Show that the values v A and vP of the speed of an earth
Chapter 13, Problem 13.112(choose chapter or problem)
Show that the values \(v_{A}\) and \(v_{P}\) of the speed of an earth satellite at the apogee A and the perigee P of an elliptic orbit are defined by the relations
\(v_{A}^{2}=\frac{2 G M}{r_{A}+r_{P}} \frac{r_{P}}{r_{A}} \ \quad v_{P}^{2}=\frac{2 G M}{r_{A}+r_{P}} \frac{r_{A}}{r_{P}}\)
where M is the mass of the earth, and \(r_{A}\) and \(r_{P}\) represent, respectively, the maximum and minimum distances of the orbit to the center of the earth.
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