Two planets have the same density but different radii. Planet A has twice the radius of Planet B. How does the acceleration due to gravity on Planet A compare to that on Planet B?

Core Concept

The acceleration due to gravity on a planet's surface is g = GM/R². Since the planets have the same density ρ, we can express mass in terms of density and radius: M = (4/3)πR³ρ. Substituting this into the gravity equation: g = G(4/3)πR³ρ/R² = (4/3)πGρR. Therefore, g is directly proportional to R. If Planet A has twice the radius of Planet B, then g_A = 2g_B. Option A is incorrect because gravity depends on radius, not just density. Option C and D would be correct if the relationship were quadratic or cubic, but it's linear.