Final answer:
This Physics problem requires the use of the universal law of gravitation to determine the exact distance at which a 72.6 kg mass experiences no net gravitational force from two other fixed masses.
Step-by-step explanation:
The question concerns the concept of gravitational force and specifically asks at what distance a 72.6 kg mass should be placed from a 712 kg mass so that it experiences a net gravitational force of zero, given that the distance between the 181 kg and 712 kg masses is fixed. This is a problem that entails using the universal law of gravitation, which states that the force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
To solve this problem, the net force on the 72.6 kg mass due to the two other masses (181 kg and 712 kg) must be set to zero. By establishing two equations that represent the gravitational forces exerted on the 72.6 kg mass by the other two masses and setting them equal to one another, we can solve for the required distance. Therefore, we'll use the gravitation equation F = G(m1*m2)/r², where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the centers of the masses.