# Geosynchronous satellite

1. Feb 8, 2010

### Cudi1

1. The problem statement, all variables and given/known data
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

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

3. 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

2. Feb 8, 2010

3. Feb 8, 2010

### Cudi1

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

4. Feb 8, 2010

### 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

5. Feb 8, 2010

### 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?

6. Feb 8, 2010

### Cudi1

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

7. Feb 8, 2010

### Spinnor

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

8. Feb 8, 2010

### 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