Editing Gravity (section)

===Newton's theory of gravitation===
{{main|Newton's law of universal gravitation}}
[[File:Portrait of Sir Isaac Newton, 1689.jpg|thumb|upright|English physicist and mathematician, Sir [[Isaac Newton]] (1642–1727)]]

Before 1684 scientists including [[Christopher Wren]], [[Robert Hooke]] and [[Edmund Halley]] determined that [[Kepler's laws of planetary motion |Kepler's third law]], relating to planetary orbital periods, would prove the inverse square law if the orbits where circles. However the orbits were known to be ellipses. At Halley's suggestion, Newton tackled the problem and was able to prove that ellipses also proved the inverse square relation from Kepler's observations.<ref name=Weinberg-1972/>{{rp|13}}
In 1684, [[Isaac Newton]] sent a manuscript to [[Edmond Halley]] titled ''[[De motu corporum in gyrum]] ('On the motion of bodies in an orbit')'', which provided a physical justification for [[Kepler's laws of planetary motion]].<ref name="Sagan-1997">{{cite book |last1=Sagan |first1=Carl |url=https://books.google.com/books?id=LhkoowKFaTsC |title=Comet |last2=Druyan |first2=Ann |publisher=Random House |year=1997 |isbn=978-0-3078-0105-0 |location=New York |pages=52–58 |author-link1=Carl Sagan |author-link2=Ann Druyan |access-date=5 August 2021 |archive-url=https://web.archive.org/web/20210615020250/https://books.google.com/books?id=LhkoowKFaTsC |archive-date=15 June 2021 |url-status=live |name-list-style=amp}}</ref> Halley was impressed by the manuscript and urged Newton to expand on it, and a few years later Newton published a groundbreaking book called ''[[Philosophiæ Naturalis Principia Mathematica]]'' (''Mathematical Principles of Natural Philosophy''). 

The revolutionary aspect of Newton's theory of gravity was the unification of Earth-bound observations of acceleration with celestial mechanics.<ref name="Longair-2009"/>{{rp|4}} In his book, Newton described gravitation as a universal force, and claimed that it operated on objects "according to the quantity of solid matter which they contain and propagates on all sides to immense distances always at the inverse square of the distances"<ref name="Principa">{{Cite book |title=The Principia, The Mathematical Principles of Natural Philosophy |first=I. |last=Newton |translator-last1=Cohen |translator-first1=I.B. |translator-last2=Whitman |translator-first2=A. |location=Los Angeles |publisher=University of California Press |date=1999}}</ref>{{rp|546}} This formulation had two important parts. First was [[Equivalence principle | equating inertial mass and gravitational mass]]. Newton's 2nd law defines force via <math>F=ma</math> for inertial mass, his law of gravitational force uses the same mass. Newton did experiments with pendulums to verify this concept as best he could.<ref name=Weinberg-1972/>{{rp|11}}

The second aspect of Newton's formulation was the inverse square of distance. This aspect was not new: the astronomer [[Ismaël Bullialdus]] proposed it around 1640. Seeking proof, Newton made quantitative analysis around 1665, considering the period and distance of the Moon's orbit and considering the timing of objects falling on Earth. Newton did not publish these results at the time because he could not prove that the [[Shell theorem| Earth's gravity acts as if all its mass were concentrated at its center]].  That proof took him twenty years.<ref name=Weinberg-1972/>{{rp|13}}

Newton's ''Principia'' was well received by the scientific community, and his law of gravitation quickly spread across the European world.<ref>{{Cite web |title=The Reception of Newton's Principia |url=http://physics.ucsc.edu/~michael/newtonreception6.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://physics.ucsc.edu/~michael/newtonreception6.pdf |archive-date=9 October 2022 |url-status=live |access-date=6 May 2022}}</ref> More than a century later, in 1821, his theory of gravitation rose to even greater prominence when it was used to predict the existence of [[Neptune]]. In that year, the French astronomer [[Alexis Bouvard]] used this theory to create a table modeling the orbit of [[Uranus]], which was shown to differ significantly from the planet's actual trajectory. In order to explain this discrepancy, many astronomers speculated that there might be a large object beyond the orbit of Uranus which was disrupting its<!--Uranus's--> orbit. In 1846, the astronomers [[John Couch Adams]] and [[Urbain Le Verrier]] independently used Newton's law to predict Neptune's location in the night sky, and the planet was discovered there within a day.<ref>{{Cite web |title=This Month in Physics History |url=http://www.aps.org/publications/apsnews/202008/history.cfm |access-date=6 May 2022 |website=www.aps.org |language=en |archive-date=6 May 2022 |archive-url=https://web.archive.org/web/20220506231353/https://www.aps.org/publications/apsnews/202008/history.cfm |url-status=live }}</ref><ref>{{Cite journal |last=McCrea |first=W. H. |date=1976 |title=The Royal Observatory and the Study of Gravitation |url=https://www.jstor.org/stable/531749 |journal=Notes and Records of the Royal Society of London |volume=30 |issue=2 |pages=133–140 |issn=0035-9149}}</ref>

Newton's formulation was later condensed into the  inverse-square law:

<math display="block">F = G \frac{m_1 m_2}{r^2}, </math>where {{mvar|F}} is the force, {{math|''m''<sub>1</sub>}} and {{math|''m''<sub>2</sub>}} are the masses of the objects interacting, {{mvar|r}} is the distance between the centers of the masses and {{math|''G''}} is the [[gravitational constant]] {{physconst|G|after=.|round=3}} While {{math|''G''}} is also called Newton's constant, Newton did not use this constant or formula, he only discussed proportionality. But this allowed him to come to an astounding conclusion we take for granted today: the gravity of the Earth on the Moon is the same as the gravity of the Earth on an apple:
<math display="block">M_\text{earth} \propto a_\text{apple}R_\text{radius of earth}^2 = a_\text{moon}R_\text{lunar orbit}^2 </math>
Using the values known at the time, Newton was able to verify this form of his law. The value of {{math|''G''}} was eventually [[Cavendish experiment|measured]] by [[Henry Cavendish]] in 1797.<ref name="Zee-2013">{{Cite book |last=Zee |first=Anthony |title=Einstein Gravity in a Nutshell |date=2013 |publisher=Princeton University Press |isbn=978-0-691-14558-7 |edition=1 |series=In a Nutshell Series |location=Princeton}}</ref>{{rp|31}}