Question

# 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 $$r_1$$ and $$r_2$$ respectively. The time period of the planet is proportional to

A
r2/51
B
(r1+r2)3/2
C
(r1r2)3/2
D
r3/2

Solution

## The correct option is A $$\displaystyle \left ( r_1+r_2 \right )^{3/2}$$Kepler's third law:Square of the time period $$T$$ is directly proportional to cube of semi-major axis i.e mean distance of the planet $$\dfrac { { r }_{ 1 }+{ r }_{ 2 } }{ 2 }$$$${ T }^{ 2 }\propto { \left( \dfrac { { r }_{ 1 }+{ r }_{ 2 } }{ 2 } \right) }^{ 3 }$$$${ T }\propto { \left( { r }_{ 1 }+{ r }_{ 2 } \right) }^{ 3/2 }$$Physics

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