Question

"two planets have the same mass, but planet a has 3 times the radius of planet

b. how do the surface gravities of the two planets compare?"

Answer 1

The gravitational acceleration on the surface of planet A is:

`g_A = (GM_A)/(r_A^2)`
where G is the gravitational constant,
`M_A` is the mass of planet A and
`r_A` its radius.

Similarly, the gravitational acceleration on the surface of planet B is:

`g_B = (GM_B)/(r_B^2)`

The ratio between the gravitational acceleration on planet A and B becomes:

`(g_A)/(g_B)= (GM_A / r_A^2)/(GM_B/r_B^2) = (M_A r_B^2)/(M_B r_A^2)`

The problem says that the two masses are equal:
`M_A = M_B` while planet A has 3 times the radius of planet B:
`r_A = 3 r_B`. Substituting into the ratio, we get:

`(g_A)/(g_B) = (M_B r_B^2)/(M_B (3 r_B)^2) = (1)/(9)`

so, gravity on planet B is 9 times stronger than planet A.