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Universal Gravitation

Problem 1.225

A satellite revolves from east to west in a circular equatorial orbit of radius R=1.00⋅104 kmR=1.00 \cdot 10^{4} \mathrm{~km} around the Earth. Find the velocity and the acceleration of the satellite in the reference frame fixed to the Earth.

Reveal Answer
 1.225. v′=2πRT+γMR=7.0 km/s,w′=γMR2(1+2πRT× \text { 1.225. } v^{\prime}=\frac{2 \pi R}{T}+\sqrt{\frac{\gamma M}{R}}=7.0 \mathrm{~km} / \mathrm{s}, \quad w^{\prime}=\frac{\gamma M}{R^{2}}\left(1+\frac{2 \pi R}{T} \times\right. ×RγM)=4.9 m/s2.\left.\times \sqrt{\frac{R}{\gamma M}}\right)=4.9 \mathrm{~m} / \mathrm{s}^{2} . Here MM is the mass of the Earth, TT is its period of revolution about its own axis.
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