Geometry of a Total Solar Eclipse

August 30, 2017 clifftop CliffNotes

Geometry of a Solar Eclipse courtesy Fred Espenak

By Dr. Michael Krawczynski, solar and planetary scientist at Washington University, St. Louis, for Clifftop

A total solar eclipse could be considered just a coincidence of geometry.  Put most simply it is when the Moon slips directly between the Sun and the Earth.  But in reality, personally experiencing the beauty and science behind this alignment is so much more.  During a total solar eclipse, the Moon casts its shadow on the planet Earth, and the center of that shadow is called the umbra.  If you are standing in that umbra, the bright photosphere of the Sun is completely blocked from view, and the viewer experiences some dramatic effects that can lead to inspiration, awe and understanding.  This coincidence of geometry is steeped in history and scientific discovery.  In ancient times, civilizations such as the Babylonians, Chinese, and Mayans were able to understand and even predict when eclipses happened.  Careful records by these cultures were used to expose patterns in this seemingly otherworldly happenstance, and indeed the tracking and predicting of eclipses was possible in ancient times and helped to understand Earth’s place in our solar system.

Comprehending the details of this coincidence in geometry leads to an appreciation of why total solar eclipses are such rare and special events on our planet. The Earth-Moon system in many ways is unique in our solar system. Indeed Mercury and Venus do not even have moons. It just so happens that our moon is about 400 times closer to Earth than the sun, and the size of the Moon is also about 400 times smaller than the Sun. That means that the Moon is about the same apparent size in the sky as the Sun.  This is an incredible coincidence and means that in order to experience a total eclipse the Sun and Moon must come into precise alignment.  Eclipses come in 3 different flavors: partial, annular, and total.  The existence of the three types of solar eclipses is the result of the Moon’s orbit being both elliptical and tilted relative to the Earth’s orbit around the Sun. Total eclipses occur when the Moon totally covers up the sun, and this can only happen when the apparent size of the Moon is equal to or greater than the sun.  This contributes even further to the rarity of a total eclipse because the Moon is only close enough to Earth to completely cover the sun for less than 35% of its orbit.    In many ways it is a matter of luck that total solar eclipses happen at all.  From the perspective of geologic time and the age of Earth, total eclipses are also becoming even rarer; the Moon is slowly receding from the earth, and in about 500 million years, the Moon will move so far away that its apparent size will be too small to ever cause another total solar eclipse.

The fleeting nature of a total solar eclipse also indicates how fast the Moon is moving in the sky.  On most nights the regal Moon seems to hang majestically amongst the stars, belying it’s blistering speed moving around the Earth. Indeed the Moon is actually traveling around the Earth at a staggering 2,288 miles an hour! This translates to a shadow speed on Earth of about 1500 miles per hour in Southern Illinois/Eastern Missouri, which is why eclipses only last seconds to minutes.

During the final seconds before the Moon covers up the sun, the last rays from the Sun’s photosphere will look like a diamond ring or a sting of beads hung in the sky.  This ‘diamond ring effect’ and ‘Baily’s beads’ are caused by the fact that there is topography (mountains and valleys) on the Moon.  Thus the edge of the Moon is not smooth but rough.  This causes the last rays of the Sun to peak through lunar valleys.  You can think of this like watching a sunset behind a mountain if you were standing on the Moon.

In addition, during a total solar eclipse, the dynamic nature of the Sun is on full display like no other moment.  Our sun is a roiling ball of gas and plasma that is fed by energy from nuclear reactions in its core.  On most days the photosphere of the sun is so bright that we cannot directly look at our celestial beacon without damaging our eyes.  The brightness of the photosphere drowns out the dimmer and in many ways more interesting outer layers of our sun.  During ‘totality,’ which is when the Moon completely blocks out the photosphere of our sun, it is safe to look at the sun directly.  What you will see are the tenuous, dim, and dynamic outer layers of the Sun.  The two layers that become visible during totality are the chromosphere and the corona.  The chromosphere is the layer of mostly hydrogen gas just above the bright photosphere.  This is the layer of the sun where prominences originate.  These prominences will be visible around the edge of the Moon during totality. They look like pinkish flames coming off the sun, but are in fact enormous eruptions of gas from the surface of the sun that can drive space weather and solar storms that cause the Northern Lights at night.  Often these prominences are several times the size of our planet.  If there are large and bright prominences occurring during totality, you may be able to see these with your naked eye, but they are best viewed with binoculars or a telescope.  The chromosphere is impressive, but the star of the show during totality is undoubtedly the ethereal corona of the sun.  This is the outer layer of the sun’s atmosphere; made of plasma it reaches temperatures of over a few million degrees.  Unlike the pink chromosphere, which can be viewed during non-eclipse times with special telescopes and satellites, the innermost corona is white and only visible during totality.  Not even orbiting satellites can see the inner part of this beautiful layer of the Sun.  The inner corona will be visible as a glowing halo around the eclipsing moon, and extends several solar diameters beyond the edge of the occulting moon.  This layer of the Sun’s atmosphere is easily seen with your naked eyes.  Look for rays of the corona extending in an East-West direction during totality.

During total eclipses the daytime sky will significantly darken, and the bright planets Venus and Jupiter will be visible to the naked eye during the day.  Maybe even more remarkable than the bright planets is the star Regulus that will be visible within 1 degree of the Sun during totality. Look for Regulus with binoculars during totality.  Regulus is the only magnitude 1 brightness star that lies in the direct path our Sun takes in its yearly march through zodiac constellations in the sky.  Thus only total eclipses that occur on the days of Aug 20-22nd will have a bright star so close to the Sun. The last such eclipse took place in Russia in 1914. Regulus is the brightest star in the constellation Leo, and thus this will be a rare opportunity to visually verify that the sun is indeed in the zodiac position of Leo! Although not visible with the naked eye, observations of the tiny shifts of stars near the Sun during totality were used to verify Einstein’s theory of general relativity.  The star positions move ever so slightly because the gravity of the Sun bends the light, changing the apparent positions of the Sun.  In the early 20th century, the precision needed for this type of scientific measurement required measurements to be made during total solar eclipses, and astronomers set off on expeditions around the world to capture these rare events.

On August 21st, 2017 we are lucky to be in the right spot to experience a total solar eclipse of our sun without needing to travel to far-flung corners of the Earth.  This event will likely be the most watched and photographed event in human history.  Enjoy all the scientific wonders that will only be visible during the short couple minutes of totality.  Be sure to observe other effects in your environment like the drop in temperature, strange behavior of animals, change in appearance of shadows and much more.  This is the first total solar eclipse visible from the continental US since 1979, and there has not been a total solar eclipse visible from St. Louis since the year 1442! But just in case there are extensive clouds during the moment of totality, thankfully we will not have to wait as long for another chance to experience this celestial event, as there is another total solar eclipse visible in Southern Illinois on April 8th, 2024.

Clifftop is hosting a Total Solar Eclipse Field Trip at their Paul Wightman Subterranean Nature Preserve, however, the free event is “sold out.”  No further reservations are being accepted.

CLIFFTOP, a local nonprofit organization, is focused on preserving and protecting area bluff lands.

A version of this article appeared in the August 18, 2017 issue of the Monroe County Independent.

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