Due 2:00 p.m. October 29, 1996
Reading Assignment: read the Towns and Gowns
chapter of Uncommon Sense.
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:
http://nssdc.gsfc.nasa.gov/planetary/planetary_home.html).
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.
