Question

Planet X has a diameter that is 3 times the diameter of Earth and a mass that is 30 times the mass of Earth. In SI units, what is the gravitational acceleration on planet X?

Answer 1

The gravitational acceleration on planet X is 32.7 m/s²

Explanation:

The acceleration due to gravity is given by

                $g=\frac{GM}{R^2}$

where G is gravitational constant, M is mass and R is radius.

For earth we have

                  g = 9.81 m/s²

            That is

                  $\frac{GM_e}{R_e^2}=9.81m/s^2$

For planet X we have

                   $R=3R_e\\\\M=30M_e$

Substituting

              $g=\frac{GM}{R^2}=\frac{G\times 30M_e}{(3R_e)^2}=\frac{30}{9}\times 9.81\\\\g=32.7m/s^2$

The gravitational acceleration on planet X is 32.7 m/s²