Coincidental Solar Eclipse?
There will be an annular solar eclipse taking place this evening (5/20/2012) viewable from the western parts of the US and eastern Asia.
This is what happens when the Moon blocks some of the light from the Sun by passing in front of it from our vantage point on Earth. It is an annular eclipse and not a total eclipse because the Moon won’t completely cover up the Sun in the sky as it does during a total solar eclipse. Solar eclipses happen in these two varieties because the distance from the Earth to the Moon varies during its orbit around Earth. Therefore, the apparent size of the Moon looks different depending on how close the Moon is to Earth, and will only cover up as much of the Sun as it can. In fact, the Moon happens to be near its furthest point now.
It is interesting to note how close the Moon comes to completely covering up the Sun, and how this depends on the geometry of the situation.
During a total solar eclipse, the Moon will cover up the Sun almost exactly without much overlap. This happens because the apparent size of the Moon as viewed from Earth is nearly the same as the apparent size of the Sun as viewed from Earth.
This can be measured by comparing the ratio of the Sun’s radius and its distance to Earth to the ratio of the Moon’s radius and its distance to Earth. According to my own calculations they only differ by factor of about 3% of the Moon ratio. This is justified since the the Moon happens to be about 400 times smaller than the Sun, but is also about 400 times closer. Bigger differences in these ratios would imply that the Moon looks smaller or larger than the Sun during an eclipse. This closeness is equivalent to the claim that the two right triangles drawn in this diagram are close to being similar.
Is there any physical reason for why these ratios are the way they are? It seems plausible that the Moon could have had a different size, and orbited a little closer or further away from Earth thereby preventing such a ‘perfect’ total eclipse from happening. The configurations we witness almost seem like some coincidence!
So what? Is there any value to this special orientation during an eclipse?
Actually, the perfect total eclipses we are lucky enough to experience are valuable opportunities for astronomical observation.
In 1919, Arthur Eddington observed a total solar eclipse and was able to experimentally verify the phenomenon of gravitational lensing—one of the theoretical predictions of general relativity, which involved the bending of distant star light due to the Sun’s gravity. In addition, these perfect total eclipses also allow for other observations of solar phenomenon.
If it were not for this ecliptic coincidence and things were any different, then how much more difficult would it have been for scientists to learn about these other astrophysical phenomenon?
At times like to think about simple problems in kinetics and kinematics. Like the velocity of a person who has been dropped from a height of 10m [very roughly 3 stories like the top of the “hard” science building at my college]. To review the physics of the problem, I do it as an order of magnitude problem*: average person of mass=80kg, g=10 m/s^2, height=10m. so we know their potential energy is about 8000 J or 8kJ from U=mgh. We know energy is conserved so we know the final energy (before the moment of impact) is 8 kJ=K=1/2 m v^2. So v^2=2(8000 J)/(80 kg)=200, v=(200)^(1/2)=10(1.41)=14.1 m/s or about 30 mph. ouch.
*those first values, the known values of the problem, are all approximate. (I am not in the mood to learn to properly format this. When I venture into quantum mechanics, I will learn how to format [most importantly, how to write h bar].When I learn to format, I’ll write something about a mass-spring system or TISE.