The center of a moon of mass m is a distance D from the center of a planet of mass M. At some distance x from the center of the planet, along a line connecting the centers of planet and moon, the net force on an object will be zero. (a)  Derive an expression for x.  (b)  If the net force is zero a distance 2/3 D from the planet, what is the ratio R of the mass of the planet to the mass of the moon, M/m?

Question
Asked Oct 11, 2019
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 The center of a moon of mass m is a distance D from the center of a planet of mass M. At some distance x from the center of the planet, along a line connecting the centers of planet and moon, the net force on an object will be zero.

 

(a)  Derive an expression for x

 

(b)  If the net force is zero a distance 2/3 D from the planet, what is the ratio R of the mass of the planet to the mass of the moon, M/m

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Expert Answer

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Step 1

(a) Equate the gravitational force due to the moon and the force due to the planet on the object

GMm
Gmm
(D-x)
X
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GMm Gmm (D-x) X

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Step 2
м
(D-x
т
х
D-x
т
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м (D-x т х D-x т

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Step 3

Solve the above equ...

xm=(D-x)M
D M
D M
or
(Vm+M
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xm=(D-x)M D M D M or (Vm+M

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