Potential energy of a satellite having mass m and rotating at a height of 6.4 ×10^6 m from the

step 1 So the question asks, thus potential energy of a satellite having mass and rotating at a height

Potential energy of a satellite having mass m and rotating...

Potential energy of a satellite having mass $\mathrm{m}$ and rotating at a height of $6.4 \times 10^{6} \mathrm{~m}$ from the surface of earth
(A) $-0.5 \mathrm{mg} \operatorname{Re}$
(B) $-\mathrm{mg} \mathrm{Re}$
(C) $-2 \mathrm{mgRe}$
(D) $4 \mathrm{mgRe}$

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Key Concepts

Gravitational Potential Energy

This is the energy associated with an object due to its position in a gravitational field. It is given by the formula U = -GMm/r, where G is the gravitational constant, M is the mass of the central body, m is the mass of the satellite, and r is the distance between the centers of the two masses. This concept is central in understanding energy in gravitational systems.

Gravitational Acceleration and Its Relation to Potential Energy

The acceleration due to gravity at a planet's surface, denoted by g, is related to the gravitational constant and the planet's mass and radius by the formula g = GM/R². This relationship allows the gravitational potential energy to be expressed in terms of g and the radius of the planet, providing a practical method for solving problems involving gravitational interactions.

Orbital Mechanics

In the study of orbital mechanics, the energy of a satellite in orbit is analyzed by considering both its kinetic and potential energy. The specific orbital energy for a circular orbit depends on the distance from the centre of the planet and helps in determining the satellite's orbital characteristics. Understanding the balance between these energies is crucial to analyzing satellite motion.

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