Question

The gravitational field strength of Planet Wobegon can be approximated as 3 N/kg. What is the gravitational field strength of a planet that has half the mass of Wobegon and 1/3 the radius?

Answer 1

27 N/kg

Step-by-step explanation:

g = G * M / r^2

where:

G is the gravitational constant

M is the mass of the planet

r is the radius of the planet

M_new = M_Wobegon / 2

r_new = r_Wobegon / 3

g_new = G * M_new / r_new^2

g_new = G * (M_Wobegon / 2) / ((r_Wobegon / 3)^2)

g_new = G * M_Wobegon / (r_Wobegon^2 / 9)

g_new = 9 * G * M_Wobegon / r_Wobegon^2

g_new = 9 * 3 N/kg

g_new = 27 N/kg