A satellite is in an elliptical orbit around a planet \(P.\) It is observed that the velocity of the satellite when it is farthest from the planet is \(6\) time less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is\(......\)

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Verified Solution

Answer & Solution

Correct Answer

(A) \(1:6\)

Detailed explanation

By angular momentum conservation

\(r _{\min } V _{\max }= r _{\max } V _{\min } \quad \ldots( i )\)

Given \(V _{\min }=\frac{ V _{ max }}{6}\)

from equation \((i)\)

\(\frac{r_{\min }}{r_{\max }}=\frac{V_{\min }}{V_{\max }}=\frac{1}{6}\)

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