How much work is done by the force of gravity on the moon after one complete orb

Question

How much work is done by the force of gravity on the moon after one complete orbit around the Earth? Given: distance from the moon to earth = 3.8 x 10^8 meters; mass of the moon = 7.3 x 10^22 kg; speed of the moon relative to the earth = 1 km/s. Work = Force*distance = (mass*acceleration*distance). Can I use F_gravity = GMm / R to obtain the magnitude of the force, and multiply that value with Circumference of orbit = 2*Pi*R_distance between the Earth and moon? In that case, I got W_gravity = 1.83 x 10^38 J ... If this is correct but there is another means to get the value for acceleration for m*a*d = F, please let me know. Many thanks!

Explanation / Answer

here,

distance from the moon to earth, r = 3.8 * 10^8 m
mass of the moon, m = 7.3 * 10^22 kg
speed of the moon relative to the earth, v = 1 km/s

Work done due to gravity force will be as gravity force is a conservative force.

A conservative force is a force with the property that the work done in moving a particle between two points is independent of the taken path.

Equivalently, if a particle travels in a closed loop, the net work done (the sum of the force acting along the path multiplied by the distance travelled) by a conservative force is zero

Work done = F * D * Cos90
w = 0 J

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