A space probe describes a circular orbit of radius nR with
Chapter 13, Problem 13.114(choose chapter or problem)
A space probe describes a circular orbit of radius nR with a velocity \(v_{0}\) about a planet of radius R and center O. Show that (a) in order for the probe to leave its orbit and hit the planet at an angle u with the vertical, its velocity must be reduced to \(a \mathbf{v}_{0}\), where
\(\mathrm{a}=\sin \mathrm{u} \frac{\overline{2(n-1)}}{\mathrm{B} n^{2}-\sin ^{2} \mathrm{u}}\)
(b) the probe will not hit the planet if a is larger than \(1 \overline{2 /(1+n)}\).
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