Last updated: 2026-06-16

Surface Gravity

Surface gravity is the acceleration that gravity gives to an object at the surface of a planet, moon, or star. It sets how much things weigh, how high you can jump, and how fast a dropped object speeds up. It follows directly from Newton's law of gravitation applied at the body's surface:

$g = \frac{GM}{R^2}$

where $G = 6.674 \times 10^{-11}\ \text{m}^3\text{kg}^{-1}\text{s}^{-2}$ is the gravitational constant, $M$ is the body's mass, and $R$ is its radius. Earth's surface gravity is about $9.81\ \text{m/s}^2$.

The competition between mass and radius is the heart of the formula: gravity grows with mass but falls off with the square of the radius. A body can be very massive yet have modest surface gravity if it is also very large.

Worked Example

Find Mars's surface gravity. Mars has 0.107 times Earth's mass and 0.532 times its radius:

$g_{\text{Mars}} = \frac{G\,(0.107\,M_\oplus)}{(0.532\,R_\oplus)^2} = \frac{0.107}{0.283}\,g_\oplus \approx 0.38\,g_\oplus \approx 3.7\ \text{m/s}^2$

So a person who weighs 70 kg on Earth would have an effective weight of about 27 kg on Mars.

Gravity Across the Solar System

Expressed as a multiple of Earth's gravity, the bodies of the Solar System span a wide range. The Moon sits at 0.17, Mars at 0.38, Venus at 0.90, and Jupiter — despite being a gas giant — at about 2.5, because its enormous radius offsets its huge mass. The Sun tops the list at roughly 28 g. These differences shape each world: low gravity lets small bodies lose their atmospheres to space, while high gravity compresses interiors and thickens atmospheres.

Related Calculations

Surface gravity is the starting point for several other quantities. The escape velocity from a body depends on the same mass and radius, $v_{\text{esc}} = \sqrt{2GM/R}$, and the gravitational force between two bodies uses the same constant $G$. For an object compressed enough that its escape velocity reaches the speed of light, the radius shrinks to the Schwarzschild radius and the body becomes a black hole.