Supermoon

Comparison of Full Moon at Perigee vs. Apogee (Courtesy NASA)

Sorry for another non-Disney post. I promise, I'm working on a park related post but this whole "supermoon" thing is bugging me. For those that didn't hear, last night's full Moon occurred at the same time as the Moon's closest approach (perigee) to Earth. On average, the Moon is 238,855 miles away. Last night, it was only 221,800 miles away. Now 17,000 miles closer may sound like quite a lot, but when you are talking about something that is a quarter of a MILLION miles away, 17,000 is really small.


I decided to do some math and see just how big a difference there was between the April and May full Moons.


Distance to April full Moon: 222,645 miles
Distance to May full Moon:  221,800 miles


That is only an 800 mile difference! That is less than the diameter of the moon (2,158 miles)! So why was no one talking about how huge the April full Moon looked? Because the media called attention to the fact that the May 5th/6th full Moon occurred at its perigee (April's did not even though it was a similar distance at time of full) and mentioned that this would cause it to look a little bigger. People went outside with what is called an Expectation Bias. Essentially you see what you expect. People expected the moon to look bigger and so the saw it as bigger.


If you do a bit more math and determine the angular diameter (like on a protractor) of the full Moons from April and May, you end up with a difference of 0.002 degrees. From Eastern to Western horizons, the sky is 180 degrees wide. If you cut it in 180 equal parts and then cut 1 of those in 2000 equal parts, last night's full Moon was a mere 2 of those (two thousands of 1 degree) larger. If you had pictures of both and put them side by side, you could see the difference, but lost in the vastness of the sky, with no reference frame to compare it too, you can't actually see that small of a difference.


Now some people went out and saw the Moon as it rose and are right to claim that it looked significantly larger. This had nothing to do with the Moon being at perigee though. The atmosphere is only 65 miles thick directly over your head but when you look at the horizon you are looking through several hundred miles of air. Light bends when it travels through air of differing temperatures. This is what causes mirages. When the Moon is near the horizon, it must travel a long way through many layers at different temperatures and this distorts the moon, kind of like a lens, making it look much bigger. This can be seen quite often around Halloween as part of the "Harvest Moon." When the moon rises overhead and is travelling through much less air, it returns to it's normal apparent size.


Now in November we will have the opposite, a full Moon and apogee (furthest point from Earth). The difference between that full Moon and last night's will be about 14%. That amount is definitely noticeable, but again, because both won't be side by side, you won't notice it in the sky.


For those who would like to do the math themselves, the formula for angular diameter is:
ς = 2 tan^-1 (¹/₂ ^d/_D)
ς is the angular diameter in degrees (sigma)
d is the diameter of the object
D is the distance between you and the object