# Total Energy of a satellite

## Homework Statement

Calculate the total energy of a geosynchronous satellite (one that orbits over a fixed spot) with a mass of 1500kg, orbiting Earth at a height of 325km with an orbital speed of 5000m/s

ET=Ek+Ep
Ek=(0.5)(m)(v)^2
Ep=(m)(g)(h)

## The Attempt at a Solution

Looking at the orbital velocity was confusing me, so I researched geosynchronous satellites. The orbital velocity is being used to keep it stationary, assuming the earth is rotating at the same velocity. So it is not used in these calculations.

Now, in this lesson we have not learned the formulas of Ek= G(mp)(mo) /rp and
Ep= -G(mp)(mo)

Therefore, I bet the what the teacher wants is just Et=mgh . I would like to believe that it is not asking us to include the orbital energy.

But again Et is not a vectory quanitiy and orbital energy is possible.

Would the total energy in this case be

Et=(mo)(0.5)(5000m/s)^2 + (mo)(g)(h)

mgh applies near the Earth's surface where g is essentially constant. Way out where the satellite is, g ain't yer usual 'g' anymore! 