Definition

Gravitational field

g = \frac{F _{g}}{m} = - \frac{GM}{r ^{2}} r

Statement

Force per unit mass at a point, directed toward the source mass M.

Symbols and units

$g$	gravitational field	N/kg
$F_{g}$	gravitational force on the test mass	N
$m$	test mass at the point	kg
$G$	gravitational constant	N·m²/kg²
$M$	source mass	kg
$r$	distance from M	m

When it applies

Any point in space around a source mass M.

Derivation

Defined exactly as the electric field is defined, dividing the force by the mass that would feel it:

g = \frac{F _{g}}{m} = - \frac{GM}{r ^{2}} r

Worked examples

Field at low Earth orbit altitude

At r = 6.77×10⁶ m (≈400 km up):

g = \frac{GM}{r ^{2}} = \frac{( 6.674 \times 1 0 ^{- 11} ) ( 5.97 \times 1 0 ^{24} )}{( 6.77 \times 1 0 ^{6} ) ^{2}} \approx 8.7 m/s^{2}

Still nearly 90% of surface gravity — astronauts in low orbit are not in a gravity-free region; they are in free fall.

Watch out for

g near Earth's surface (9.8 m/s²) is this same field evaluated at r = R_Earth — not a separate constant.

Connects to