Due: Tuesday November 28, 1995
1. The earth circles around the sun at a distance of about 150,000,000 kilometers, moving at about 29 km per second.
(a) What is the earth's acceleration towards the sun, in meters per second per second?
(b) The sun attracts the earth gravitationally with a force GMm/r², where G = 6.67x10^(-11), M is the mass of the sun and m is the mass of the earth. From the above data, including your answer to (a), figure out the mass of the sun.
(c) Our solar system is part of the Milky Way galaxy. We are about 30,000 light years from the center of the galaxy, which we are circling at about 250 km per second. Find our acceleration towards the center of the galaxy. (One light year, the distance light travels in one year, is about 1013 kilometers.)
(d) It can be shown that the gravitational attraction our solar system feels from the rest of the galaxy is roughly the same as if all the galactic mass were concentrated at the center. Assuming that to be true, find the mass of the galaxy, and express it as a multiple of the mass of the sun.
(Note: the assumption in (d) neglects stars further from the center than we are, but these are a fairly small fraction of the whole galaxy, so this is not a bad approximation.)
2. (This question was used by Albert Michelson to explain to his children how he hoped to detect an aether wind. It contains some ideas that will be useful in discussing relativity.)
Suppose we have a river of width w (say, 100 feet), and two swimmers who both swim at the same speed v feet per second (say, 5 feet per second). The river is flowing at a steady rate, say 3 feet per second. The swimmers race in the following way: they both start at the same point on one bank. One swims directly across the river to the closest point on the opposite bank, then turns around and swims back. The other stays on one side of the river, swimming upstream a distance (measured along the bank) exactly equal to the width w of the river, then swims back to the start. Who wins?
(Hint: the swimmer going directly across the river must be swimming partly upstream to compensate for the current. Try to picture this swimmer's velocity vector relative to the water. What must be the magnitude of the upstream component? You know the magnitude of the velocity vector. Can you figure from this the magnitude of the cross stream component? This will tell you the time to get across.)
3. (a) Find out what Thomas Jefferson thought of Isaac Newton, and write a couple of sentences or so summarizing TJ's opinion.
(b) Write a few sentences on how the Scientific Revolution (that is, mainly, the work of Galileo and Newton) influenced the Founding Fathers and hence the Declaration of Independence, etc., (if at all).