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Kepler's Law

A planet P is...

Question

A planet P is moving in an elliptical path around the sun S. Speed of planet in positions P and Q are $v_{1}$ and $v_{2}$ respectively with SP= $r_{1}$ and SQ= $r_{2}$ , then $\frac{v_{1}}{v_{2}}$ is equal to

$\frac{r_{1}}{r_{2}}$

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$\frac{r_{2}}{r_{1}}$

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constant

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${(\frac{r_{1}}{r_{2}})}^{2}$

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Solution

The correct option is B
$\frac{r_{2}}{r_{1}}$

Angular momentum of planet about the center of sun is constant.

i.e., $m v r s i n θ = c o n s t a n t$

At position P and Q, $θ = 90^{\circ}$ and m = mass of planet = constant

$∴$ vr = constant

or $\frac{v_{1}}{v_{2}} = \frac{r_{2}}{r_{1}}$

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Similar questions

A planet P is moving in an elliptical path around the sun S. Speed of planet in positions P and Q are $v_{1}$ and $v_{2}$ respectively with SP= $r_{1}$ and SQ= $r_{2}$ , then $\frac{v_{1}}{v_{2}}$ is equal to

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A planet P is moving in an elliptical path around the sun S. Speed of planet in positions P and Q are v1 and v2 respectively with SP= r1 and SQ= r2, then v1v2 is equal to

The correct option is B r2r1 Angular momentum of planet about the center of sun is constant. i.e., mvrsinθ=constant At position P and Q, θ=90∘ and m = mass of planet = constant ∴ vr = constant or v1v2=r2r1

A planet P is moving in an elliptical path around the sun S. Speed of planet in positions P and Q are $v_{1}$ and $v_{2}$ respectively with SP= $r_{1}$ and SQ= $r_{2}$ , then $\frac{v_{1}}{v_{2}}$ is equal to

The correct option is B
$\frac{r_{2}}{r_{1}}$

Angular momentum of planet about the center of sun is constant.

i.e., $m v r s i n θ = c o n s t a n t$

At position P and Q, $θ = 90^{\circ}$ and m = mass of planet = constant

$∴$ vr = constant

or $\frac{v_{1}}{v_{2}} = \frac{r_{2}}{r_{1}}$