The gravitational potential energy of a particle of mass m moving under the influence of a fixed mass M is given by - , where G

Question

10 months ago

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The gravitational potential energy of a particle of mass m moving under the influence of a fixed mass M is given by - , where G

is the universal gravitational constant and r is the distance between the masses. What is the total energy of the mass m if it is in a circular orbit about mass M

Physics

1 answer:

djverab [1.8K] · Answer 1 · 2024-03-08T08:26:48+03:00

-GMm/2r is the total energy of the mass m if it is in a circular orbit about mass M.

Given

A particle of mass m moving under the influence of a fixed mass's M, gravitational potential energy of formula -GMm/r, where r is the separation between the masses and G is the gravitational constant of the universe.

As the Gravity Potential energy of particle = -GMm/r

Total energy of particle = Kinetic energy + Potential Energy

As we know that

Kinetic energy = 1/2mv²

Also, v is equals to square root of GM/r

v = √GM/r

Put the value of v in the formula of kinetic energy

We get,

Kinetic Energy = GMm/2r

Total Energy = GMm/2r + (-GMm/r)

= GMm/2r - GMm/r

= -GMm/2r