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Universal Gravitation

Problem 1.224

A satellite revolving in a circular equatorial orbit of radius R=2.00⋅104R=2.00 \cdot 10^{4} km from west to east appears over a certain point at the equator every τ=11.6\tau=11.6 hours. Using these data, calculate the mass of the Earth. The gravitational constant is supposed to be known.

Reveal Answer
 1.224. M=(4π2R3/γT2)(1+T/τ)2=6⋅1024 kg, where T is  the period of revolution of the Earth about its own axis. \begin{aligned} &\text { 1.224. } M=\left(4 \pi^{2} R^{3} / \gamma T^{2}\right)(1+T / \tau)^{2}=6 \cdot 10^{24} \text { kg, where } T \text { is }\\ &\text { the period of revolution of the Earth about its own axis. } \end{aligned}
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