How big a coincidence is the Sun and Moon having almost equal apparent sizes?

Question

It's consensus that the very similar apparent sizes of the Moon and the Sun as seen from Earth is a coincidence (as already answered in this site).

This provides us with almost exact total solar eclipses and other interesting sights, such as this one shared in Fermat's Library's tweet:

Here's a great photo of the ISS by J. Mccarthy.

The reason why the ISS keeps its relative size against both the Sun and the Moon is due to a remarkable coincidence: the diameter of the Moon is 400x smaller than the diameter of the Sun, but it is also 400x closer to us!

This state of affairs is not permanent, of course - as the moon keeps retreating from us - but total solar eclipses are estimated to keep occurring for the next 600 million to 1 billion years from now.

We're currently unable to answer how big this coincidence is, since we don't have enough statistical data on planet-moon systems yet, however we do have models of solar system formation.

So my question is, irrespective of the presence of intelligent beings or the possibility of actually observe total eclipses:

• According to our knowledge of planet formation, how unlikely is this coincidence?

Answer 1

Moons in the solar system range in size from about 0 to a little larger than our moon. The distance must be close enough that other planets won't pull it loose and I suppose far enough that it won't hit Earth when at closest. You could figure out a number from this.

But our moon is unusual in that it is much larger fraction of the planet than other moons. Mars has tiny moons that don't make total eclipses. Something the size of Mars hit proto-Earth and launched a huge amount of debris into space. Some of it must have escaped and some returned to Earth. What are the odds that something so big would be left in orbit?

As I understand it, many systems form with a lot of small objects everywhere, and large gas giants in the outer reaches. The giants throw small objects everywhere. If an object is ejected, it isn't thrown again. Over time, objects get ejected until none are left. On average small objects migrate out and gas giants migrate in. Many systems have a hot Jupiter close the the Sun, an Oort cloud, and nothing else. This process started in our system, and is responsible for the late heavy bombardment. But it stopped short of completion. What are the odds of our system running out of small objects before Jupiter got to the inner planets?

From looking at our system, distant gas giants may well have moons big enough to cover a tiny apparent Sun. Do they count? Suppose Venus had a big moon. Would it count? Their atmospheres are so thick that you couldn't see the eclipse from the surface. If they have a surface. For that matter, most of the surface of the Earth is covered with enough water that you couldn't see an eclipse. Supposing they do count, how likely is it that there will be distant gas giants with large moons?

We need more data before we can answer these questions.