Match the following Table-1 Table-2 (A) time period of an...

Match the following
Table-1 Table-2
(A) time period of an earth
(P) Independent of mass of Satellite in circular orbit $\quad$ satellite
(B) Orbital velocity of satellite
(Q) independent of radius of orbit
(C) Mechanical energy
(R) independent of mass of earth
(S) none

Key Concepts

Orbital Period

In orbital mechanics, the orbital period is the time a satellite takes to complete one full orbit around a central body. According to Kepler’s third law and Newtonian gravitation, the orbital period in a circular orbit is independent of the satellite’s own mass because the mass cancels out during derivation, leaving the period dependent only on the radius of the orbit and the mass of the central body.

Orbital Velocity

Orbital velocity in a circular orbit is the constant speed a satellite must maintain to sustain its closed trajectory due to the balance between gravitational pull and centripetal force. The velocity is derived from the gravitational constant, the mass of the central body, and the orbit radius; importantly, despite involving motion, it is independent of the satellite’s mass since that parameter cancels out in the governing equations.

Mechanical Energy in Orbits

Mechanical energy in orbital dynamics is the sum of the kinetic energy and gravitational potential energy of the satellite. Unlike the orbital period and velocity, the mechanical energy is a function of the satellite’s mass as well as the orbital radius and the mass of the central body, meaning it does not exhibit the same mass independence seen in other orbital parameters.

Mass Independence in Orbital Mechanics

A fundamental principle in orbital mechanics is that several key parameters, such as the orbital period and orbital velocity in a circular orbit, do not depend on the mass of the orbiting object. This results from the fact that the mass of the satellite cancels out when equating gravitational and centripetal forces, thereby simplifying the expressions to depend only on the mass of the central body and the orbital radius.

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