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Question: A planet of mass m moves around the sun of mass M in an elliptical orbit. The maximum and minimum di...

A planet of mass m moves around the sun of mass M in an elliptical orbit. The maximum and minimum distance of the planet from the sun are r1 and r2 respectively. The time period of the planet is proportional to –

A

r13/2\mathrm { r } _ { 1 } ^ { 3 / 2 }

B

C

(r1 + r2)3/2

D

(r1 – r2)3/2

Answer

(r1 + r2)3/2

Explanation

Solution

According to Kepler's law T2 µ a3

Here a = semi-major axis =

\ T2 µ (r1+r22)3\left( \frac { \mathrm { r } _ { 1 } + \mathrm { r } _ { 2 } } { 2 } \right) ^ { 3 }

T µ (r1+r22)3/2∝(r1+r2)3/2\left( \frac { \mathrm { r } _ { 1 } + \mathrm { r } _ { 2 } } { 2 } \right) ^ { 3 / 2 } \propto \left( \mathrm { r } _ { 1 } + \mathrm { r } _ { 2 } \right) ^ { 3 / 2 }