# Newton's 4th law

Gold Member
Why do we not refer to Newton's universal law of gravitation as Newton's 4th law. Why are his first three packaged together: inertial mass, f=ma, action/reaction, while his 4th, f=Gmm/r^2 stands alone?

Because these three laws are the fundamental basis for describing motion in Newtonian mechanics. They are collectively referred to as "Newton's three laws of motion". Obviously his law of universal gravitation doesn't constitute a "4th law of motion", and so there you have it.

AlephZero
Homework Helper
Because that is what Newton did.

He gave the first three numbered "Axioms, or Laws of Motion" in the preface to "Principia".

Most of Book I (about 200 pages of rather dense math, in my translation) is a derivation of the "unversal law of gravitation" and its consequences, starting from the laws of motion and the observational evidence of Kepler's laws of planetary motion, which state what happens to orbits in the solar system, but not why it happens. Newton treats this as an exercise in math, not a "law": if Kepler's "laws" are true, then universal gravitation follows from them.