- #1

Johfb

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## Homework Statement

Calculate the energy of a 100kg satellite associated with a geostationary orbit around a planet.

## Homework Equations

Kepler's 3rd Law:

[tex]T^{2} = \left( \frac{4 \pi^{2}}{GM_{p}} \right)r^{3}[/tex]

Velocity equation:

[tex]v = \sqrt{\frac{GM_{p}}{r}}[/tex]

Planet mass:

[tex]M_{p} = 5 \times 10^{20} kg[/tex]

Satellite mass:

[tex]m_{s} = 100 kg [/tex]

## The Attempt at a Solution

Given the mass of the planet (M_{p}) I rearranged Kepler's 3rd law to get the radius of the geostationary orbit, then used the velocity equation to calculate the velocity of the satellite in this geostationary orbit.

I thought that I should then calculate the energy of the satellite by using the equation:

[tex]E = \frac{1}{2}mv^{2} - \frac{GM_{p}m_{s}}{r}[/tex]

However this gives the result of [itex]E < 0[/itex] ! :uhh:

I'm sure it's a rather simple question but I just can't figure it out at the moment..