AST 307 · Introductory Astronomy

Fall 2003

AST 307
Homework #2
Due Friday Sep. 12
 We talked about the apparent motion of Mars on the celestial sphere
in class. It usually moves in the prograde direction, but moves appears
to move retrograde when we are passing it. Draw a picture showing Venus
and the Earth orbiting the Sun, and use it to figure out when Venus moves
prograde and retrograde.
 Halley's comet has a perihelion distance (closest distance to the
Sun) of 0.36 AU and an aphelion distance (farthest from the Sun) of 36
AU. Its speed at perihelion is 70 km/sec. (I made up some round
numbers to make the answers come out reasonably simple. They aren't
quite right, but they're close.) Use Kepler's laws to answer the
following questions.
a) What is the semimajor axis, a, of Halley's orbit?
b) What is Halley's speed at aphelion?
c) What is the period of Halley's orbit?
d) What is the speed of an object in circular orbit 0.36 AU from the Sun?
e) What is the speed of an object in circular orbit 36 AU from the Sun?
f) Notice how these last two speeds compare to Halley's speed at those
two distances. Is the difference sensible (qualitatively)?
 Assume you are in a spaceship floating in space far from any stars
or planets, and you have your rocket engines off. Assume your mass is
50 kg, the mass of your spaceship is 500 kg, and the length of your
spaceship is 10 m.
a) If you push off from one end of the spaceship with a force of 10 Nt,
what is your acceleration while you are pushing?
b) If you push for one second, what is your speed after you stop pushing
and start coasting away from the end of the spaceship? Assume you and
the spaceship started out with zero velocity.
c) At this time what is the speed of the spaceship?
d) You coast down to the other end of the spaceship. How long does it
take for you to get to the other end? Ignore your height.
e) When you reach the other end of the spaceship, you push just hard and
long enough to come to a stop relative to the spaceship. At this point
what is the speed of the spaceship?
f) How far did the spaceship move during all of this?
If you didn't take the motion of the spaceship into account in
determining how long it took you to coast the length of the ship, go
back and redo that question taking it into account.
