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## Homework Statement

A satellite is in circular polar orbit radius r around Earth (radius R, mass M). Clocks C on satellite and C0 on south pole of earth. Show the ratio of the rate of C to C0 is approximately

[tex] 1 +\dfrac{GM}{Rc^2} - \dfrac{3GM}{2rc^2} [/tex]

## Homework Equations

[tex] d\tau = (1+\dfrac{2\phi}{c^2})^{0.5} dt [/tex] where tau is proper time, and t is coordinate time of a stationary observer near a massive object, and phi is the scalar gravitational potential at that point.

## The Attempt at a Solution

want to compare rates of measurement of proper time?

can easily work out both gravitational potentials, and hence get

[tex] d\tau_{C_0} = (1- \dfrac{2GM}{Rc^2})^{0.5} dt [/tex]

and

[tex] d\tau_{C} = (1-\dfrac{2GM}{rc^2})^{0.5} [/tex]

then I worked out [itex] \dfrac{d\tau_{C}}{d\tau_{C_0}} [/itex], using binomial expansion on both and got:

[tex] 1 +\dfrac{GM}{Rc^2} - \dfrac{GM}{rc^2} [/tex]... not quite right.

HOW DO YOU USE LATEX ON HERE? haha...

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