Is it a coincidence that both the sun and moon look of same size from earth?

The sun is huge when compared to moon. Despite the huge difference in their size and distance from earth, Is it purely coincidental that they both look almost the same from earth?

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The coincidence isn't so much that they appear very similar sizes from Earth, but that we are alive to see them at the point in time in which they appear very similar sizes. The moon is slowly moving away from the Earth, and at some point in the future the moon will be unable to totally eclipse the sun and conversely, if you could step far into prehistory, you would be able to see the moon with a much greater angular diameter than you see it now.

Most research I've found on the topic seem to be unavailable through my institute, however I did find one paper, "Outcomes of tidal evolution", which references results from Goldreich's research on the subject.

This qualitative description of the eventual disruption of the Earth-Moon system is confirmed by the results of Goldreich's numerical integration, which showed that the moon will recede to 75 Earth radii, when spin-orbit synchronism will be reached; then the Moon's orbit will decay steadily inward because of the influence of the Sun.

For reference, the Moon is currently at a distance of approximately 60.3 Earth radii. As such, the moon will steadily move away until synchronism would be reached, and from that point begin to recede towards the Earth due to the tidal affects of the Sun on the Earth disturbing the synchronization. It would seem that at some eventual point in the far distant future, it will return to this coincidental position once again.

Counselman III, Charles C. "Outcomes of tidal evolution." The Astrophysical Journal 180 (1973): 307-316.

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Adding references to support your statements is a really good way to make your answer more valuable –  Jeremy Apr 23 at 21:14
@Jeremy Added some research, thank you for the reminder. –  Mitch Goshorn Apr 23 at 23:18
What do they mean by "spin-orbit synchronism"? –  Py-ser Apr 24 at 2:43
This refers to tidal locking between two bodies. In this case, reaching a point where the Earth and Moon are tidally locked. This is important, as the mechanism for the Moon moving away from the Earth is due to the tidal forces of unsynchronized movement between the two. As they reach synchronization the distance would stabilize, if not for the additional tidal forces from the Sun destabilizing the system. –  Mitch Goshorn Apr 24 at 2:50
The Moon's rotation is already synchronized to its orbit. In the distant future, the Earth's rotation will also synchronize to the Moon's orbit, so the Moon will be visible only from one hemisphere and a day will be a month long (and a month will be even longer than it is now). Pluto and Charon are mutually locked in this way. –  Keith Thompson May 1 at 1:23

As a matter of fact, yes, it is only a coincidence.

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Of course the apparent relative sizes of the sun and moon are coincidental. What other rational explanation is there?

Maybe NASA built the moon that way on purpose. LOL

oops ...

"For reference, the Moon is currently at a distance of approximately 37.5 Earth radii."

I wonder where that odd figure came from. This "37.5" radii figure is very inaccurate. The current geocentric lunar distance averages about 60.3 earth radii, not 37.5 radii.

384401 km = Mean distance to moon
6367.448 km = Mean radius of earth

(384401 / 6367.448) = 60.3 earth radii

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JayT - Checked the math; I had mistakenly used miles rather than kilometers. Thank you for pointing it out - updating my answer accordingly. –  Mitch Goshorn Aug 10 at 12:59