z4QRFZM2SCSX2QmPC7DMWg

Registration links coming soon

7/16/24           Physical and Mental Health

8/20/24           Back to School

9/17/24           Environment and Sustainability

1015/24          Solar Cycle and Solar Max

11/19/24         Bonus Science

12/17/24         Parker’s Perihelion

View recordings and PowerPoint slide deck of completed webinars at:

https://drive.google.com/drive/folders/1JFU1cd9urAnG514nIGCpm3YXtaQy0i7S

Exploring the Heliosphere

This is my new book for the general public about our sun and its many influences across the solar system. I have already written several books about space weather but not that specifically deal with the sun itself, so this book fills that gap.

We start at the mysterious core of the sun, follow its energies to the surface, then explore how its magnetism creates the beautiful corona, the solar wind and of course all the details of space weather and their nasty effects on humans and our technology.

I have sections that highlight the biggest storms that have upset our technology, and a discussion of the formation and evolution of our sun based on Hubble and Webb images of stars as they are forming. I go into detail about the interior of our sun and how it creates its magnetic fields on the surface. This is the year of the April 2024 total solar eclipse so I cover the shape and origin of the beautful solar corona, too. You will be an expert among your friends when the 2024 eclipse happens.

Unlike all other books, I also have a chapter about how teachers can use this information as part of their standards-based curriculum using the NASA Framework for Heliospheric Education. I even have a section about why our textbooks are typically 10 – 50 years out of date when discussinbg the sun.

For the amateur scientists and hobbyists among you, there is an entire chapter on how to build your own magnetometers for under $50 that will let you monitor how our planet is responsing to solar storms, which will become very common during the next few years.

Basic book details: 239 pages; 115 ilustrations; 6 tables; 70,000 words;

There hasn’t been a book like this in over a decade, so it is crammed with many new discoveries about our sun during the 21st century. Most books for the general public about the sun have actually been written in a style appropriate to college or even graduate students.

My book is designed to be understandable by my grandmother!

Generally, books on science do not sell very well, so this book is definitely written without much expectation for financial return on the effort. Most authors of popular science books make less than $500 in royalties. For those of you that do decide to get a copy, I think it will be a pleasurable experience in learning some remarkable things about our very own star! Please do remember to give a review of the book on the Amazon page. That would be a big help.

Yep…I want to get the e-book version ($5): Link to Amazon.

Yep…I want to get the paperback version ($15): Link to Amazon.

Oh…by the way…. I am a professional astronomer who has been working at NASA doing research, but also education and public outreach for over 20 years. Although I have published a number of books through brick-and-morter publishing houses, I love the immediacy of self-publishing on topics I am excited about, and seeing the result presented to the public within a month or two from the time I get the topic idea. I don’t have to go through the lengthy (month-year) tedium of pitching an idea to several publishers who are generally looking for self-help and murder mysteries. Popular science is NOT a category that publishers want to support, so that leaves me with the self-publishing option.

Other books you might like:

Exploring Space Weather with DIY Magnetometers. ($7). Link to Amazon.

History of Space Weather: From Babylon to the 21st Century. (paperback, $30) (ebook, $5). Link to Amazon.

Solar Storms and their Human Impacts (e-book; $2) Link to Amazon.

The 23rd CycleL Learning to live with a stormy star. – Out of print.

DIY magnetometers for studying space weather!

Aurora are a sign that the sun is stormy and that Earth’s magnetic field is changing rapidly.

This page is a supplement to my new book ‘Exploring Space Weather with DIY Magnetometers‘, which is avalable at Amazon by clicking [HERE]. This $8.00 B/W book contains 146 pages and has 116 illustrations and figures that describe six different magnetometers that you can build for under $60.00. I will be posting updates to my magnetometer designs on this page along with new storm data examples as the current sunspot cycle progresses. For convenience, the sections below are tied to updates to the corresponding chapters in the book. In each instance, I have compared my design data for the magnetic D-component (angular deviation from True Geographic North) to the corresponding data from the Fredericksburg Magnetic Observatory (FRD) in Virginia.

What is Space Weather?

Chapter 2: Earth’s Magnetic Field

Chapter 3: Basic Soda Bottle Designs (under $10.00)

A soda bottle design that detects the daily Sq ionospheric current. Black is the soda bottle data and red is the FRD observatory D-component data. I used an 8-meter separation for the laser spot to get the best sensitivity.
Soda bottle measurements (black dots) and FRD magnetometer data (red line) for the Kp=4 storm on July 14 (blue bar). Also shown are the diurnal Sq deviations that occur during the daytime (yellow bars sunrise to sunset). The Kp=4 event was barily visible above the Sq deviation which was also maximal near the time of the afternoon storm. Note that the soda bottle measurements do follow the magnetic D-component deviations seen by the FRD magnetic observatory, which again testifies to the accuracy of the soda bottle system using an 8-meter separation.

Chapter 5: A Dual Hall Sensor Design ($20.00)

Figure 72. Black is the instrument data and red is the FRD observatory data.
Figure 5.6 Sq effect. Black line is the instrument data and red line is the FRD observatory data.

Chapter 6: The Smartphone Magnetometer

Figure 6.11. Example of smartphone data (dots) and the Kp index (gray bars). Smartphone data roughly correlates with geomagnetic storm severity near Kp=3-4.

Chapter 7: The Photocell Comparator ($40.00)

Fig 7.23. Black is the instrument data and red line is the FRD observatory data. The pronounced dip is the diurnal Sq effect.
Fig 7.26. Black line is the instrument data. Red line is the FRD observatory data. A Kp=4 geomagnetic storm occured between 30-33 hours.

Chapter 8: The Arduino Magnetometer with the RM3100 sensor ($60.00)

Fig 8.35 Sq effect seen by the instrument (black line) and the FRD observatory (red line).
Data for the RM3100 (black) and the FRD magnetic observatory (red line) during the Kp=4 geomagnetic storm on July 14 (blue bar). This event, as for the plot from the soda bottle system shown above, was barely seen above the Sq current deviation for July 14 which was clearly seen during the daytime (yellow bar). Note, however, that the RM3100 follows very accurately the magnetic D-component deviations seen by the FRD observatory.

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.

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!

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!

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.

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)