Question

 Suppose that in the distant future, astronauts are exploring a planet in another solar system. They find that the radius of the planet is 6.8 x 10³ km and the acceleration due to gravity on its surface is 15.3 m/s². What is the mass of the planet?  

Answer 1

By the law of universal gravitation:

$$mg=\frac{GMm}{R^2},\\\space\\ M=\frac{gR^2}{G}=1.06·10^{25}\text{ kg}.$$