Answer:
the acceleration due to gravity g at the surface is proportional to the planet radius R (g ∝ R)
Explanation:
according to newton's law of universal gravitation ( we will neglect relativistic effects)
F= G*m*M/d² , G= constant , M= planet mass , m= mass of an object , d=distance between the object and the centre of mass of the planet
if we assume that the planet has a spherical shape, the object mass at the surface is at a distance d=R (radius) from the centre of mass and the planet volume is V=4/3πR³ ,
since M= ρ* V = ρ* 4/3πR³ , ρ= density
F = G*m*M/R² = G*m*ρ* 4/3πR³/R²= G*ρ* 4/3πR
from Newton's second law
F= m*g = G*ρ*m* 4/3πR
thus
g = G*ρ* 4/3π*R = (4/3π*G*ρ)*R
g ∝ R
