A planet moves around the sun (mass = Ms ) 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

Question

A planet moves around the sun (mass = Ms ) 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 (A) T=π √((r + R)3/2 G Ms) (B) T=π √((r + R)3/3 G Ms) (C) T=π √((r + R)3/G Ms) (D) T=π √(2 (r + R)3/G Ms)

Tardigrade Admin · 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 \frac{r _{0}^{3} 0}{G M _{S}} = 2 π \frac{( \frac{r + R}{2} ) ^{3}}{G M _{S}}

T = π \frac{( r + R ) ^{3}}{2 G M _{s}}

Q. 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

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

$T = π \frac{( r + R ) ^{3}}{3 G M _{s}}$

$T = π \frac{( r + R ) ^{3}}{G M _{s}}$

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

Q. A planet moves around the sun (mass = Ms​ ) 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

T=π2GMs​(r+R)3​​

T=π3GMs​(r+R)3​​

T=πGMs​(r+R)3​​

T=πGMs​2(r+R)3​​

Q. 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

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

$T = π \frac{( r + R ) ^{3}}{3 G M _{s}}$

$T = π \frac{( r + R ) ^{3}}{G M _{s}}$

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