How is it possible that during a solar eclipse the moon fits exactly in the sun?

Answer

This is indeed a coincidence.

In addition, the Earth-Moon distance is on average 384 000 km, but is between 363 000 and 406 000 km. If we have a solar eclipse at a time when the Moon happens to be approximately at its furthest distance, the lunar disk is slightly smaller than the solar disk and we have an annular eclipse.

However, enjoy it now because the (average) distance of the Moon is increasing very slowly, a result of the decrease in the Earth’s rotation. And that in turn is a result of a tidal interaction between the Earth and the Moon. The first to work this out mathematically was Darwin’s son.

In the distant future, all eclipses will thus become annular. But now we are talking about a distant future. The Earth-Moon distance is now increasing by 3.8cm per year. Note that this is the current value and it is not constant over time. So you cannot calculate backwards with that number, nor can you calculate in the future.

Photo © nachans cc2.0 on Flickr.