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
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
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.