Leaving the distance between the 181 kg and the 712 kg masses fixed, at what distance from the 712 kg mass (other than infinitely remote ones) does the 72.6 kg mass experience a net force of zero? Answer in units of m

The force due to gravitation is equal to zero for each of the masses.

M1 = 181kg

M2 = 712kg

m = 72.6kg

The distance between M1 and M2 is said to be fixed, therefore no value should be given I. e it's a constant.

From the formula for gravitational force we have that

F = GMm/r^2

GmM1 / (d-r) ^2. = GmM2/r^2

where r is the distance between the 72.6 kg and 712kg

d is the distance between M1 and M2

Solving mathematically

r (√M1+√M2) = d√M2

r = d√M2/√M1 + √M2

d*26.68 / 13.45+26.68

d*26.68/40.13

r = 0.665d