AST 301
Homework #8
Due Friday April 4
1. The Sun is about 25,000 ly from the center of the Milky Way galaxy. It orbits around the center with a speed of about 225 km/s.
a) What is the distance of the Sun from the center in kilometers? In AU?
b) What is the circumference of the Sun's orbit around the center in kilometers?
c) What is the period of the SunŐs orbit in seconds and in years?
d) Use Kepler's 3rd law to calculate the mass (in solar masses) inside of the Sun's orbit.
2. If you were running a 5km race on a 400m track and got forced to the outside so that on each turn the radius of the circle you
went around was 1m greater than the person inside you ran, how much farther would you have to run than he or she would?
Hints: First ask how many times you have to go around the track. In running the race you go around a circle (or two half circles)
this many time, plus running the straightaways, but everyone goes the same distance on the straightaways, so you don't have to
include them in your calculation. Next it might be easiest to assume some radius for the turns, although the radius you assume
won't affect your answer. If the inside runner ran a 20m radius circle you would run a 21m circle. Calculate the circumferences
of these circles and subtract to find the extra distance you have to run on each lap, then multiply by the number of laps you have to run.
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