d^2χ/dt^2=-k^2(1+m) χ/r^3+Σi k^2mj [(χj-χ/ρj^3) – (χj/rj^3)]

This is the general equation of motion of a planet or comet (m) with the sun as origin of coordinates. m subscript j is the action of disturbing planets. This same equation can be used for the motion of a satellite around its primary.

Newton only describes the forces acting between two point masses that are inertial, not rotating or subject to acceleration. If the distance between m subscript a and m subscript b is r, then thf force acting between them is

F=k^2mamb/r^2

K depends on units of mass, time and length. If the sun, for example is taken as unity and mean solar day and astronomical unit as length then k= Gaussian constant (0.01720209895) this is exact.