Answer to Question #283691 in Physics for duo

Question

Leaving the distance between the 253 kg and the 604 kg masses fixed, at what distance from the 604 kg mass (other than infinitely remote ones) does the 39 kg mass experience a net force of zero?

Answer 1

By Newton's law of universal gravitation:

$$G\dfrac{M_1m}{x^2}=G\dfrac{M_2m}{(d_{12}-x)^2},\\\space\\ \dfrac{M_1}{x^2}=\dfrac{M_2}{(d_{12}-x)^2},\\\space\\ x^2(M_1-M_2)-2xd_{12}M_1+d_{12}^2M_1=0.$$

This is the equation for the distance from mass of m = 39 kg to the mass of M₁ = 604 kg.