Newton's 4th Law: Unpacking Gravitational Force

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SUMMARY

Newton's universal law of gravitation, expressed as f=Gmm/r^2, is not classified as his 4th law of motion because it does not describe motion directly. The first three laws—inertial mass, f=ma, and action/reaction—are collectively known as "Newton's three laws of motion" and serve as the foundation for Newtonian mechanics. In "Principia," Newton presents these laws as axioms, while the law of universal gravitation is derived from them and is based on observational evidence from Kepler's laws of planetary motion. Thus, the distinction lies in the nature of the laws themselves, with the first three focusing on motion and the fourth addressing gravitational force.

PREREQUISITES
  • Understanding of Newton's three laws of motion
  • Familiarity with gravitational force concepts
  • Basic knowledge of Kepler's laws of planetary motion
  • Mathematical proficiency to interpret f=Gmm/r^2
NEXT STEPS
  • Research the derivation of Newton's universal law of gravitation
  • Study the implications of Kepler's laws on planetary motion
  • Explore the mathematical foundations of Newtonian mechanics
  • Examine the historical context of Newton's "Principia" and its impact on physics
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Students of physics, educators teaching classical mechanics, and anyone interested in the historical development of gravitational theories will benefit from this discussion.

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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?
 
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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:smile:.
 
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.
 

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