5.E: Inertia (Exercises)
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Q1
Carry out the details of the calculation of the gravitational Doppler effect in section 5.2.
Q2
A student argues as follows. At the center of the earth, there is zero gravity by symmetry. Therefore time would flow at the same rate there as at a large distance from the earth, where there is also zero gravity. Although we can’t actually send an atomic clock to the center of the earth, interpolating between the surface and the center shows that a clock at the bottom of a mineshaft would run faster than one on the earth’s surface. Find the mistake in this argument.
Q3
Somewhere in outer space, suppose there is an astronomical body that is a sphere consisting of solid lead. Assume the Newtonian expression