Notes on Relativity and Cosmology - Physics Department, UCSB

7.6. HOMEWORK PROBLEMS 191
(c) Suppose that a set of small stones are released from high above the
earth as shown below. Describe what happens to the configuration of
stones as time passes, and describe the relative acceleration between
the outer stones and the central stone. Are the stones close enough
together that we can describe them by ‘local measurements’ (in the
sense of the equivalence principle) with respect to the central stone?
That is, are they close enough together that these freely falling objects
are indistinguishable from inertial objects in a global inertial frame?
x
y
Earth
7-2. The earth falls freely in a gravitational field that is largely due to the
moon 7 . Moreover, the earth is surrounded by a sphere of liquid called the
ocean. Based on your answers to problem 1, do you expect the ocean to
be perfectly round? Draw a picture of its shape.
7-3. The spacetime diagram below is drawn in the reference frame of a small
lab sitting on the earth (which experiences a Newtonian gravitational field
of g = 10m/s 2 ). Which of the worldlines shown below has the greatest
proper time? Explain why the answer you chose is correct.
7 For the purposes of this problem, the moon is more important than the Sun. Can you see
why? Hint: Think back to problem 1.