Question

Weight and g: Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B

Answer 1

Answer:

the radius of planet B is $\sqrt{2}$ times the radius of planet A

Explanation:

The surface gravity of a planet is given by

$g=\frac{GM}{R^2}$

where

G is the gravitational constant

M is the mass of the planet

R is the radius of the planet

For the two planets in the problem, we have:

$g_A = g_B$ (same gravity)

$M_B = 2 M_A$ (planet B has twice the mass of planet A)

So we can write

$\frac{GM_A}{R_A^2}=\frac{GM_B}{R_B^2}\\\frac{M_A}{R_A^2}=\frac{2M_A}{R_B^2}\\R_B^2 = 2R_A^2 \rightarrow R_B = \sqrt{2} R_A$

so, the radius of planet B is $\sqrt{2}$ times the radius of planet A.