Question

At what distance from the center of the Earth is the gravitational pull towards the Earth the exact same as the pull towards the Moon? Show all calculations

Answer 1

since the force due to moon and earth on mass m is same so,\[\[\frac{GM_{moon}m}{r_{moon}^2}=\frac{GM_{earth}m}{r_{earth}^2}\]\]

or,

\[\frac{M_{moon}}{r_{moon}^2}=\frac{M_{earth}}{r_{earth}^2}\]

or,

\[r_{earth}=\sqrt{\frac{M_{earth}}{M_{moon}}}r_{moon}\]