physics

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Two artificial satellites, 1 and 2, orbit the Earth in circular orbits having radii R1 and R2. If R2=2R1, the accelerations a2 and a1 of the satellites are related how?

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The centripetal acceleration of a satellite in a circular orbit is V^2/R , but V is a function of R also. For an earth satellite
GM/R^2 = V^2/R
where g is the universal constant of gravity and M is the mass of the earth. Therefore
V^2 = GM/R, and V^2 is inversely proportional to R.

That means that the acceleration V^2/R is inversely proportional to R^2. So if R2 = 2 R1, the acceleration at 2 is 1/4 as much.

I could have obtained this result more easily by recognizing that the acceleration is the gravitation force divided by satellite mass m, and the force is inversely proportional to R^2.

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