Help with Hartle: Calculating Elapsed Time

[HeLLe]

Help with Hartle!

Hello,
I find Hartle's working very confusing. I was wondering if someone could help me decode this problem:

Three observers are standing near each other on the surface
of the Earth. Each holds an accurate atomic clock. At time t = 0 the first observer
throws their clock straight up so that it returns at time T as measured by the clock
of the second observer, who holds their clock in their hand for the entire time interval.
The third observer carries their clock up to the maximum height reached by the thrown
clock, and back down, moving with constant speed on each leg of the trip and returning
in time T.
Calculate the total elapsed time measured on each clock assuming that the maximum
height is much smaller than the radius of the Earth. Include gravitational effects but
calculate to order 1/c2 only using non-relativistic trajectories. Which clock registers
the longest proper time? Why is this?

I am assuming the clocks higher in the gp tick faster, but how the heck do we calculate the total elapsed time, and what's up with observer #3 ??

Thanks!

 

[HeLLe]

Will I get any replies?

 

[Dick]

You are being asked to calculate proper time along three different paths to some approximation. Write each path in terms of, say, local coordinate time. Now what's the definition of proper time along a path with a given metric tensor?