Calculating the Total Energy of a Geosynchronous Satellite in Orbit

[Cudi1]

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

Homework Equations

Et= Ek-Ep
Et= -1/2(GMem)/r

The Attempt at a Solution

im guessing the answer should be negative, using the mass of Earth being 5.98*10^24, but its wielding an incorrect answer constantly ,im getting Et= 8.9*10^10J ( i calculated radius being... r= radius of Earth + height= 6.7*10^6 m, am i suppose to use a different mass instead of the mass of earth, thank you

 

[Spinnor]

I think your orbital height is wrong, see:

http://en.wikipedia.org/wiki/Geosynchronous_satellite

 

[Cudi1]

how would you find orbital height? quite confused thank you for the help

 

[Spinnor]

At a geosynchronous orbit you can figure the required orbital velocity to match the Earth's rotation, one orbit every 24 hours. We want the centripetal force equal the force of gravity,

F = GmM/R^2 = mv^2/R

 

[Cudi1]

yes , its orbiting Earth at 325km or 3.25*10^5m
Et= kinetic + potential energy= (mv^2/r- GMem/r^2) is that correct?

 

[Cudi1]

sorry, kinetic is 1/2(mv^2)

 

[Spinnor]

yes , its orbiting Earth at 325km or 3.25*10^5m
Et= kinetic + potential energy= (mv^2/r- GMem/r^2) is that correct?

Looks good except the potential energy goes as 1/r.

 

[Cudi1]

oh , so it would be Et= 1/2(mv^2) - (GMem/r) and thank you for the help
im getting the total energy is -1.82*10^12j