HOW TO Calculate the period of a satellite orbiting the Moon?

[匿名]

2018-10-12 1:12 am

Calculate the period of a satellite orbiting the Moon, 92 km above the Moon's surface. Ignore effects of the Earth. The radius of the Moon is 1740 km.

回答 (2)

Captain Matticus, LandPiratesInc

2018-10-12 1:18 am

✔ 最佳答案

t = 2 * pi * sqrt(a^3 / (G * M))

a is the semi-major axis of the orbit. Let's just assume that it's circular

a = 92 + 1740 = 1832 km = 1832000 m = 1.832 * 10^(6) m
G = 6.67408 * 10^(-11) [m^3 / (kg * s^2)]
M = 7.34767309 * 10^(22) kg

2 * pi * sqrt(1.832^3 * 10^(18) m^3 / (6.67408 * 7.34767309 * 10^(-11) * 10^(22) [m^3 * kg / (kg * s^2)]) =>
2 * pi * sqrt(1.832^3 * 10^(18) s^2 / (6.67408 * 7.34767309 * 10^(11)) =>
2 * pi * sqrt(1.832^3 * 10^(18 - 11) / (6.67408 * 7.34767309)) seconds =>
2 * pi * sqrt(0.12538199457521700071906050543999 * 10^(7)) seconds =>
2 * pi * sqrt(1.2538199457521700071906050543999 * 10^6) seconds =>
7.0355403075440447587685610450475... * 10^3 seconds =>
7035.54 seconds

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quantumclaustrophobe

2018-10-12 1:16 am

Period T = 2 x pi x SQRT(r^3 / Gm) r is the radius of the orbit (so 1740km + 92km), G is the Gravitational constant, and m is the mass of the moon in kg.

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