A spacecraft is on a journey to the moon. The masses of Earth and the moon are respectively 5.98x10^24kg and 7.35x10^22kg. The distance between centers of Earth and the moon is 3.85x10^8m. At what point , as measured from the center of Earth , does the gravitational force exerted on the craft by Earth precisely balance the gravitational force exerted by the moon ?

Question

A spacecraft is on a journey to the moon. The masses of Earth and the moon are respectively  5.98x10^24kg and 7.35x10^22kg. The distance between centers of Earth and the moon is 3.85x10^8m. At what point , as measured from the center of Earth , does the gravitational force exerted on the craft by Earth precisely balance the gravitational force exerted by the moon ?

anonymous · Answer

The question is when is F(Moon)=F(Earth) and you know Newton's equation for the force of gravity.
$$F_{g}=G \frac{m_{1} m_{2}}{r^2}$$
Where r is the distance between the masses.
Hint:
|dw:1337461821815:dw|
You would expect the equilibrium point to be near the Moon since it has lower mass.