We just passed through the biggest ‘solar storm’ in the last 20 years caused by the massive naked-eye sunspot group called AR-3664. Its size was 15 times the diameter of Earth and rivaled the size of the famous Carrington sunspot of September, 1859. Since it first appeared on May 2, it remained inactive until May 9 when it released an X2.2-class solar flare at 10:10 UT.
This enormous and violent release of energy stimulated the launch of six coronal mass ejections of which three merged to become an intense ‘cannibal CME’ that arrived near Earth on May 10 at 16:45 UT. Its south-directed magnetic field was perfect for imparting the maximum amount of energy to our planet’s magnetosphere. For a transit time of about 24-hours, it was traveling at a speed of about 1,700 km/s when it arrived. It sparked a G5-level extreme geomagnetic disturbance with a Kp index of 9 between May 10, 21:00 UT and May 11, 03:00 UT.
On May 9th at 06:54 UT AR-3664 produced an X-3.9 flare. This was followed on May 11 with a fourth major X-5.8 flare at 1:39 UT, which caused an immediate shortwave radio blackout across the entire Pacific Ocean that lasted for several hours. It is expected that the May 11 flare sparked anoher CME that may arrive near Earth on Monday evening May 13.
The last G5 geomagnetic storm that we experienced was way back in October 28 to November 5, 2003. These Halloween Storms caused power outages in Sweden and damaged transformers in South Africa. Despite many recent cautionary comments in the news media about cellphone and satellite outages and power grid problems, as yet none of these have been identified but perhaps in the next few weeks these technological impacts may start to be mentioned as anecdotes begin to surface.
Unfortunately, many areas on the East Coast were covered by clouds during this three-day period and missed the opportunity to see these major aurorae. However, my DIY magnetometer (see my earlier blog on how to build your own $50 magnetometer (located in Kensington, Maryland (latitude 39o N) was able to keep up with the invisible changes going on, and produced a very respectable record of this entire storm period. As a scientist, I am often working with things I cannot directly see with my eyes, so the fact that I had my trusty magnetometer to reveal these invisible changes around me was pretty cool!
This graph shows a side-by-side comparison of the data recorded by my RM3100 magnetometer (black) and the magnetometer at the Fredericksberg Magnetic Observatory (red). I have shifted and rescaled the plots so you can more easily see how similar they are. This is very satisfying because it shows that even a simple home-made magnetometer can perform very well in keeping up with the minute changes in the geomagnetic field. This plot shows the variation in the so-called D component, which is the local magnetic declination angle. Mathematically is is defined by D = arctan(Bx/By). It’s the angle relative to geographic North that your local compass points.
Below is a slightly different graph of the RM3100 data. As you can see in the first part of the above plot between 36 and 63 UT hours, the smooth change is caused by the diurnal Sq current effect that is correlated with the solar elevation angle. During this storm period, it is assumed to have behaved smoothly during the actual storm, so in the graph below I have subtracted it from the magnetometer data. The result is that I have now isolated the changes due to the storm itself. The top row of numbers are the 3-hour Kp index averages from NOAA. The marked times are for EDT in Maryland. Universal Time is 4 hours ahead of EDT.
This was, indeed, a very powerful storm that lasted about 42 hours. This places it among a handful of exceptional geomagnetic storms that includes the great Carrington Storm of August 28 to Septemer 5, 1859.
Why is this important? Well, in the grand scheme of things it may not matter much, but as an astronomer it is still a lot of fun to have access to the invisible universe from the comfort of my suburban home. I will let geophysicists have all the fun deciphering all the bumps and wiggles and what they tell us about our magnetic field and solar storms!
Meanwhile, my gear is primed and ready to go to detect this Monday’s next storm. Some predict that it may be even bigger then the one we just experienced. It’s interesting how the Carrington Storm was actually two major storms separated by a few days, with the CME from the first storm also canibalizing several other CMEs that were also enroute.
Like the introduction of hand calculators into the classroom in the 1970s, ChatGPT offers enormous promise but currently suffers from a variety of negative expectations. Some of the arguments against students using calculators in the 1970s classroom are being used today against ChatGPT. I think there are some applications that work very well if you consider ChatGPT to be an intelligent ‘hand calculator’ in the math and physical science classroom. Here is an example I came up with without much effort!
I. Student Pre-Requisite Knowledge
The following example requires students to work with Scientific Notation, calculating the volume of spheres and shells, and working with the mass:density:volume relationship.
II. Exoplanet Interior Modeling
Astronomers have discovered over 5000 exoplanets orbiting other stars. We call these ‘exoplanets’ so that they don’t get confused with the ‘planets’ in our solar system. From a careful study of these exoplanets, astronomers can figure out how long they take to orbit their stars, their distance from the star, their diameters and their masses. How do they use this information to figure out what the insides of these exoplanets look like? This activity will show how a simple knowledge of mass, volume and density provides the clues!
III. Mass, Density and Volume
Mass, volume and density are related to each other. If two things occupy the same volume but have different masses, the less-massive one will have the lower density.
Density = Mass / Volume.
Example 1: A Prospector had his sample weighed to be 20 grams, and its volume calculated by water displacement and found to be 4 cubic centimeters. If pure gold has a density of 19.3 gm/cc, is his sample actually gold or is it iron pyrite (density 5.0 gm/cc)?
Answer: Density = 20 gm/4 cc = 5 gm/cc so it’s iron pyrite or ‘Fools Gold’.
Example 2: A basic principle of physics is that light things of low density float on top of denser things. Why do you have to shake a bottle of salad dressing before you use it?
ChatGPT Query: There are five different liquids mixed together in a bottle. After 10 minutes they sort themselves out. The liquids are: Olive oil ( 0.92 g/cc ), water ( 1.0 g/cc), molassis ( 1.4 g/cc) , vinegar ( 1.0006 g/cc), honey (1.43 g/cc). From bottom to top, how will the liquids separate themselves?
IV. Designing Mercury with a One-Component Interior Model
Mercury was formed close to the sun where only iron and nickel-rich compounds could condense into a planet. Let’s model Mercury and see what we discover. The actual mass of Mercury is 0.055 times Earth.
Step 1 – Use the formula for the volume of a sphere V=4/3 pR3 and with a known radius for Mercury of Rm = 2.43×106 meters to get the volume of the planet of V = 6×1019 m3.
Step 2 – Calculate the mass of Mercury for various choices of density. Give the predicted mass for Mercury in multiples of Earth’s mass of 5.97×1024 kg.
Step 3: Test your knowledge: For a density of 5000 kg/m3 and a radius of 2.43×106 meters, what is the mass of Mercury for these selected values? Give your answer to two significant figures.
Volume = 4/3p (2.43×106meters)3 = 6.0×1019 m3
Mass = 5000 x Volume = 3.0×1023 kg
Mase(Earth units) = 3.0×1023 kg /5.97×1024 kg = 0.05 times Earth
Use ChatGPT to generate data for plotting. Enter this question into the window:
ChatGPT Query: A sphere has a radius of 2.43×10^6 meters. What is the mass of the sphere if its density is 5000 kg per cubic meter? Express your answer in units of Earth’s mass of 5.97 x 10^24 kg. Give your answer to two significant figures.
Repeat the ChatGPT query four times to generate a mass estimate for densities of 4000, 4500, 5000, 5500 and 6500 kg/m3. Plot these points on a graph of mass versus density and draw a line through the values. Which density gives the best match to the observed mass of Mercury of 0.055 Mearth? (Answer: about 5500 kg/m3).
V. Designing Mars with Two-Component Models
Now we add two components together for planets that have a high density core and a lower density mantle. These would have formed farther out than the orbit of Mercury but with masses lower than than of Earth. The mathematical model consists of a spherical core with a radius of Rc, surrounded by a spherical shell with an inner radius of Rc and an outer radius of Rp, where Rp is the observed planetary radius. Mathematically the model looks like this:
M = Dc x 4/3p Rc3 + Dm x 4/3p ( Rp3 – Rc3)
Draw a diagram of the planet’s interior showing Rc and Rp and confirm that this is the correct formula for the total mass of the planet where Dc is the core density, and Dm is the mantle density.
Test Case: An exoplanet is discovered with a mass of 5.97×10^24 kg and a radius of 6,378 kilometers. If the radius of its core is estimated to be Rc = 3,000 km and its core density is 7000 kg/m3, what is the average density of the mantle material?
Dm = (5.97×1024 – 7000 x 1.1×1020)/9.8×1020 = 5300 kg/m3
Check your answer with ChatGPT using this query. A planet consists of a core region with a radius of Rc and a mantle region extending to the planet’s surface at a radius of Rp. If the planet is a perfect sphere with a radius Rp = 6378 km and Rc = 3000 km, with a total mass of 5.97×10^24 kg, for a core density of 7000 kg/cubic meters, what is the average mantle density? Give the answer to two significant figures.
Now lets use ChatGPT to generate some models and then we can select the best one. We will select a mantle density from three values, 2000, 3000 and 4000 kg/m3. The core density Dc will be fixed at Dc = 9000 kg/m3. We will use the measured radius for Mars of Rp = 3.4×106 meters, and its total mass of Mm = 6.4×1023 kg. We then vary the core radius Rc. We will plot three curves on a graph of Rc versus Mm one for each value of the assumed mantle density. Use this ChatGPT query to generate your data points.
ChatGPT Query: A planet is modeled as a sphere with a radius of Rp=3.4×10^6 meters. It consists of a spherical core region with a radius of Rc surrounded by a spherical shell with an inner radius of Rc and an outer radius of Rp. The core of the planet has a density of 9000 kg/cubic meters. The radius of the core Rc = 30% of the planet’s radius. If the density of the mantle is 2000 kg/cubic meter, what is the total mass of the planet in multiples of the mass of Earth, which is 5.97×10^24 kg? Give your answer to two significant figures?
Repeat this query by changing the mantle density and the core radius values and then plot enough points along each density curve to see the trend clearly. An example of an Excel spreadsheet version of this data is shown in this graph:
This graph shows solutions for a two-component mars model where the mantle has three different densities (2000, 3000 and 4000 kg/m3). The average density of mars is 3900 kg/m3. Which core radius and mantle density combinations seem to be a better match for Mar’s total mass of 0.11 Mearth for the given density of the mantle?
VI: Modeling Terrestrial Planets with a three-component interior.
The most general exoplanet model has three zones; a dense core, a mantle and a low-density crust. This is the expected case for Earth-like worlds. Using our Earth as an example, rocky exoplanets have interiors stratified into three layers: Core, mantle, crust.
Core material is typically iron-nickel with a density of 9000 kg/m3
Mantle material is basaltic rock at a density of 4500 kg/m3
Crust is low-density silicate rich material with a density of 3300 kg/m3
The basic idea in modeling a planet interior is that with the three assumed densities, you vary the volume that they occupy inside the exoplanet until you match the actual mass (Mexo) in kilograms and radius (Rexo) in meters of the exoplanet that is observed. The three zones occupy the radii Rc, Rm, Rp
We will adjust the core and mantle radii until we get a good match to the exoplanet observed total mass and radius. Let’s assume that the measured values for the Super-Earth exoplanet mass is Mp = 2.5xEarth = 1.5×1025 kg, and its radius is Rp = 1.5xEarth = 9.6×106 meters.
Core Volume Vcore = 4/3p Rc3
Mantle Volume Vm = 4/3 p (Rm3 – Rc3)
Crust Volume Vcrust = 4/3 p (Rp3 – Rm3)
So the total Mass = (9000 Vcore + 4500Vm + 3300Vcrust)/Mp
Rc ,Rm and Rp are the core, mantle and planet radii in meters, and the total mass of the model is given in multiples of the exoplanet’s mass Mp.
Let’s do a test case that we work by hand to make sure we understand what we are doing.
Choose Rc = 30% of Rp and Rm = 80% of Rp. What is the predicted total mass of the exoplanet?
Rc = 0.3 x 9.6×106 meters = 2.9×106 meters.
Rm = 0.8x 9.6×106 meters = 7.7×106 meters.
Then
Vcore = 4/3p (2.9×106)3 = 1.0×1020 m3
Vm = 4/3p ( (7.7×106)3 – (2.9×106)3) = 1.8×1021 m3
Then Mass = (9000 Vcore + 4500 Vm + 3300Vcrust)/Mp
Mass = (9×1023 kg + 8.1×1024 kg + 5.9×1024 kg)/1.5×1025 kg = 1.0 Mp
Now lets use ChatGPT to generate some models from which we can make a choice.
Enter the following query into ChatGPT to check your answer to the above test problem.
ChatGPT Query: A spherical planet with a radius of Rp consists of three interior zones; a core with a radius of Rcore, a mantle with an inner radius of Rc and an outer radius of Rm, and a crust with an inner radius of Rm and an outer radius of Rp=9.6×10^6 meters. If the density of the core is 9000 kg/m^3, the mantle is 4500 kg/m^3 and the crust is 3300 kg/m^3, What is the total mass of the planet if Rc = 30% of Rp and Rm = 80% of Rp? Give your answer for the planet’s total mass in multiples of the planet’s known mass of 1.5×10^25 kg, and to two significant figures.
Re-run this ChatGPT query but change the values for the mantle radius Rm and core radius Rc each time. Plot your models on a graph of Rc versus the calculated mass Mp on curves for which Rm is constant. An example of this plot is shown in the excel spreadsheet plot below.
For example, along the black curve we are using Rm=0.8. At Rc = 0.5 we have a model where the core extends to 50% of the radius of the exoplanet .The mantle extends to 80% of the radius, and so the crust occupies the last 20% of the radius to the surface. With densities of 9000, 4500 and 3300 kg/m3 respectively, the Y-axis predicts a total mass of about 1.1 times the observed mass of the exoplanet (1.00 in these units). With a bit of fine-tuning we can get to the desired 1.00 of the mass. But what about the solution at (0.3, 1.00) ? In fact, all of the solutions along the horizontal line along y = 1.00 are mathematically valid.
Question 1: The exoplanet is located close to its star where iron and nickel can remain in solid phase but the lower density silicates remain in a gaseous phase. Which of the models favors this location at formation?
Answer: The exoplanet should have a large iron/nickel core and not much of a mantle or crust. This favors solutions on the y=1.00 line to the right of x=0.5.
Question 2: The exoplanet is located far from its star where it is cool enough that silicates can condense out of their gas phase as the exoplanet forms. Which of the models favor this location?
Answer: The exoplanet will have a small iron/nickel core and a large mantle and crust. This favors models to the left of x= 0.5.
So here you have some examples for how ChatGPT can be used as an intelligent calculator once the students understands how to use the equations and is able to explain why they are being used for a given modeling scenario.
I would be delighted to get your responses and suggestions to this approach . Just include your comment in the Linkedin page where I have posted this idea.
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.
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.
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.
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.
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.
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.
“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.
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.
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!
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
[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/
When I was learning astronomy in the 60s and 70s, we were still debating whether Big Bang or Stady State were the most accurate models for our universe. We also wondered about how galaxies like our Milky Way formed, and whether black holes existed. The idea that planets beyond our solar system existed was pure science fiction and no astronomers spent any time trying to predict what they might look like. As someone who has reached the ripe old age of 70, I am amazed how much progress we have made, from the discovery of supermassive black holes and exoplanets, to dark matter and gravitational radiation. The pace of discovery continues to increase, and our theoretical ideas are now getting confirmed or thrown out at record pace. There are still some issues that remain deliciously mysterious. Here are my favorite Seven Mysteries of the Universe!
1-How to Build a Galaxy: In astronomy, we used to think that it would take the universe a long time to build galaxies like our Milky Way, Thanks to the new discoveries by the Webb Space Telescope, we now have a ring-side seat to how this happens, and boy is it a fast process!
The oldest galaxies discovered with the Hubble Space Telescope date back to between 400 and 500 million years after the Big Bang. A few weeks ago, Webb spotted a galaxy that seems to have formed only 300 million years after the Big Bang. Rather than the massive galaxies like the Milky Way, these young galaxies resemble the dwarf galaxies like the Large Magellanic Cloud, perhaps only 1/10 the mass of our galaxy and filled with enormus numbers of massive, luminous stars. The above image from Hubble is a nearby galaxy called M-33 that has a mass of about 50 billion suns. There were lots of these smaller galaxies being formed during the first 300 million years after the Big Bang.
It looks like the universe emerged from the Dark Ages and immediately started building galaxies. In time, these fragments collided and merged to become the more massive galaxies we see around us, so we are only just starting to see how galaxy-building happens. Our Milky Way was formed some 1 billion years after the Big Bang, so the galaxy fragments being spotted by Webb have another 700 million years to go to make bigger things. Back in 2012, Hubble had already discovered the earliest spiral galaxy seen by then; a galaxy called Q2343-BX442, camping out at 3 billion years after the Big Bang. In 2021, an even younger spiral galaxy was spotted, called BRI 1335-0417, seen as it was about 1.4 billon years after the Big Bang.
So we are now watching how galaxies are being formed almost right before our eyes! Previous ideas that I learned about as an undergraduate, in which galaxies are formed ‘top-down’ from large collections of matter that fragment into stars, now seem wrong or incomplete. The better idea is that smaller collections of matter form stars and then merge together to build larger systems – called the ‘bottom-up’ model. This process is very, very fast! Among the smallest of these ‘galaxies’ are things destined to become the globular clusters we see today.
2-Supermassive Black Holes: The most distant and youngest supermassive black hole was discovered in 2021. Called J0313-1806, its light left it to reach us when the universe was only 670 million years old. Its mass, however, is a gargantuan 1.6 BILLION times the mass of our sun. Even if the formation of this black hole started at the end of the Dark Ages ca 100 million years after the Big Bang, it would have to absorb matter at the rate of three suns every year on average. That explains its quasar energy, but still…it is unimaginable how these things can grow so fast! The only working idea is that they started from seed masses about 10,000 the mass of our sun and grew from there. But how were the seed masses formed? This remains a mystery today.
3-The Theory of everything: The next Big Thing that I have been following since the 1960s is the search for what some call the Theory of Everything. Exciting theoretical advancements were made in the 1940s and 1960s to create accurate mathematical models for the three nongravity forces, called the electromagnetic, weak and strong forces. Physicists call this the Standard Model, and every physicist learns its details as students in graduate school. By the early 1980s, string theory was able to add gravity to the mix and go beyond the Standard Model. It appeared that the pursuit of a unified theory had reached its apex. Fifty years later, this expectation has all but collapsed.
Experiments at the Large Hadron Collider continue to show how the universe does not like something called supersymmetry in our low-energy universe. Supersymmetry is a key ingredient to string theory because it lets you change one kind of particle (field) into another, which is a key ingredient to any unified theory. So the simplest versions of string theory rise or fall based on whether supersymmetry exists or not. For over a decade, physicists have tried to find places in the so-called Standard Model where supersymmetry should make its appearance, but it has been a complete no-show. Its not just that this failure is a problem for creating a more elegant theory of how forces works, but it also affects astronomy as well.
Personally, when string theory hit the stage in the 1980’s I, like many other astronomers and physicists, thought that we were on the verge of solving this challenge of unifying gravity with the other forces, but this has not been the reality. Even today, I see no promissing solutions to this vexing problem since apparently the data shows that simple string theory is apparently on a wrong theoretical track.
One cheerful note: For neutrinos, the path from theoretical prediction to experimental observation took 25 years. For the Higgs boson, it took 50 years. And for gravitational waves, it took a full 100 years. We may just have to be patient…for another 100 years!
4-Dark Matter: The biggest missing ingredient to the cosmos today is called dark matter. When astronomers ‘weigh’ the universe, they discover that 4.6% of its gravitating ‘stuff’ is in ordinary matter (atoms,. stars, gas, neutron stars etc), but a whopping 24% is in some other ‘stuff’ that only appears by its gravity. It is otherwise completely invisible. Putting this another way, it’s as though four out of every five stars that make up our Milky Way were completely invisible.
Dark matter in Abell 1679.
Because we deeply believe that dark matter must be tracable to a new kind of particle, and because the Standard Model gives us an accounting of all the kinds of elementary particles from which our universe is built, the dark matter particle has to be a part of the Standard Model…but it isn’t!!!! Only by extending the Standard Model to a bigger theory (like string theory) can we logically and mathematically add new kinds of particles to a New Standard Model- one of which would be the dark matter particle. String theory even gives us a perfect candidate called the neutralino! But the LHC experiments have told us for over a decade that there is nothing wrong with the Standard Model and no missing particles. Astronomers say that dark matter is real, but physicists can’t find it….anywhere. Well…maybe not ALL astronomers think it’s real. So the debate continues.
Personally, I had heard about ‘missing mass’ in the 1960s but we were all convinced we would find it in hot gas, dim red dwarf stars or even black holes. I NEVER thought that it would turn out to be something other than ordinary matter in an unusual form. Dark matter is so deeply confounding to me that I worry we will not discover its nature before I, myself, leave this world! Then again, there isnt a single generation of scientists that has had all its known puzzles neatly solved ‘just in time’. I’m just greedy!!!
5- Matter and Antimatter: During the Big Bang, there were equal amounts of matter and anti matter, but then for some reason all the antimatter dissappeared leaving us with only matter to form atoms, stars and galaxies. We don’t know why this happened, and the Standard Model is completely unhelpful in giving us any clues to explain this. But next to dark matter, this is one of the most outstanding mysteries of modern, 21st century cosmology. We have no clue how to account for this fact within the Standard Model, so again like Dark Matter, we see that at cosmological scales, the Standard Model is incomplete.
6- Origin of Time and Space: Understanding the nature of time and space, and trying to make peace with why they exist at all, is the bane of any physicists existence. I have written many blogs on this subject, and have tried to tackle it from many different angles, but in the end they are like jigsaw puzzels with too many missing pieces. Still, it is very exciting to explore where modern physics has taken us, and the many questions such thinking has opened up in surprising corners. My previous blog about ‘What is ‘Now’ is one such line of thinking. Many of the new ideas were not even imagined as little as 30 years ago, so that is a positive thing. We are still learning more about these two subjects and getting better at asking the right questions!
7-Consciousness: OK…You know I would get to this eventually, and here it is! Neuroscientists know of lots of medical conditions that can rob us of consciousness including medical anesthesia, but why we have this sense about ourselves that we are a ‘person’ and have volition is a massively hard problem. In fact, consciousness is called the ‘Hard Problem’ in neuroscience..heck…in any science!
The ‘Soft Problem’ is how our senses give us a coherant internal model of the world that we can use to navigate the outside world. We know how to solve the Soft Problem, just follow the neurons. We are well on our way to understanding it thanks to high-tech brain imaging scanners and cleverly-designed experiments. The Hard Problem is ‘hard’ because our point-of-view is within the thing we are trying to undertand. Some think that our own ‘wet ware’ is not up to the task of even giving us the intelligence to answer this qustion. It will not be the first time someone has told us about limitations, but usually these are technological ones, and not ones related to limits to what our own brains can provide as a tool.
So there you have it.
My impression is that only Mysteries #1 and #2 will make huge progress. The Theory of Everything is in experimental disarray. For antimatter, there has been no progress, but many ideas. They all involve going outside the Standard Model. Dark matter might be replaced by a modification of gravity at galactic and cosmological scales.
Beyond these ‘superficial’ mysteries, we are left with three deep mysteries. The origin of space, time and consciousness remain our 21st century gift to children of the 22nd century!
Well,
astronomers finally did it. Nearly 100 years ago, Albert Einstein’s theory of
General Relativity predicted that black holes should exist. Although it took
until the 1960’s for someone like physicist John Wheeler to coin the name ‘black
hole’ the study of these enigmatic objects became a cottage industry in
theoretical physics and astrophysics. In fact, for certain kinds of astronomical
phenomena such as quasars and x-ray sources, there was simply no other
explanation for how such phenomena could generate so much energy in such an
impossibly small volume of space. The existence of black holes was elevated to
a certainty during the 1990s as studies of distant galaxies by the Hubble Space
Telescope turned in tons of data that clinched the idea that the cores of most
if not all galaxies had them. In fact, these black holes contained millions or
even billions of times the mass of our sun and were awarded a moniker all their
own: supermassive black holes. But there was still one outstanding problem for
these versatile engines of gravitational destruction: Not a single one had ever
been seen. To understand why, we have to delve rather deeply into what these
beasties really are. Hang on to your seats!
General relativity is the
preeminent theory of gravity, but it is completely couched in the language of
geometry – in this case the geometry of what is called our 4-dimensional
spacetime continuum. You see, in general relativity, what we call space is just
a particular feature of the gravitational field of the cosmos within which we
are embedded rather seamlessly. This is all well and good, and this perspective
has led to the amazing development of the cosmological model called Big Bang
theory. Despite this amazing success, it is a theory not without its problems.
The problems stem from what happens when you collect enough mass together in a
small volume of space so that the geometry of spacetime (e.g. the strength of
gravity) becomes enormously curved.
The very first thing that happens
according to the theory is that a condition in spacetime called a Singularity
forms. Here, general relativity itself falls apart because density and gravity
tend towards infinite conditions. Amazingly according to general relativity,
and proved by the late Stephen Hawkins, spacetime immediately develops a zone
surrounding the Singularity called an event horizon. For black holes more
massive than our sun, the distance in kilometers of this spherical horizon from
the Singularity is just 2.9 times the mass of the black hole in multiples of
the sun’s mass. For example, if the mass of a supermassive black hole is 6.5
billion times the mass of our sun, its event horizon is at 6.5 billionx2.9 or
19 billion kilometers. Our solar system has a radius of only 8 billion km to
Pluto, so this supermassive black hole is over twice the size of our solar
system!
Now the problem with event
horizons is that they are one-way. Objects and even light can travel through
them from outside the black hole, but once inside they can never return to the
outside universe to give a description of what happened. However, it is a
misunderstanding to say that black holes ‘suck’ as the modern colloquialism goes.
They are simply points of intense gravitational force, and if our sun were
replaced by one very gently, our Earth would not even register the event and
continue its merry way in its orbit. The astrophysicist’s frustration is that
it has never been possible to take a look at what is going on around the event
horizon…until April 10, 2019.
Researchers using the radio telescope interferometer system called the Event Horizon Telescope were able to synthesize an image of the surroundings of the supermassive black hole in the quasar-like galaxy Messier-87 – also known as Virgo A by early radio astronomers after World War II, and located about 55 million light years from Earth. They combined the data from eight radio telescopes scattered from Antarctica to the UK to create one telescope with the effective diameter of the entire Earth. With this, they were able to detect and resolve details at the center of M-87 near the location of a presumed supermassive black hole. This black hole is surrounded by a swirling disk of magnetized matter, which ejects a powerful beam of plasma into intergalactic space. It has been intensively studied for decades and the details of this process always point to a supermassive black hole as the cause.
Beginning in 2016, several petabytes of data were gathered from the Event Horizon Telescope and a massive press conference was convened to announce the first images of the vicinity of the event horizon. Surrounding the black shadow zone containing the event horizon was a clockwise-rotating ring of billion-degree plasma traveling at nearly the speed of light. When the details of this image were compared with supercomputer simulations, the mass of the supermassive black hole could be accurately determined as well as the dynamics of the ring plasma. The round shape of the event horizon was not perfect, which means that it is a rotating Kerr-type black hole. The darkness of the zone indicated that the event horizon did not have a photosphere of hot matter like the surface of our sun, so many competing ideas about this mass could be eliminated. Only the blackness of a black hole and its compact size now remain as the most consistent explanation for what we are ‘seeing’. Over time, astronomers will watch as this ring plasma moves from week to week. The next target for the Event Horizon Telescope is the four million solar mass black hole at the center of the Milky Way called Sgr-A*. Watch this space for more details to come!!
We have truly
entered a new world in exploring our universe. Now if someone could only do
something about dark matter!!!
An astronomer's point-of-view on matters of space, space travel, general science and consciousness
