Question

Planet X has a mass 7.27 times that of the

Earth and a radius 4.13 times the radius of
the Earth.
What is the acceleration due to gravity on
the surface of Planet X, measured in units of g
(the gravitational acceleration on the surface
of the Earth)?

Answer 1

0.426g

Step-by-step explanation:

Since the gravitational acceleration on a planet is in the following formula:

`g = G(M)/(R^2)`

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

So if Planet X has a mass 7.27 times that of Earth and radius of 4.13 that of Earth, the ratio in gravitational acceleration g shall be

`(g_X)/(g_E) = (GM_X/R_X^2)/(GM_E/R_E^2)`

`(g_X)/(g) = (M_X)/(M_E)((R_E)/(R_X))^2`

`(g_X)/(g) = (7.27)/(4.13^2) = 0.426`

`g_X = 0.426g`