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

Question

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 1.44E+6 m and use 6.38E+6 m as the radius of the earth. The period of the orbit of the satellite is 6.88E+3 s and it has a mass of 120 kg.

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

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

Explanation / Answer

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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?

answer

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

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

angular momentum L = mvr = 2?m(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 = 2?L/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 = 2?L/h = 4?2mr2/T

ln(n) = ln(4?2m/T) + 2ln(r)

?n/n = 2?r/r

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

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