Physics

Physics

Problem

On an exoplanet the surface acceleration due to gravity is 15 m/s215\,\text{m/s}^2. Assuming the planet’s average density is 5.5×103 kg/m35.5\times10^{3}\,\text{kg/m}^3 (the same as Earth) and using G=6.67×10−11 N m2/kg2G = 6.67\times10^{-11}\,\text{N m}^2\text{/kg}^2, estimate the radius of the planet.
Intuitive explanation

The key is connecting surface gravity to the planet's physical properties using the gravitational acceleration formula. Since g=GMR2g = \frac{GM}{R^2} and mass relates to density and volume (M=ρ⋅43πR3M = \rho \cdot \frac{4}{3}\pi R^3), you can substitute to get gg in terms of radius and density alone. This lets you solve for RR without needing the planet's mass directly—a powerful move when density is given.

Intuitive explanation

The key is connecting surface gravity to the planet's physical properties using the gravitational acceleration formula. Since g=GMR2g = \frac{GM}{R^2} and mass relates to density and volume (M=ρ⋅43πR3M = \rho \cdot \frac{4}{3}\pi R^3), you can substitute to get gg in terms of radius and density alone. This lets you solve for RR without needing the planet's mass directly—a powerful move when density is given.

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