Time Period and Elliptical Orbit Axes – Rankers Physics
Topic: Gravitation
Subtopic: Keplers Law

Time Period and Elliptical Orbit Axes

A satellite revolves around a planet in an elliptical orbit of minor and major axes \(a\) and \(b\) respectively. If T be the time period of the satellite, then \(T^2\) is proportional to
\(\left(\frac{a+b}{2}\right)^3\)
\(\left(\frac{a-b}{2}\right)^3\)
\(a^3\)
\(b^3\)

Solution:

According to Kepler's Third Law, \(T^2\) is proportional to the cube of the semi-major axis. Since the major axis is given as \(b\), the semi-major axis is \(b/2\), making \(T^2 \propto b^3\).

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