All Problems Universal Gravitation
Problem 1.225
A satellite revolves from east to west in a circular equatorial orbit of radius \(R=1.00 \cdot 10^{4} \mathrm{~km}\) around the Earth. Find the velocity and the acceleration of the satellite in the reference frame fixed to the Earth.
\[ \text { 1.225. } v^{\prime}=\frac{2 \pi R}{T}+\sqrt{\frac{\gamma M}{R}}=7.0 \mathrm{~km} / \mathrm{s}, \quad w^{\prime}=\frac{\gamma M}{R^{2}}\left(1+\frac{2 \pi R}{T} \times\right. \] \(\left.\times \sqrt{\frac{R}{\gamma M}}\right)=4.9 \mathrm{~m} / \mathrm{s}^{2} .\) Here \(M\) is the mass of the Earth, \(T\) is its period of revolution about its own axis.