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The energy required to be spent by a satellite of mass m and speed v and orbital radius r in completing a circular orbit once round the earth of mass M is
  • a)
    GMm/r
  • b)
    2GMm/r
  • c)
    GMm/2r
  • d)
    zero
Correct answer is 'D'. Can you explain this answer?
Verified Answer
The energy required to be spent by a satellite of mass m and speed v a...
As the satellite is bounded by earth's gravitational field and has some velocity, it would completely revolve around the circular orbit without any external energy required.
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Most Upvoted Answer
The energy required to be spent by a satellite of mass m and speed v a...
Ans is 0 Since the satellite is bounded by earth's gravitational field and it also has tangential acceleration
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Community Answer
The energy required to be spent by a satellite of mass m and speed v a...
The energy required to complete a circular orbit once round the earth is zero.

Explanation:
To understand why the energy required is zero, let's break down the different types of energy involved in this scenario.

1. Gravitational Potential Energy (GPE):
When an object is at a certain height in a gravitational field, it possesses gravitational potential energy. The GPE of an object of mass m at a distance r from the center of the Earth of mass M is given by the equation:

GPE = -GMm/r

Where G is the gravitational constant.

2. Kinetic Energy (KE):
The kinetic energy of an object is the energy it possesses due to its motion. The kinetic energy of an object of mass m moving at a speed v is given by the equation:

KE = (1/2)mv^2

3. Total Mechanical Energy (TME):
The total mechanical energy of an object is the sum of its potential energy and kinetic energy. In this case, since the satellite is in a circular orbit, we can assume that the total mechanical energy is constant throughout the orbit.

TME = GPE + KE

Energy Conservation in Circular Orbit:
In a circular orbit, the gravitational force provides the necessary centripetal force to keep the satellite in orbit. The centripetal force is given by the equation:

F = (mv^2)/r

Since the gravitational force is the centripetal force, we have:

GMm/r^2 = (mv^2)/r

Simplifying this equation, we get:

v^2 = GM/r

Substituting this equation into the equation for kinetic energy, we have:

KE = (1/2)m(GM/r)

Since the total mechanical energy is constant, the change in potential energy must be equal in magnitude but opposite in sign to the change in kinetic energy. In other words:

ΔGPE = -ΔKE

Since the change in potential energy is negative, the change in kinetic energy must be positive. Therefore, the energy required to complete a circular orbit once round the Earth is zero.

Conclusion:
The correct answer is option D: zero. The satellite in a circular orbit around the Earth does not require any additional energy to complete one orbit. The gravitational potential energy is converted into kinetic energy, and vice versa, resulting in a constant total mechanical energy throughout the orbit.
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