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ASTRONOMY
1.
(Pro
(2009)
Spring 2009
1
thi
pare with the Sun's gravlta
10
--" 1.Calculate
the Roche limits for Jupiter and Saturn, assuming the density of material of
Compare these Roche limits to the outer radii of the rings for these two planets
1 g cm(1.81 RJupiter and 8 RSaturn, respectively).
3.
or this problem, use the mean temperatures
to
=44 K.
for Mercury to be T=700 K and for
Us'
our answers to a) and b), could these two planets r
their original atmospheres?
4.
id N sa orbits the sun in an elliptical orbit with a h .
and perihelion distance
do of the asteroid is 35%. Assuming that
Nyssa is a
e with a radius of 41 km, calculate the sur a
at
. e IOn and at aphelion.
--.. 2. (Ida/Dactyl
binary) The asteroids Ida and Dactyl form a binary system with orbital
period of 24 hours. We can approximate both asteroids as spheres with average radii of
15.7 km for Ida, and 1.5 km for Dactyl. The average density of material that makes up
these asteroids is 2.6 g cm-3. The system orbits the Sun at a distance of 3 AU.
(a) Calculate
the masses of Ida and Dactyl.
(b) Calculate the orbital separation
(a) of the Ida-Dactyl
system.
(c) Calculate the force of gravity between these two bodies and compare it to the force
of gravity between Sun and Dactyl.
--. 3. The Galactic Center.
t
At the center of the Milky Way there is a mysterious
radio source Saggitarius A * (Sgr A *). Scientists have observed stars to orbit Sgr A * with
surprisingly high velocities. One of these stars, S2, at its closest approach to Sgr A * of
17 light-hours, was moving at 5000 km S-l! By combining measurements of S2 from over
10 years, we have been able to established
.the star's orbit, which is highly eccentrie
(e=0.87), and has a period of 15.2 yr. Assuming the orbit is in the plane of the sky.
(a) Calculate the semi-major
axis of this orbit (in AU).
(b) Calculate the mass of the object that S2 orbits (in units of M0).
(c) Assuming the object is a black hole calculate the Schwarz schild radius (in units of
R0 and AU).
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