Calculators/Physics/Gravitational field

Gravitational field

Field strength g · gravitational force · celestial bodies

Gravitational field — illustration
g = G·M / r²
9.8195 m/s²

Gravitational constant G = 6.674·10⁻¹¹ N·m²/kg². At Earth's surface (M = 5.97·10²⁴ kg, r = 6371 km) the field strength g ≈ 9.81 m/s². Scientific notation: e.g. 5.97e24.

The gravitational field strength at a distance rr from a mass MM is the acceleration it gives to bodies:

g=G Mr2g=\frac{G\,M}{r^2}

and the gravitational force between masses MM and mm (Newton's law of universal gravitation):

F=G M mr2F=\frac{G\,M\,m}{r^2}

where G=6.674⋅10−11 N⋅m2kg2G=6.674\cdot10^{-11}\ \tfrac{\text{N·m}^2}{\text{kg}^2}. Both quantities fall off with the square of the distance. The presets contain the masses and radii of Earth, the Moon, Mars and the Sun — for Earth this gives the familiar g≈9.81 ms2g\approx9.81\ \tfrac{\text{m}}{\text{s}^2}.

Examples

Earth's surface (M=5.97·10²⁴, r=6371 km)
→ g = GM/r² ≈ 9.81 m/s²
Moon's surface
→ g ≈ 1.62 m/s² (about 6× less than on Earth)

Frequently asked questions

Why are you lighter on the Moon?+

Because the Moon has a smaller mass, so the field strength g ≈ 1.62 m/s² — about six times less than on Earth. The mass of a body does not change, but its weight (F = mg) decreases.

How does the field strength depend on altitude?+

It falls off with the square of the distance from the centre of the planet (g ~ 1/r²). At high altitude g is noticeably smaller than at the surface.

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