## Physics 109n Homework #7

Due 2:00 p.m. October 29, 1996

1. Since the moon has no atmosphere, it is possible for a spaceship to be in orbit just a few miles above the surface (to clear the mountains) indefinitely, without needing to use fuel, once it's up to speed.

The purpose of this question is to figure out just how fast this spaceship needs to be moving to maintain this orbit. The reasoning parallels that used in the discussion of Newton's cannon on a mountain.

(a) Given that the acceleration due to gravity near the moon's surface is one-fifth of its value on earth, if you drop something while standing on the moon, how fast is it moving one second after you release it? (Give the answer in meters per second).

(Note: actually the moon's gravity is around 17% of earth's, I'm just trying to keep the figures simple.)

(b)What was its average speed during the first second of its falling?

(c) Use your answer to (b) to figure out how far it fell in the first second.

(d) Now think about the spaceship. Imagine it is initially traveling at some high speed parallel to the moon's surface, which we take to be flat at this point. For it to orbit the moon properly, the distance it falls below a straight line in one second must be just the distance the (curved) surface of the moon falls away below it over the distance the spaceship moves horizontally in one second. But we know from c) above how far it falls in one second. So, we have to figure out over what horizontal distance the moon's surface curves below a straight line by this amount. Draw a picture of a suitable triangle, with one corner at the center of the moon, to figure out how far the spaceship moves in one second.

(e) How long does the spaceship take to do one complete orbit of the moon?

2. Kepler discovered his laws by studying the orbits of planets around the sun. Does his third law also work for the satellites of Jupiter? (You can get the necessary info at this site:

Check the Galilean satellites, and a couple of others.

3. China was well ahead of Europe technologically in the late Middle Ages. List a few (say, four or five) reasons why Europe overtook China in scientific development, with a few lines (again, say four or five) explaining each.