Circular Orbits

Their Way

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


My Way

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.