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Kepler's laws of planetary motion

A planet of mass m is moving in an elliptical orbit about the

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A planet of mass $m$ is moving in an elliptical orbit about the sun (mass of sun $= M$ ). The maximum and minimum distances of the planet from the sun are $r_{1}$ and $r_{2}$ respectively. The period of revolution of the planet will be proportional to

r_{1}^{3/2}

r_{2}^{3/2}

(r_{1} - r_{1})^{3/2}

(r_{1} + r_{2})^{3/2}

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Updated on: Feb 18, 2023

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Luna Discussed

A planet of mass

m

is moving in an elliptical orbit about the sun (mass of sun

= M

). The maximum and minimum distances of the planet from the sun are

r_{1}

and

r_{2}

respectively. The period of revolution of the planet will be proportional to

11 mins ago

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11 mins ago

Text solutionVerified

Semi-major axis of elliptical path,

a = \frac{r _{1} + r _{2}}{2}

From Kepler's law of period, we have

∴ T^{2} \propto a^{3} \Rightarrow T \propto a^{3/2}

∴ T \propto (r_{1} + r_{2})^{3/2}

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Question Text	A planet of mass $m$ is moving in an elliptical orbit about the sun (mass of sun $= M$ ). The maximum and minimum distances of the planet from the sun are $r_{1}$ and $r_{2}$ respectively. The period of revolution of the planet will be proportional to
Updated On	Feb 18, 2023
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 5
Upvotes	647
Avg. Video Duration	8 min

A planet of mass $m$ is moving in an elliptical orbit about the sun (mass of sun $= M$ ). The maximum and minimum distances of the planet from the sun are $r_{1}$ and $r_{2}$ respectively. The period of revolution of the planet will be proportional to

Text solutionVerified

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A planet of mass $m$ is moving in an elliptical orbit about the sun (mass of sun $= M$ ). The maximum and minimum distances of the planet from the sun are $r_{1}$ and $r_{2}$ respectively. The period of revolution of the planet will be proportional to