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Standard XII

Physics

Escape Speed

A planet of m...

Question

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}]^{1 / 2}

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[r_{2}]^{1 / 2}

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{[r_{1} - r_{2}]}_{1}^{1 / 2}

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{[r_{1} + r_{2}]}_{1}^{3 / 2}

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Solution

The correct option is B ${[r_{1} + r_{2}]}_{1}^{3 / 2}$
As per kepler's third law of planetary motion,'

$T^{2} α R^{3}$ where R is the semi major axis.

$R = \frac{r_{1} + r_{2}}{2}$

$T α {(r_{1} + r_{2})}^{3 / 2}$

Answer is option D.

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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 r1 and r2 respectively. The period of revolution of the planet will be proportional to:

The correct option is B [r1+r2]3/2As per kepler's third law of planetary motion,'T2αR3 where R is the semi major axis.R=r1+r22Tα(r1+r2)3/2Answer is option D.

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:

The correct option is B ${[r_{1} + r_{2}]}_{1}^{3 / 2}$
As per kepler's third law of planetary motion,'

$T^{2} α R^{3}$ where R is the semi major axis.

$R = \frac{r_{1} + r_{2}}{2}$

$T α {(r_{1} + r_{2})}^{3 / 2}$

Answer is option D.