Distance of a satellite from the earths surface.

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To determine the distance of a television satellite in a 24-hour orbit from the Earth's surface, Kepler's Laws can be applied. The gravitational force equation GMm/r² and the angular velocity equation GM/r = ω² are relevant, where G is the gravitational constant and M is the Earth's mass. The angular velocity can be calculated by converting the orbital period of 24 hours into radians per second. By using these formulas, one can derive the satellite's altitude above the Earth's surface. Understanding these principles is essential for solving the problem accurately.
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1. A television satellite is in circular orbit about the Earth, with a sidereal period of exactly 24h. What is the distance from the Earths surface?



2. I think I have to use Kepler's Laws. Confused as to how to do it without the mass of each. I guess I could find out the mass of the Earth but then..? Can anyone point me in the right direction?
 
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pwphysics101 said:
1. A television satellite is in circular orbit about the Earth, with a sidereal period of exactly 24h. What is the distance from the Earths surface?



2. I think I have to use Kepler's Laws. Confused as to how to do it without the mass of each. I guess I could find out the mass of the Earth but then..? Can anyone point me in the right direction?

GMm/r2 = ω2r

GM/r = ω2

You know G and M (or can look them up)

ω is the angular velocity. If the period is 24 hours then you know 24 hours is the amount of time it takes for the satellite to travel 2∏ radians. You should probably convert that into radians/sec
 
Thanks! :)
 
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