A) for a solar eclipse to occur, the moon must be located between the earth and the sun. however, both the earth’s and the moon’s orbits are not circles but ellipses. the distance between the earth and the moon varies between 357,000 and 407,000 km. the distance between the earth and the sun varies between 147.1 × 106 and 152.1 × 106 km. calculate the range of solid angles under which the moon and the sun can appear, and decide which orbit is more important to make a solar eclipse total or not anywhere on earth. (use these radii: earth: 6371 km; moon: 1737 km; and sun: 696,000 km.)
b) even if the combination of distances should make a solar eclipse total, it is not always total. why could that be?
c) due to tidal friction, the mean earth-moon distance increases by 3.8 cm/year. how many more years will total solar eclipses be possible on earth? (source of numerical values: nasa planetary fact sheets)