# Energy required to move an object in orbit?

1. Jan 4, 2010

### Peto

The International Space Station, with a mass of 370,000 kg, is orbiting the Earth at a height 335 km and needs to be boosted to an orbit of 352 km. Calculate the energy needed to boost the ISS to its new height.

m = 370,000 kg
M = 5.98 x 10^24 kg
G = 6.67 x 10^-11 Nm^2/kg^2
Initial distance from earths center = (6.38 x 10^6m) + 335000m
Final distance form eath's center = (6.38 x 10^6m) + 352000m

Using Ep = GMm/r

I calculated
Epi = (6.67x10^-11)(5.98x10^24)(370000)/((6.38x10^6)+(335000)) = 2.316682247E13

and

Epf = (6.67x10^-11)(5.98x10^24)(370000)/((6.38x10^6)+(352000)) =2.316676064E13

I found the difference of the two, and took it as my answer, 6.2x10^7 J

I feel I'm doing something wrong, Thanks in advance for any help!

2. Jan 4, 2010

### mgb_phys

Have you considered the difference in speed (and so Kinetic energy) for the two orbits?

3. Jan 6, 2010

### Peto

Hmmm, so I would have to find the total energy,

Et = Ep + Ek = G Mm/r + .5mv^2

ok I think I got it now.

4. Jan 6, 2010

### mgb_phys

Remember that V is also a function of r and M (there is a fixed speed for each orbital height)

5. Jan 6, 2010

### Peto

yes, v = sqrt(MG/r)

so figuring out the difference in total energy, would that give me the amount of energy needed to boost the space station to its new height?
what I mean is, does difference in total energy = amount of energy required to boost to new height?

6. Jan 6, 2010

### mgb_phys

Yes actualy thats the minimum energy, assuming you want it to orbit in the same direction