Category Archives: Eclipse

Astronomy, Eclipse

The Last Total Solar Eclipse…Ever!

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

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

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

Predicting total solar eclipses

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

Earth orbit evolution

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

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

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

Lunar orbit evolution.

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

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

Simple Linear Model

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

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

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

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

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

A More Accurate Calculation.

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

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

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

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

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

Will there be anyone there to care? Probably not.

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

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

Have a nice day!

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

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

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

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

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

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

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

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

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

Astronomy, Eclipse, NASA

Eclipse Postscript

In a previous blog in June , I described the August 21, 2017 eclipse and what to expect from it, along with the many resources available at the NASA website that fill-in the details of this event as we were expecting it to unfold.  This website, by the way,  went crazy for the eclipse and got over 2 billion hits from tens of millions of daily visitors. For myself, I was not prepared for the surge of emotions I would feel even after glimpsing only 15 seconds of this event between gaps in the clouds over Carbondale, Illinois. Why Carbondale? I described in a 2014 Huffington Post article how this would be the place where the eclipse lasted the longest, 2 minutes and 40 seconds, and so this is where NASA Edge decided to park us for our major public outreach activities and NASA TV interviews.

I had been interviewed by a number of TV and radio reporters as well as a memorable Facebook interview with Curiosity. My article at NASA on the airline flights that would see the eclipse got quite a bit of traction. It was fun to see my articles on smartphone eclipse photography get so much press like this one at BuzzFeed, or this one at WIRED.  I even presented my smartphone tips to 1000 students at a local high school, which was carried by the local TV station WSIL-TV. Amazingly, despite my public ‘expertise’ on the matter, I did not bother using my smartphone at all in the brief time that the eclipse showed itself!

I mentioned in an interview with Carolyn Cerda also on WSIL-TV how I had brought along my cameras and hoped to grab just one image of this event. This was after many weeks of debating with myself whether I should even bother with photography at all. I knew how easy it was to get lost among the f/stops and exposure speeds in pursuit of a trophy to commemorate this event. I certainly didn’t want to waste precious time wrestling with the very finicky smartphone telephoto lens set up. But I also wanted to spend as much time as possible letting the emotions wash over me, just as they had done for millions of other people down through the thousands of years of human history. Could I, too, experience the fear that had so commonly been the popular experience? Or would my science protect me from these irrational feelings like some coat-of-armor? I had no idea, and in many of my TV interviews I said as much.

So I compromised.

I would run my digital, Sony camcorder during totality, and on the same tripod bracket, I would set my Nikon D3000 to a fixed f/stop and exposure speed selected to highlight the dazzling bright inner corona and any prominences or blood-red chromospheric light that may be present. I would hold the shutter release down so that the camera took bursts of a dozen photos, and periodically snap photos at mid-eclipse, and on each side of the 2.5-minute window to catch Baily’s Beads and anything else going on. It sounded like a good plan, and one in which I could still spend all of my eyeball time looking at totality and not at my camera!

This turned out to be a very good choice!

The clouds did roll in and cover the entire eclipse except for the last 15 seconds of totality. I snapped a few pictures like the one above using the clouds themselves to filter the intense sunlight, revealing a diminishing crescent sun. Had my NASA activities allowed us to be located a mile east rather than by Saluki Stadium at the Southern Illinois University, Carbondale campus, I would have been treated to a full 2.5 minutes of eclipse. But 15 seconds was just enough time to send chills down my spine and have the experience of a lifetime.

My photos turned out not to be too bad. The montage below was posted on my Facebook page within an hour or so, and although a bit fuzzy for the clouds, it was clear I had seen the entire circumferential inner corona, several red spots along the solar limb as the chromosphere peaked through, and the delightful Diamond Ring of sunlight streaking through a deep lunar canyon! My camcorder also showed the emergence of the sun from totality, capturing the dense clouds and the screams from the thousands of people looking on. This also went up on my Facebook page to the delight of dozens of my friends and family!

But how did I feel?

It was frustrating to see the crescent sun dip in to the dense clouds at the start of totality, and to watch the clock tick out the next few minutes, but as we reached mid-eclipse the scenery around me turned to twilight so quickly that I actually gasped in amazement! Hopefully, and with cameras at the ready I waited and then suddenly the brightening of a small portion of the cloud heralded that the eclipsed sun was about to make its appearance. When it did, everyone shouted and I watched with amazement, not really understanding what it was I was seeing. I immediately placed my finger on the shutter button, let the camera’s machinery take a series of 100 images, and hoped for the best. Again I was not dissappointed.

A dark object appeared surrounded by an intense ring of light. I thought this was just the reflection of sunlight on the cloud, but in an instant I realized this was no sun glint for there was no brilliant solar disk to illuminate it. Instead, it was the corona itself, brighter to the naked eye than I ever could have imagined! Within a few seconds the moon began to move off the western edge of the solar disk and slowly but steadily a single bright point of light appeared and grew in brightness until I could no longer stare at it with my eye through the digital display of my camcorder.

There was so much noise and ruckus from everyone else cheering that it was hard for me to collect and reflect on my thoughts – a process that took several days and repeated sharing of my experiences with family and friends. I had only experienced the ‘tip of an iceberg’ in the emotions that had hit me, and some were no doubt muted by the confusion of what I was seeing so briefly. I could only imagine what the full two minutes would have brought to mind.

I was not prepared for the days to follow. My sense of loss was something ineffable that I could not quite shake. I drifted from day to day, occasionally gawking at the many gorgeous online photos taken by more savvy photographers and old-hands at totalities. But you have to start somewhere, and at least for the first time in my life as an astronomer I can describe to my students,not only why we have eclipses and how our ancestors regarded them, but as with the Northern Lights, I can now add my own tiny voice to describing them in purely human terms!