Most people know about total and partial lunar eclipses, but I learned today about penumbral lunar eclipses, which is when the umbra, direct shadow of Earth misses the moon but it still is in the penumbra, the weaker outside part of the shadow. The source said 1/3 lunar eclipses are penumbral and looking at a chart of upcoming eclipses, that appears about right.
My question is, why is the ratio so low? The penumbra is a lot larger than the umbra, so I would expect there to be a greater chance of entering that area than the umbra, and therefore more frequent penumbral eclipses. But it isn’t so. Why not?
ETA: Technically all eclipses do pass through the penumbra, but only ones that don’t hit the umbra either totally or partially are called penumbral
At the distance of the moon, the Earth’s umbral shadow is about 3 moon diameters wide. It’s penumbral shadow is about 4.5 moon diameters wide, which is 0.75 diameters on either side… So to get a penumbral eclipse the center of the shadow must pass from half a diameter inside the penumbral shadow to half a diameter outside it. This is a total of 0.75 diameters, but that can happen on either side so 1.5 diameters. To get an umbral eclipse the center of the shadow must pass withing 0.5 diameters on either side for a total of 4 diameters.
Assuming random location (and I doubt that’s exactly right; I’d guess centering is more likely) 1.5/4 = 37.5% of lunar eclipses should be penumbral. This is about what you report.
Ahh ok thanks. I guess all the diagrams greatly exaggerate the size difference for illustrative purposes lol. Their penumbra looks like a giant cone widening forever.