A. Calculate the angular momentum of a satellite circling the Earth as a result

Question

A. Calculate the angular momentum of a satellite circling the Earth as a result of its orbital motion about the Earth. Assume that the satellite is at a height of 1.60E+6 m and use 6.38E+6 m as the radius of the earth. The period of the orbit of the satellite is 7.09E+3 s and it has a mass of 290 kg.

{ I tried to use moment of inertia and I got my final answer 1.046e13 kgm^2/s } but still I got it wrong.

B. If the angular momentum of the satellite obeys Bohr's quantization rule (L = n(h/2p)), determine the value of the quantum number, n.

C. By what fraction would the radius of the satellite's orbit have to be increased to increase the quantum number by 1?

Explanation / Answer

I am not familiar with Bohr's quantization, but I can help you with angular momentum:

a) Angular momentum is L = mvXr or I. They will both work, let us use mvXr

The velocity is constant in circular orbit, so v=d/t The distance is 2r in one period T. The distance to the center is the height 1.6e6 m PLUS the radius of Earth 6.38e6 m.

L = ( 290 kg )[ 2(1.6e6 m + 6.38e6 m ) / 7.09e3 s ] ( 1.6e6 m + 6.38e6 m ) = 1.637e13 kgm2/s

This also works if you use I, where I = mr2, and =2/T

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