Question

Is there a possible explanation for the apparent equal size of sun and moon or is this a coincidence?

(An explanation can involve something like tide-lock effects or the anthropic principle.)

Answer 1

It just happens to be a coincidence.

The current popular theory for how the Moon formed was a glancing impact on the Earth, late in the planet buiding process, by a Mars sized object. This caused the break up of the impactor and debris from both the impactor and the proto-Earth was flung into orbit to later coallesce into the Moon. So the Moon's size just happens to be random.

Plus the Moon was formed closer to the Earth and due to tidal interactions is slowly drifting away. Over time (astronomical time, millions and millions of years) it will appear smaller and smaller in the sky. It will still always be roughly the size of the Sun but total solar eclipses will become rarer and rarer (they will be more and more annular or partial). Likewise in the past, it was larger and total eclipses were both longer and more common.

Answer 2

The current popular theory for how the Moon formed was a glancing impact on the Earth, late in the planet buiding process, by a Mars sized object. This caused the break up of the impactor and debris from both the impactor and the proto-Earth was flung into orbit to later coallesce into the Moon. So the Moon's size just happens to be random.

Plus the Moon was formed closer to the Earth and due to tidal interactions is slowly drifting away. Over time (astronomical time, millions and millions of years) it will appear smaller and smaller in the sky. It will still always be roughly the size of the Sun but total solar eclipses will become rarer and rarer (they will be more and more annular or partial). Likewise in the past, it was larger and total eclipses were both longer and more common.

oth the moon and the earth's orbits are eccentric, and so the ratio between the sun's and moon's apparent diameter varies with the time of year. When the moon is at perigee, and the earth at aphelion, the moon will seem larger than the sun than when the moon is at apogee and earth at perihelion.

However, the eccentricities of these orbits are low, and the moon always seems "about the same" as the sun. This is a coincidence, both that its size is what it is, and that we're here to observe it. The moon is and will continue to recede from the earth. Eventually, the moon will appear smaller than the sun's disk and won't be able to completely eclipse it anymore.

It seems like this question has its roots in intelligent design (I've heard this argument made in favor of ID before). Were the moon designed to be the same size as the sun's disk, you would think that the earth and moon's orbits wouldn't be eccentric, and that the moon wouldn't gradually receded from the earth, in order to preserve that symmetry.