Gravitational Field Strength (Surface Gravity)

Gravitational Field Strength (Surface Gravity)

Every planet, moon, or star produces a gravitational field proportional to its mass and inversely proportional to the square of the distance from its center — at the surface, this gives the familiar "surface gravity" that determines how much objects weigh there. Comparing surface gravities across bodies explains why an astronaut can leap so much higher on the Moon than on Earth.This same relationship, applied instead at orbital altitude rather than at the surface, underlies satellite orbit design; applied at the surface it is what mission planners use to work out how much a lander's structure and legs need to withstand on touchdown at a body with unfamiliar gravity.

Newton's law of gravitation gives the surface field strength as g = GM/r². where G_grav is the gravitational constant, M_planet is the mass of the body, r_planet is its radius, and g_surf is the resulting surface gravitational acceleration.

Apply Newton's law of gravitation at the surface: the mass sets the strength of the pull while the radius squared in the denominator means a larger body of the same mass has weaker surface gravity.

Results

With Earth-like mass and radius, the result comes out very close to the familiar 9.8 m/s², confirming the formula against a value everyone has an intuitive feel for. Plugging in a different body's mass and radius — the Moon, at roughly 1/6th Earth's surface gravity, or a neutron star, at values millions of times higher — shows immediately how dramatically surface gravity varies across the range of astronomical bodies.

Assumptions & limitations

• Spherically symmetric mass distribution.
• Point evaluated at the surface (radius r from the center).
• No rotation-induced centrifugal correction included.
• Body treated as isolated (no other significant nearby masses).

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