# Energy of a Satellite

1. Jan 16, 2004

### rdn98

A 1700 kg satellite is orbitting the earth in a circular orbit with an altitude of 1800 km.

a) How much energy does it take just to get it to this altitude?
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Ok, I just need help getting the setup on this first part.

The amount of energy need to get to this altitude would the sum of the initial potential and kinetic energies, right?

So -GMm/r + .5mv^2 = total energy?

where r= Radius of earth + altiude (m)

I can figure out the velocity using escape velocity equation, but I get this big negative answer. Thats not right, so whats the right way to do this?

2. Jan 16, 2004

### enigma

Staff Emeritus
This is correct.

By definition, total energy is zero if you are on an escape trajectory. That means that any bound orbit will have a negative energy.

To find the velocity, use the Vis-Viva equation, which relates energy, velocity, semi-major axis and orbital distance (and the escape velocity is drawn from the equation as well)

$$\epsilon = \frac{V^2}{r}-\frac{\mu}{r}=-\frac{\mu}{2a}$$

Where $\epsilon$ is total energy
$\mu$ is the gravitational parameter, G*M
r is the distance from the earth
and a is the semi-major axis of the orbit (r for circular, infinity for parabolic or escape velocity)

Last edited: Jan 16, 2004
3. Jan 17, 2004

### HallsofIvy

Staff Emeritus
But the original problem said "just to get it to this altitude". My guess would be that you should not take into account the kinetic energy of moving in orbit. "Just to get it to this altitude" would seem to me to be the energy necessary to get up to that altitude, not to be in orbit at that altituded.