Question

This question is kind of urgent, I'd really appreciate help (setting up equation).

At what distance in kilometers from the surface of the earth on a line from center to center would the gravitational force of the earth on a body be exactly balanced by the gravitational force of the moon on the body?

Answer 1

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Answer 2

I've solved to this point, but not sure what to do with r2. \[(\sqrt{M1})(R-r2)+==\]

Answer 3

I am not sure if your result is valid, but there is a trick to make r2 disappear!
This can be easily done by observing that r1+r2=R.

\[\frac{GM_{e}m}{r_{1}^{2}}=\frac{GM_{m}m}{r_{2}^{2}}\]
after some manipulation,
\[r_{2}=\sqrt{\frac{M_{m}}{M_{e}}r_{1}^{2}}\]
Sub R=r2+r1, where R is the distance from the center of the earth to the center of the moon,
\[r_{1}=\frac{R}{\sqrt{\frac{M_{m}}{M_{e}}+1}}\]

For your question you must minus the Earth's radius from r1

Answer 4

And, of course, subtract out the radius of the Earth from r1.