The period of a satellite in circular orbit around a planet...

The period of a satellite in circular orbit around a planet is independent of
(A) the mass of the planet
(B) the radius of the planet
(C) mass of the satellite
(D) all the three parameters (A), (B) and (C)

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Key Concepts

Kepler’s Third Law

Kepler’s Third Law of planetary motion states that the square of the period of an orbit (T²) is proportional to the cube of the semi-major axis of that orbit (r³) divided by the mass of the central body (M), when expressed as T = 2??(r³/GM). This relation applies to circular orbits and shows that while the period depends on the orbital radius and the mass of the central object, it does not include the mass of the orbiting satellite.

Gravitational and Centripetal Force Balance

In circular orbital motion, the gravitational force provides the necessary centripetal force to keep the satellite in orbit. Setting the gravitational force (G*M*m/r²) equal to the centripetal force (m*v²/r) leads to the cancellation of the satellite's mass (m) in the equations, demonstrating why the period of the orbit is independent of the satellite's mass.

Mass Independence in Orbital Mechanics

A key concept in orbital mechanics is that the motion of a satellite in orbit does not depend on its own mass. This mass cancellation arises from the derivation of the orbital period using Newton's law of gravitation coupled with the dynamics of circular motion, indicating that factors such as the planet's mass and the distance from the planet center determine the orbital characteristics, not the mass of the satellite.

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