Why is it that the lunar disk precisely covers the solar disk during a solar eclipse? Is it just an extraordinary coincidence?
Yes, it IS just a coincidence that both the Sun and Moon have the same angular size in the sky, allowing the Moon to precisely cover the solar disk. Although the Sun's diameter is about 375 times larger than the Moon's, the Sun is also about 375 times farther away. Both, therefore, appear to have an angular diameter of about 1/2 degree as seen from Earth.
Because tidal forces are gradually slowing the Earth's rotation and increasing the Moon's distance from Earth, thousands of years from now the Moon will appear smaller in the sky and NOT be able to cover the Sun's disk. That will leave future generations with only ANNULAR eclipses, showing a bright ring of light around the Moon during totality.
Paul Walorski, B.A., Part-time Physics/Astronomy Instructor
'The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.'