Editing Newton's laws of motion (section)

=== Momentum conservation and the third law ===
[[File:JKepler (cropped).jpg|alt=Portrait of Johannes Kepler|left|thumb|151x151px|Johannes Kepler <br/>(1571–1630)]]
[[Johannes Kepler]] suggested that gravitational attractions were reciprocal — that, for example, the Moon pulls on the Earth while the Earth pulls on the Moon — but he did not argue that such pairs are equal and opposite.<ref>{{Cite book |last=Jammer |first=Max |title=Concepts of Force: A Study in the Foundations of Dynamics |date=1999 |publisher=Dover Publications |isbn=978-0-486-40689-3 |location=Mineola, N.Y. |pages=91, 127 |oclc=40964671 |author-link=Max Jammer |orig-date=1962}}</ref> In his ''[[Principles of Philosophy]]'' (1644), Descartes introduced the idea that during a collision between bodies, a "quantity of motion" remains unchanged. Descartes defined this quantity somewhat imprecisely by adding up the products of the speed and "size" of each body, where "size" for him incorporated both volume and surface area.<ref>{{Cite web |last=Slowik |first=Edward |date=2021-10-15 |title=Descartes' Physics |url=https://plato.stanford.edu/entries/descartes-physics/ |access-date=2022-03-06 |website=[[Stanford Encyclopedia of Philosophy]]}}</ref> Moreover, Descartes thought of the universe as a [[Plenum (physics)|plenum]], that is, filled with matter, so all motion required a body to displace a medium as it moved. 

During the 1650s, Huygens studied collisions between hard spheres and deduced a principle that is now identified as the conservation of momentum.<ref>{{Cite journal |last=Erlichson |first=Herman |date=February 1997 |title=The young Huygens solves the problem of elastic collisions |url=http://aapt.scitation.org/doi/10.1119/1.18659 |journal=[[American Journal of Physics]] |language=en |volume=65 |issue=2 |pages=149–154 |doi=10.1119/1.18659 |bibcode=1997AmJPh..65..149E |issn=0002-9505}}</ref><ref>{{Cite journal |last=Smith |first=George E. |date=October 2006 |title=The vis viva dispute: A controversy at the dawn of dynamics |url=http://physicstoday.scitation.org/doi/10.1063/1.2387086 |journal=[[Physics Today]] |language=en |volume=59 |issue=10 |pages=31–36 |doi=10.1063/1.2387086 |bibcode=2006PhT....59j..31S |issn=0031-9228}}</ref> [[Christopher Wren]] would later deduce the same rules for [[Elastic collision|elastic collisions]] that Huygens had, and [[John Wallis]] would apply momentum conservation to study [[Inelastic collision|inelastic collisions]]. Newton cited the work of Huygens, Wren, and Wallis to support the validity of his third law.<ref>{{Cite journal |last=Davies |first=E. B. |date=2009 |title=Some Reflections on Newton's "Principia" |url=https://www.jstor.org/stable/25592244 |journal=[[The British Journal for the History of Science]] |volume=42 |issue=2 |pages=211–224 |doi=10.1017/S000708740800188X |jstor=25592244 |s2cid=145120248 |issn=0007-0874}}</ref>

Newton arrived at his set of three laws incrementally. In a [[De motu corporum in gyrum|1684 manuscript written to Huygens]], he listed four laws: the principle of inertia, the change of motion by force, a statement about relative motion that would today be called [[Galilean invariance]], and the rule that interactions between bodies do not change the motion of their center of mass. In a later manuscript, Newton added a law of action and reaction, while saying that this law and the law regarding the center of mass implied one another. Newton probably settled on the presentation in the ''Principia,'' with three primary laws and then other statements reduced to corollaries, during 1685.<ref>{{cite book|first=George E. |last=Smith |chapter=Newton's Laws of Motion |title=The Oxford Handbook of Newton |isbn=978-0-199-93041-8 |publisher=Oxford University Press |doi=10.1093/oxfordhb/9780199930418.013.35 |date=December 2020 |editor-first1=Eric |editor-last1=Schliesser |editor-first2=Chris |editor-last2=Smeenk |oclc=972369868 |no-pp=yes |at=Online before print}}</ref>