Question

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. Natividad, Joshua - [e-mail] @theexpertta - tracking id: 1F76-1A-38-41-94BC-19489. In accordance with Expert TA's Terms of Service. copying this information to any solutions sharing website is strictly forbidden. Doing so may result in termination of your Expert TA Account. show answer No Attempt 50% Part (a) Derive an expression for x.

Answer 1

Answer:

$x=\dfrac{D}{1+\sqrt{\dfrac{m}{M}}}$

Explanation:

Mass of moon = m

Mass of planet =M

We know that gravitational force given as

$F=G\dfrac{m_1m_2}{d^2}$

$F'=G\dfrac{m'M}{x^2}$

$F=G\dfrac{m'm}{(D-x)^2}$

Given that force is zero so

F=F'

$G\dfrac{m'm}{(D-x)^2}=G\dfrac{m'M}{x^2}$

$\dfrac{m}{(D-x)^2}=\dfrac{M}{x^2}$

$\dfrac{x}{D-x}=\sqrt{\dfrac{M}{m}}$

$\dfrac{D-x}{x}=\sqrt{\dfrac{m}{M}}$

$x=\dfrac{D}{1+\sqrt{\dfrac{m}{M}}}$