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Two artificial satellites of the same mass are moving around the earth in circular orbits of different radii. In comparison to the satellite with lesser orbital radius, the other satellite with higher orbital radius will have :

(A) greater kinetic energy.
(B) greater potential energy.
(C) greater total energy
(D) greater magnitude of angular momentum, about the centre of the circular orbit.

1 Answer

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Final answer:

In circular orbits, the artificial satellite with a greater radius will have higher potential energy, total energy, and angular momentum, but lesser kinetic energy compared to the one with a smaller radius.

Step-by-step explanation:

For two artificial satellites of the same mass moving around the Earth in circular orbits of different radii, the satellite with a higher orbital radius will have greater potential energy, total energy, and angular momentum. This is because potential energy and magnitude of angular momentum for a satellite in circular orbit increase with the radius of the orbit. However, its kinetic energy will be less than that of the satellite with a lesser orbital radius since the orbital speed decreases with increasing radius.

Let's break down each component:

  • Potential Energy: Higher orbital radius means the satellite is further from Earth, increasing gravitational potential energy due to the formula U = -GMm/r, where U is potential energy, G is the gravitational constant, M and m are the masses of Earth and the satellite, and r is the distance from the center of Earth to the satellite.
  • Total Energy: The total energy, which is the sum of kinetic and potential energy, will also be greater as the increase in potential energy with radius dominates the decrease in kinetic energy.
  • Angular Momentum: Angular momentum, given by L = mvr (where v is orbital velocity and r is orbital radius), increases because the increase in orbital radius has a larger effect than the decrease in orbital velocity.

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