What is Newton's law of universal gravitation?

F = G m₁ m₂ / r², where G = 6.674 × 10⁻¹¹ N m²/kg². Every pair of point masses attracts the other along the line joining them with this magnitude.

Is r measured from the surface or the centre?

From the centre of each body. For a satellite at altitude h above Earth, r = R_Earth + h, not just h.

What is gravitational field strength?

g = F/m = GM/r². The field strength at a point is the force per unit mass on a test mass placed there, measured in N/kg or m/s².

Gravitational field lines spread out over a sphere of area 4πr². The field strength is inversely proportional to that area, giving an inverse-square law in distance.

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Physics

Universal gravitation calculator

Compute the gravitational attraction between any two masses, with presets for Earth-Moon, Sun-Earth and Earth-satellite pairs.

Inputs

PresetMass m₁ (kg)Mass m₂ (kg)Separation r (m)Centre to centre distance

G = 6.674e-11 N m²/kg²

Common bodies (mass, radius)

Earth: M = 5.972e+24 kg, R = 6.371e+6 m
Moon: M = 7.342e+22 kg, R = 1.737e+6 m
Mars: M = 6.417e+23 kg, R = 3.390e+6 m
Sun: M = 1.989e+30 kg, R = 6.960e+8 m
Jupiter: M = 1.898e+27 kg, R = 6.991e+7 m

Result

Gravitational force F

4348N

Field due to m₂ at m₁

7.281e-22m/s²

Field due to m₁ at m₂

8.696m/s²

F = G m₁ m₂ / r², g = G M / r².

How this calculator works

The calculator multiplies the two masses, divides by the square of their separation, and multiplies by G = 6.674 × 10⁻¹¹ N m²/kg² to get the gravitational force. It then computes the gravitational field strength each mass would produce at the location of the other.

Common questions

What is Newton's law of universal gravitation?: F = G m₁ m₂ / r², where G = 6.674 × 10⁻¹¹ N m²/kg². Every pair of point masses attracts the other along the line joining them with this magnitude.
Is r measured from the surface or the centre?: From the centre of each body. For a satellite at altitude h above Earth, r = R_Earth + h, not just h.
What is gravitational field strength?: g = F/m = GM/r². The field strength at a point is the force per unit mass on a test mass placed there, measured in N/kg or m/s².
Why is r squared?: Gravitational field lines spread out over a sphere of area 4πr². The field strength is inversely proportional to that area, giving an inverse-square law in distance.