Total energy of a body in a circular orbit

In summary, the conversation discusses the movement of a particle under the influence of a single central force. It is mentioned that the force always acts towards the center, resulting in zero work done by the force and conservation of energy. The potential energy at a particular radius can be calculated, but there is uncertainty on how to find the kinetic energy of the particle. The force from the potential field is identified as the centripetal force responsible for the object following a circular path.
  • #1
Jahnavi
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Homework Statement


circular path.jpg


Homework Equations



The Attempt at a Solution



Is the particle moving under the influence of a single central force ?

Since the force always acts towards the center , work done by the force is zero . Energy is conserved . Potential energy at a particular radius can be found . But how do we find the kinetic energy of the particle ?
 

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  • #2
Jahnavi said:
But how do we find the kinetic energy of the particle
The force from the potential field is the centripetal force that makes the object follow a circular path
 
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  • #3
BvU said:
The force from the potential field is the centripetal force that makes the object follow a circular path

Thanks !
 
Last edited:
  • #4
You're welcome
 
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Related to Total energy of a body in a circular orbit

What is the total energy of a body in a circular orbit?

The total energy of a body in a circular orbit is the sum of its potential energy and kinetic energy. It is a constant value and remains the same throughout the orbit.

How is the total energy of a body in a circular orbit calculated?

The total energy of a body in a circular orbit can be calculated using the formula E = -GmM/2r, where G is the gravitational constant, m is the mass of the orbiting body, M is the mass of the central body, and r is the radius of the orbit.

What is the significance of the total energy of a body in a circular orbit?

The total energy of a body in a circular orbit determines the stability of the orbit. If the total energy is negative, the orbit is bound and the body will continue to orbit indefinitely. If the total energy is positive, the orbit is unbound and the body will eventually escape the gravitational pull of the central body.

How does the total energy of a body in a circular orbit change with the radius of the orbit?

The total energy of a body in a circular orbit is inversely proportional to the radius of the orbit. As the radius increases, the total energy decreases and vice versa.

Can the total energy of a body in a circular orbit be zero?

Yes, the total energy of a body in a circular orbit can be zero. This occurs when the orbit is at the critical radius, where the gravitational potential energy and kinetic energy are equal in magnitude.

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