Editing Inverse-square law (section)

===Gravitation===
[[Gravity|Gravitation]] is the attraction between objects that have mass. Newton's law states:

{{quote|The gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance. The force is always attractive and acts along the line joining them.<ref name=Newton1>Proposition 75, Theorem 35: p. 956 – I.Bernard Cohen and Anne Whitman, translators: [[Isaac Newton]], ''The Principia'': [[Mathematical Principles of Natural Philosophy]]. Preceded by ''A Guide to Newton's Principia'', by I.Bernard Cohen. University of California Press 1999 {{ISBN|0-520-08816-6}} {{ISBN|0-520-08817-4}}</ref>}}

<math display="block">F=G\frac{m_1 m_2}{r^2}</math>

If the distribution of matter in each body is spherically symmetric, then the objects can be treated as point masses without approximation, as shown in the [[shell theorem]].  Otherwise, if we want to calculate the attraction between massive bodies, we need to add all the point-point attraction forces vectorially and the net attraction might not be exact inverse square. However, if the separation between the massive bodies is much larger compared to their sizes, then to a good approximation, it is reasonable to treat the masses as a point mass located at the object's [[center of mass]] while calculating the gravitational force.

As the law of gravitation, this [[Law of universal gravitation|law]] was suggested in 1645 by [[Ismaël Bullialdus]]. But Bullialdus did not accept [[Kepler's laws of planetary motion|Kepler's second and third laws]], nor did he appreciate [[Christiaan Huygens]]'s solution for circular motion (motion in a straight line pulled aside by the central force).  Indeed, Bullialdus maintained the sun's force was attractive at aphelion and repulsive at perihelion. [[Robert Hooke]] and [[Giovanni Alfonso Borelli]] both expounded gravitation in 1666 as an attractive force.<ref>Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses. See page 239 in: {{Cite book |title=General history of astronomy |date=2009 |publisher=[[Cambridge University Press]] |isbn=978-0-521-54205-0 |editor-last=Taton |editor-first=René |editor-link=René Taton |edition=1. |volume=2 Pt. A: Planetary astronomy from the Renaissance to the rise of astrophysics Tycho Brahe to Newton |location=Cambridge |pages=233–274 |chapter=The Newtonian achievement in astronomy |editor-last2=Wilson |editor-first2=Curtis |editor-last3=Hoskin |editor-first3=Michael A.}}</ref> Hooke's lecture "On gravity" was at the Royal Society, in London, on 21 March.<ref>{{Cite book |last=Birch |first=Thomas |author-link=Thomas Birch |url=https://books.google.com/books?id=lWEVAAAAQAAJ |title=The History of the Royal Society of London |date=1756 |volume=2 |pages=68–73}}; see especially pages 70–72.</ref> Borelli's "Theory of the Planets" was published later in 1666.<ref>{{Cite book |last=Borelli |first=Giovanni Alfonso |author-link=Giovanni Alfonso Borelli |url=https://books.google.com/books?id=YZk_AAAAcAAJ |title=Theoricae mediceorum planetarum ex causis physicis deductae |date=1666 |publisher=Ex typographia S.M.D. |bibcode=1666tmpe.book.....B |language=la |trans-title=Theory [of the motion] of the Medicean planets [i.e., moons of Jupiter] deduced from physical causes}}</ref>  Hooke's 1670 Gresham lecture explained that gravitation applied to "all celestiall bodys" and added the principles that the gravitating power decreases with distance and that in the absence of any such power bodies move in straight lines. By 1679, Hooke thought gravitation had inverse square dependence and communicated this in a letter to [[Isaac Newton]]:<ref name="Hooke1680">{{Cite journal |last=Koyré |first=Alexandre |author-link=Alexandre Koyré |year=1952 |title=An Unpublished Letter of Robert Hooke to Isaac Newton |journal=[[Isis (journal)|Isis]] |volume=43 |issue=4 |pages=312–337 |doi=10.1086/348155 |jstor=227384 |pmid=13010921 }}</ref> 
''my supposition is that the attraction always is in duplicate proportion to the distance from the center reciprocall''.<ref>Hooke's letter to Newton of 6 January 1680 (Koyré 1952:332).</ref>

Hooke remained bitter about Newton claiming the invention of this principle, even though Newton's 1686 ''[[Philosophiæ Naturalis Principia Mathematica|Principia]]'' acknowledged that Hooke, along with Wren and Halley, had separately appreciated the inverse square law in the [[Solar System]],<ref>Newton acknowledged Wren, Hooke and Halley in this connection in the Scholium to Proposition 4 in Book 1 (in all editions): See for example: {{Cite book |last=Newton |first=Isaac |author-link=Isaac Newton |url=https://books.google.com/books?id=Tm0FAAAAQAAJ |title=The Mathematical Principles of Natural Philosophy |date=1729 |publisher=B. Motte |page=66}}</ref> as well as giving some credit to Bullialdus.<ref>In a letter to Edmund Halley dated 20 June 1686, Newton wrote:  "Bullialdus wrote that all force respecting ye Sun as its center & depending on matter must be reciprocally in a duplicate ratio of ye distance from ye center." See: {{Cite book |last1=Cohen |first1=I. Bernard |author-link=I. Bernard Cohen |url=https://books.google.com/books?id=3wIzvqzfUXkC |title=The Cambridge Companion to Newton |last2=Smith |first2=George E. |author-link2=George E. Smith |date=2002 |publisher=Cambridge University Press |isbn=978-0-521-65696-2 |pages=204}}</ref>