Formulas & tables/Physics/Gravitation/Gravitational acceleration at the surface

Gravitational acceleration at the surface

g = \dfrac{GM}{R^2}

Result unit: m/s²

What it describes

The gravitational acceleration at the surface of a body of mass M and radius R. It explains why g differs on every planet.

g

gravitational acceleration

[m/s²]

G

gravitational constant

[N·m²/kg²]

M

mass of the celestial body

[kg]

R

radius of the body

[m]

From the law of universal gravitation F=GMm/R² and F=mg: the mass m cancels, leaving g=GM/R².

When you compute g for any body, compare the gravity of planets, or find the weight on another planet.

g of Earth (M=5.97·10²⁴ kg, R=6.37·10⁶ m)?

Substitutiong = 6.674·10⁻¹¹·5.97·10²⁴ / (6.37·10⁶)²

Resultg ≈ 9.81 m/s².

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