## Physics 109N Pledged Homework #2

Due 2:00, Thursday November 21, 1996

1. Read pages 3 - 33 of Einstein's Relativity.

(a) Explain in your own words just what is meant by a Frame of Reference (also called a "body of reference" and a "system of co-ordinates" by Einstein).

(b) Explain what is meant by the Principle of Relativity.

(c) Why is the Principle of Relativity satisfied in Einstein's example of a stone dropped from the train window, even though the path of the stone is quite different in the two frames?

(d) State what is the problem in reconciling the Principle of Relativity with the usual rule for finding relative velocities, that is, a person on a train walking at speed u towards the front of the train, which is moving at speed v along the track, will be moving at u + v relative to the track.

2. Read the section "About Freedom" in Einstein's Ideas and Opinions.

Write a few lines on any correspondence you find between this and Cromer's discussion of the conditions in society necessary for science to flourish.

3. Read Einstein's discussion of Newton in pages 253 - 258 of Ideas and Opinions.

(a) Write a few lines on what Einstein sees as Newton's great contribution to knowledge.

(b) Write a few lines on what Einstein sees as unexplained by Newton's theory.

4. A quote from the French poet Paul Valéry (1871-1945): "One had to be a Newton to notice that the moon is falling, when everyone sees that it doesn't fall".

Write a half-page or so explanation of this apparent paradox for a friend who knows very little science, including brief explanations of the relevant Newton's Laws.

5. Check out the Kepler's Laws site linked to the notes, and in particular study the simulation for Kepler's Third Law.

(a) The satellites that transmit TV signals for home dish reception are all in what are called "geosynchronous" orbits, the satellites go once around the earth in close to 24 hours. Why were they placed in those particular orbits? In other words, how does that help reception of the TV signal?

(b) To be precise, they go around once in 23 hours and 56 minutes. Why isn't it exactly 24 hours?

(c) Use Kepler's Third Law and what you already know (or can look up) about the moon to predict the radius of the orbit of a geosynchronous satellite. Compare your result with the data given at the Kepler's Laws site, and explain any differences.

6. The (almost) ultimate weighing job: estimating the mass of our galaxy.

The solar system is closer to the edge than the middle of our galaxy (the Milky Way), and is moving in an approximately circular path at about 250 kilometers per second. The radius of the circle -- the distance to the center of the galaxy -- is about 30,000 light years, where one light year is the distance light travels in one year.

The solar system's circular motion about the center of the galaxy is caused by the gravitational attraction from the other stars in the galaxy. This turns out to be not too different from what it would be if we lumped them all together in the middle in one huge mass M. Find this mass by the same method we used to find the earth's mass and the sun's mass, given G = 6.67 x 10-11.

Assuming the sun is a typical star, estimate how many stars there are in our galaxy.