(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A satellite of mass 4500 kg orbits the Earth in a circular orbit of radius of 7.6 x 10^6 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0 x 10^24 kg.

What is the speed of the satellite?

What is the minimum amount of energy required to move the satellite from this orbit to a location very far away from the Earth?

2. Relevant equations

F = mSatellite*a = G*mEarth*mSatellite/r²

a = G*mEarth/r² = v²/r -> v=SQRT(G*mEarth/r)

r = 7.6 x 10^6 km

mEarth = 6 × 10^24 kg

v = 7272.88 m/s

minimum amount of energy = increase of potential energy = 0 - (-GMm/r) = GMm/r = 6.67*10^(-11)*6.0*10^24*4500/7.6*10^6 = 2.38e11 J

3. The attempt at a solution

I know that I obtained the correct velocity, but when I try to solve for the energy required I get the wrong answer. Is the above equation for calculating the minimum amount of energy incorrect? What should I be doing?

Thanks in advance!

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# Calculating minimum energy to remove satellite from orbit

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