Question

At a certain point between Earth and the Moon, the net gravitational force exerted on an object by Earth and the Moon is zero. The Earth-Moon centre-to-centre seperation is 3.84 x 10^5 km. The mass of the Moon is 1.2% the mass of Earth . . a) where is this point located? Are there any other such points? . . b) What is the physical meaning of the root of the quadratic equation whose value exceeds the Earth-Moon distance?

Answer 1

The related equation is
F = G mE mM/d^2
Given the distance between the two:
F = G mE mM/(384000-d^2)

mM is 1.2 of mE and applying law of proportionality:

mE/d^2 = 0.012 mE/(384000-d^2)

Solving for d using the calculator, the answer is
d1 =5.88x10^5 km and d2 =2.86 x10^5 km.
The net gravitation is the distance where d2 =2.86 x10^5 km. There is no physical meaning when d1 =5.88x10^5 km