Need help with a physics question.?

Question

The Earth has mass m=5.93 X 10^24 kg and radius r=6.38 X 10^6 m. A satelitte in a geosynchronous orbit will stay above the same point on the Earth, since the period of the orbit is the same as the period of the Earth's rotation. What is the altitude for geosynchronous orbits? You will need to use the formula

F= G x M1 x M2 / r^2

to calculate the gravitational force on the satellite.

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So that is the question, I just need to know what to solve for, I should be able figure out the equations to use and whatnot. Thanks.

Answer 1

Since you don't want the equations, you want to start with a satellite in uniform circular motion. The centripetal acceleration on the satellite is provided entire by gravity between it and earth. So you want to start the problem by equating centripetal acceleration to force on the satellite due to gravity between it and Earth.

Break down centripetal acceleration to mass of the satellite, radius of orbit, and angular frequency of the satellite revolving about the earth. You have force due to gravity. Solve for radius of the orbit using known angular frequency of satellite orbit, mass of Earth, and gravitational constant. Once you find the radius of the orbit, you can find the height above the surface of the Earth.

Answer 2

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Answer 3

i dont know how to do this but it should end up about 36 000 km i think.

Answer 4

Wikipedia has your answer: