(B) The centripetal force required for the circular motion of the planet is provided by the gravitational force of attraction.The gravitational force

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(B) The centripetal force required for the circular motion of the planet is provided by the gravitational force of attraction.The gravitational force is given as $F_g \propto R^{-5/2}$.The centripetal force is given by $F_c = m \omega^2 R = m \left( \frac{2\pi}{T} \right)^2 R = \frac{4\pi^2 m R}{T^2}$.Equating the two forces: $\frac{m R}{T^2} \propto R^{-5/2}$.Rearranging for $T^2$: $\frac{1}{T^2} \propto \frac{R^{-5/2}}{R} = R^{-7/2}$.Therefore,$T^2 \propto R^{7/2}$.

Class 11 Physics Gravitation Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

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Imagine a light planet revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force of attraction between the planet and the star is proportional to $R^{-5/2}$,then ${T^2}$ is proportional to:

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A
$R^3$
B
$R^{7/2}$
C
$R^{5/2}$
D
$R^{3/2}$

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Gravitation

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Motion of Satellites in Circular Orbits and Planets in Elliptical Orbits

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Imagine a light planet revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force of attraction between the planet and the star is proportional to $R^{-5/2}$,then ${T^2}$ is proportional to:

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