NSW · HSCModule 5
Universal gravitation calculator
Compute the gravitational attraction between any two masses, with presets for Earth-Moon, Sun-Earth and Earth-satellite pairs.
Inputs
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.
For the worked example, see our dot point answer on Newton's law of universal gravitation.
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.