Observational
Astronomy
1911.231:
HW #4
1.
Eclipses.
We do not see an eclipse at every new and full moon because the Moon’s orbit is
not perfectly aligned with the ecliptic.
The Moon’s orbit has a 5 degree inclination relative to the ecliptic and
so the Moon is not in the ecliptic at every new and full moon.
The Moon must be within a certain angular distance of the ecliptic during a
full or new phase for there to be an eclipse.
The conditions for a solar eclipse are more stringent than a lunar
eclipse, and the conditions are can only be met twice per year.
2.
A Farther
Moon.
The moon would be about half the angular size (0.25 degrees) and the Sun would
still be 0.5 degrees. Thus, there could
be no total lunar eclipse. However, annular eclipse would be more common
despite appearing different. Lunar eclipses would still occur because the moon
is much bigger than the Earth and would still cast enough of a shadow to
eclipse the Moon.
3.
A Smaller
Earth.
Solar eclipse would be the same if the Earth was half its size. Solar eclipses would still only be visible
for a small region of the Earth. Lunar
eclipse would still occur. However, the
Earth’s shadow would be smaller so lunar eclipses would be shorter.
4.
Planetary
Periods.
The sidereal period is the time it takes a planet to orbit the Sun relative to
the background stars. The synodic period is the time it takes a planet to go through
a “phase” cycle as viewed from Earth (i.e., superior conjunction to superior
conjunction).
Conjunction is when the ecliptical longitude of a
planet and the Sun are the same.
Opposition is when the ecliptical longitude of a
planet and the Sun differ by 180 degrees
Greatest elongation is when the difference between the
ecliptical longitude of a inferior planet and the Sun
reaches it maximum.
5.
Understanding
Kepler's Third Law.
a.
M1 = 1 solar mass and M2 is negligible for
planet
a = 1 AU
P2 = a3 / (M1 + M2)
P2 = 13 / 1 = 1
P = 1 year
b.
M1 = 4 solar mass and M2 is negligible for
planet
a = 1 AU
P2 = a3 / (M1 + M2)
P2 = 13 / 4 = 1/4
P = 0.5 years
6.
New Comet.
P = 1000 years P2
= a3
a3 = P2 = 10002 = 106
a = 100 AU
7. |lJup - lSun| = 180 degrees
lsun = 348 degrees.
lJup = 168 degrees
8. |lMer - lSun| = 0 degrees
Sun on the Vernal Equinox: lsun
= 0 degrees, RA = 0 hours
lMer = 0 degrees near the ecliptic: Mercury near the Vernal Equinox
RA of Mercury should be about 0 hours!