An artificial satellite moving in a circular orbit around...

An artificial satellite moving in a circular orbit around earth has a total (kinetic + potential energy) $E_{0}$, its potential energy is
(A) $-\mathrm{E}_{0}$
(B) $1.5 \mathrm{E}_{0}$
(C) $2 \mathrm{E}_{0}$
(D) $\mathrm{E}_{0}$

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Key Concepts

Circular Orbital Motion

Circular orbital motion refers to the movement of a body in a stable, constant-radius orbit around a central mass where the gravitational force provides the necessary centripetal force. This concept is crucial for understanding how satellites operate, as the forces in balance determine the satellite's velocity and the characteristics of its orbit.

Gravitational Potential Energy

Gravitational potential energy in the context of orbital mechanics is defined as the energy due to the position of an object in a gravitational field. For satellites, it is given by a negative value that represents the bound state of the satellite to the Earth. This negative energy indicates that work must be done to remove the satellite from the influence of the Earth’s gravity.

Energy Relationships in Orbital Mechanics

In a circular orbit, the total mechanical energy, which is the sum of kinetic and potential energies, has a specific relationship with each component. The kinetic energy is exactly half the magnitude but positive compared to the potential energy (which is negative), leading to a total energy that is negative and equal to half the potential energy. This relationship, derived from the balance of forces in circular motion, is a fundamental aspect of orbital dynamics.

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