How this calculator works
Every pair of masses attracts. The inverse-square law makes the attraction four times weaker when separation doubles. For spherical, symmetric bodies outside one another, their centres can be treated as point masses. This Newtonian model omits relativistic effects and nonspherical mass distributions. G is taken as the CODATA 2022 central value; its measurement uncertainty is not propagated.
Formula
F = G m1 m2/r²; r = sqrt(G m1 m2/F); m1 = Fr²/(Gm2); G = 6.67430 × 10^-11 m³ kg^-1 s^-2.
Worked example
Masses of 2 kg and 3 kg separated by 2 m attract with 1.001145 × 10^-10 N. Two 1 kg masses at 2 m attract with 1.668575 × 10^-11 N.
Advertisement
Frequently asked questions
Is separation measured from the surfaces?
No. Enter centre-to-centre distance for this model.
Why are laboratory forces so small?
G is very small in SI units, so ordinary masses exert tiny mutual gravitational forces.
Can I use this inside a planet?
Not by treating the whole planet as a point mass. Only the enclosed mass contributes for an ideal spherical distribution.