Question

Two identical objects freely floating in space are separated by a distance of 3 m. If they feel a gravitational
attraction of 0.25 N, find the mass of each object.

Answer 1

The Newton's law of universal gravitation says

$$F=G\frac{m_1m_2}{r^2}.$$

Hence, when the objects are identical, the mass of object

$$m=\sqrt{Fr^2/G}$$ $$=\sqrt{0.25\times 3^2/6.67\times 10^{-11}}=1.8\times 10^5\:\rm kg$$