When a small object orbits a massive one, such as a moon going about its planet, say, it experiences an acceleration towards it. In perfect circular motion (an approximation), that acceleration is: r⍵²,where r is the radius of the orbit and ⍵ is its angular speed, which is 2π/t, where t is its orbital period. We know this from Newton.
We know also from Kepler's third law that
r³/t² = k,
where k is the Kepler 'constant' for that system.
Hence the acceleration
r⍵² = r4π²k/r³ = 4π²k/r²
This is the famous inverse-square law for the gravitational force (also from Newton of course).
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