What is the mechanical energy of a satellite in a circular orbit?

The velocity of a satellite in a circular orbit is:

v ² = GM ⁄ r

Multiplying both sides by m,

mv ² = GMm ⁄ r

The mechanical energy of a satellite in a circular orbit is:

ME = ½ mv ² − GMm ⁄ r

Substituting the previous equation into this equation:

ME = ½ mv ² − mv ² = − ½ mv ²

For a satellite in a circular orbit, we have:

ME = −KE

What is the weight of a satellite in a circular orbit?

The velocity of a satellite in a circular orbit is:

v ² = GM ⁄ r

Multiplying both sides by m,

mv ² = GMm ⁄ r

The weight of a satellite in a circular orbit is:

W = GMm ⁄ r − ½ mv ²

Substituting the previous equation into this equation:

W = mv ² − ½ mv ² = ½ mv ²

For a satellite in a circular orbit, we have:

W = KE

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They have negative energy. Negative energy is stupid.