# HW #10 - Department of Physics and Astronomy

```Astronomy 101, Sec 2: Homework Set #10
Due: May 15, 2007
Chp 13
1. Density of a White Dwarf: calculate the density of a white dwarf star of 1 solar mass
that has a radius of 104 km.
Mass of Sun  1.989  10 30 kg  1.989  10 33 g
R  10 4 km  10 7 m  10 9 cm
Volume  43 R 3  4.189  10 27 cm 3
Density 
1.989  10 33 g
Mass

 4.748  10 5
27
3
Volume 4.189  10 cm
2. Calculate the Schwarzschild Radius of the Sun:
2GM
R 2
M  1.989  10 30 kg
c  3  10 8 m/s
c
2GM
R  2  2948 m  2.948 km
c
g
cm 3
G  6.67  10 -11 m 3 kg -1s -2
3. Given that the Sun moves in a circular orbit of radius 8.5 kpc around the center
of the Milky Way and that its orbital speed is 220 km/s, work out how long it takes
the Sun to complete one orbit of the galaxy.
3.085678  1013 km
radius  8.5 kpc  8500 pc 
 2.623  1017 km
1 pc
distance  rate  time
time 


distance Circumfere nce of orbit 2R 2 2.623  1017 km



 7.491  1015 s
rate
orbital speed
v
220 km/s
time  7.491  1015 s  238 million years
4. What would the Milky Way look like in the night sky to an observer on a planet
at the very edge of the galaxy? What would it look like to an observer at the galactic
nucleus?
At the edge of the galaxy, the Milky Way would not look too different if you happen to
be looking toward the center. However, if you are looking away from the center, you
would see a very low density of stars uniformly distributed in the sky. You might see an
increase in star density where the plane of the Milky Way intersects your horizon.
From the nucleus of the galaxy, you’d probably see a very high star density uniformly
distributed over your head at all times. The plane of the galaxy might be barely
noticeable since the overall star density is so high.
```