Gravitational Field Strength

g = \frac{GM}{r^{2}}

g =

M =

r =

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Constant used — built into this formula, no need to enter

G = 6.6743 \times 10^{-11}\ \text{m}^{3}\text{/(kg}{\cdot}\text{s}^{2}\text{)}

Newtonian constant of gravitation

Learning zone

Divide Newton's law of gravitation by the test mass and what remains is the field itself: g = GM/r², the acceleration any object feels at distance r, regardless of what it is made of. At Earth's surface, g = 6.674 × 10⁻¹¹ × 5.97 × 10²⁴ / (6.371 × 10⁶)² ≈ 9.82 m/s² — matching the measured free-fall value once Earth's spin is accounted for. Cavendish's 1798 torsion-balance measurement of G turned this equation around and, as headlines put it, "weighed the Earth."

The inverse-square fall-off is steep near a planet but gentle far away: on the Moon (M = 7.35 × 10²² kg, r = 1.737 × 10⁶ m) the same formula gives 1.63 m/s², a sixth of Earth's pull, which is why Apollo astronauts bounded rather than walked. And at the ISS's altitude, g is still about 8.7 m/s² — nearly nine-tenths of surface gravity. Astronauts float not because gravity is absent, but because they and their station are falling together.

Gravitational Field Strength

g = \frac{GM}{r^{2}}

Where

$g$ = Field strength
$M$ = Central mass
$r$ = Distance

Missing one of these? Work it out first, then come back

Field strength — Newton's Second Law, Final Velocity (Uniform Acceleration)
Central mass — Orbital Velocity, Orbital Period
Distance — Speed, Distance & Time, Apparent Brightness (Inverse-Square Law)

Part of this formula set

Gravitation and orbital mechanics

8 formulasNewton's inverse-square law and what falls out of it in orbit — field strength, orbital speed and period, Kepler's third law, and escape velocity.