Question

8. The gravitational field strength between two objects

is the sum of two vectors pointing in opposite
directions. Somewhere between the objects, the
vectors will cancel, and the total force will be zero.
Determine the location of zero force as a fraction of
the distance r between the centres of two objects
of mass m, and m₂.

Answer 1

F1 = G M1 m / x^2 gravitational force on test mass m due to M1

F2 = G M2 m / (R - x)^2 gravitational force on test mass m due to M2

M1 / x^2 = M2 / (R - x)^2

(R - x)^2 / x^2 = M2 / M1

(R - x) / x = (M2 / M1)^1/2 where x is distance from M1 and R is total distance between objects

Check: x = R / 2 then M1 = M2 as it should