A satellite moving in a circular orbit around earth has a total (kinetic + potential) energy E_o. Its potential energy will be ____

Question

Question

This question was previously asked in

Official Soldier Technical Paper : [Goa] - 23 Feb 2020

Answer 1

CONCEPT:

Some definition of energy:

Terms	Gravitational Potential Energy (U)	The kinetic energy of a satellite (KE)	The total energy of a system (T)
Definition	The gravitational potential energy of a body at a point is defined as the amount of work done in bringing the body from infinity to that point against the gravitational force.	The kinetic energy of a satellite in a circular orbit is half its gravitational energy and is positive instead of negative.	The sum of the kinetic and gravitational potential energy of a system is its total energy and this total energy is conserved in orbital motion.
Mathematical expression	\( U=-\frac{GMm}{r}\)	\(KE=\frac{GMm}{2r}\)	\( T=-\frac{GMm}{2r}\)
	Where M = mass of earth, m = mass of the body, r = distance from the earth	Where M = mass of earth, m = mass of the body, r = distance from the earth	Where M = mass of earth, m = mass of the body, r = distance from the earth

EXPLANATION:

Given - The total energy of a system (T) = E_o

\(⇒ E_o=-\frac{GMm}{2r}\) ------- (1)

\(⇒ U=-\frac{GMm}{r}\)

Equation 1 can be written as

\(⇒ E_o=\frac{U}{2}\)

⇒ U = 2E_o