Astro/EPS C12 (2008) – Mike Wong
Problem Set 4 Solution Guide
1 Eclipse
Problem 1A
Solar eclipses only happen when the Moon is in the Earth’s orbital plane, so
that the Sun, Moon, and Earth are lined up and the Moon’s shadow falls on
the Earth. But because there is a 5◦tilt between the Moon’s orbital plane and
the Earth’s orbital plane, the Moon is not usually in the Earth’s orbital plane.
It crosses the Earth’s orbital plane twice during its monthly orbit around the
Earth, but a solar eclipse occurs only when that crossing falls exactly during
the new moon.
Problem 1B
A total solar eclipse occurs when the Sun is completely covered by the Moon. If
the Moon were twice its current angular size, events which are now total solar
eclipses would remain total solar eclipses, and some near-miss events which are
now partial solar eclipses would become total solar eclipses. As for partial solar
eclipses, a few would be reclassified as total solar eclipses, but even more partial
solar eclipses would occur that would not have due to the moon’s larger angular
size (and hence the probability of its penumbra falling on the Earth).
The diagram below shows what the sky looks like from Earth. The new Moon
is shown drifting across the Sun. The range of paths falling within the “total”
zone increases by a lot (it more than doubles). The range of paths falling within
the “partial” zone increases by only a little bit (about 5%).
TOTAL
PARTIAL
PARTIAL
TOTAL
PARTIAL
Moon
Sun
PARTIAL
1
