A moon of mass m and radius a is orbiting a planet of mass M and of radius b at a distance d (center-to-center) in a circular orbit. Derive an expression for the total mechanical energy E of the moon in terms of m, M, d and the gravitational constant G.

Question
Asked Dec 13, 2019
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A moon of mass m and radius a is orbiting a planet of mass M and of radius b at a distance d (center-to-center) in a circular orbit.

 Derive an expression for the total mechanical energy E of the moon in terms of mMd and the gravitational constant G

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Expert Answer

Step 1

Given:

Mass of moon = m

Radius of moon = a

Mass of planet =  M

Radius of planet = b

Distance between the center of moon and planet = d

Step 2

Since moon is rotating in the circular path. Therefore, centripetal force experienced by the moon is

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mv? F. where, mis the mass of moon vis the velocity of moon dis the center to center distance between the moon and planet

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Step 3

Gravitational force experienced by...

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GMm Fe d? where, mis the mass of moon M is the mass of planet dis the center to center distance between the moon and planet Gis the gravitational constant

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Science

Physics

Gravitation