At what distance from the Earth will a spacecraft be equally attracted by the Earth and the Moon? The distance from the Earth to the Moon is approximately $385000km$, and the mass of the Earth is about $82$ that of the Moon. Gravitational attraction between two bodies varies directly as the product of their masses and inversely as the square of distance between them.
The answer is $347 000 km$ but I can't seem to set up the question correctly to get there.
Thanks.
Match the gravitational forcesas follows,
$$G\frac{m_em}{d_e^2}= G\frac{m_mm}{(d-d_e)^2}$$
Solve to get the distance from the earth,
$$d_e=\frac{d}{\sqrt{\frac{m_m}{m_e}}+1}=\frac{385000 }{ \sqrt{ \frac1{82}}+1}=346712 km$$