Massive vs. Smaller Satellites: Understanding Orbiting Speeds

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A more massive communications satellite does not orbit more slowly than a smaller one because gravitational force increases with mass, but so does the inertia of the satellite. Both forces balance out, resulting in the same orbital speed when at the same distance from the planet. The centripetal force required for circular motion is determined by the satellite's distance from Earth rather than its mass. Kepler's laws indicate that the orbital period is independent of the satellite's mass, focusing instead on the distance from the planet. Thus, the mass of the satellite does not affect its orbital speed.
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Homework Statement


why a more massive communications satellite doesn't orbit more slowly than a smaller one?


Homework Equations





The Attempt at a Solution



The larger satellite will have more mass but it will also have a far greater gravitational force acting on it no matter where it is orbiting. These two will cancel each out. So they will freefall at the same rate providing it is the same distance from the planet.
 
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rafterman said:

Homework Statement


why a more massive communications satellite doesn't orbit more slowly than a smaller one?

Things to think about:
1. What type of orbit does communications satellites orbit the Earth in?
2. What force provides the acceleration for this orbit?
3. This force is the centripetal force, which can be written down for an object in circular motion.
4. Equating these two expressions should tell you the answer to your question.
 
Consider Kepler's law and what role the satellite mass plays in determing the orbital period.
 
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