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 1.26E+6 m and use 6.38E+6 m as the radius of the earth. The period of the orbit of the satellite is 6.64E+3 s and it has a mass of 180 kg.

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?

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Explanation / Answer

A.) H = 1.26E+6 m, R = 6.38E+6 m, T = 6.64E+3 s, m = 180 kg.

r = R + H, v = 2r/T

angular momentum L = mvr = 2m(R + H)2/T = 9.94E+12 kgm2s

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.

n = 2L/h = 9.42E+46

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

n = 2L/h = 42mr2/T

ln(n) = ln(42m/T) + 2ln(r)

n/n = 2r/r

r/r = 0.5*1/n = 5.31E-48

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