A planet moves around the sun (mass = M s ) in an elliptical orbit such that its minimum and maximum distance from the sun are r and R respectively. The period of revolution of this planet around the

Question

A planet moves around the sun (mass = M s ) in an elliptical orbit such that its minimum and maximum distance from the sun are r and R respectively. The period of revolution of this planet around the sun is

TestHub · Accepted Answer

The length of the semi-major axis of the elliptical orbit of the planet is

$a = \frac{r + R}{2}$

If we assume that there is a hypothetical planet which moves around the sun in a circular orbit of radius $r_{0} = \frac{r + R}{2}$ , then the time period of this hypothetical planet and our given planet will be same. The time period of a planet around the sun in circular orbit is

$T = 2 π \sqrt{\frac{{r^{3}}_{0}}{G M_{s}}} = 2 π \sqrt{\frac{{(\frac{r + R}{2})}^{3}}{G M_{s}}}$

$T = π \sqrt{\frac{{(r + R)}^{3}}{2 G M_{s}}}$

Physics - Gravitation Question with Solution | TestHub

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