Editing Equivalence principle (section)

=== Tests of the strong equivalence principle ===
The strong equivalence principle can be tested by 1) finding orbital variations in massive bodies (Sun-Earth-Moon), 2) variations in the gravitational constant (''G'') depending on nearby sources of gravity or on motion, or 3) searching for a variation of Newton's gravitational constant over the life of the universe<ref name=Will2014/>{{rp|47}}

Orbital variations due to gravitational self-energy should cause a "polarization" of solar system orbits called the [[Nordtvedt effect]]. This effect has been sensitively tested by [[Lunar Laser Ranging experiments]].<ref>{{cite web | url=http://funphysics.jpl.nasa.gov/technical/grp/lunar-laser.html | title=Fundamental Physics of Space – Technical Details | access-date=7 May 2005 | archive-url=https://web.archive.org/web/20161128185551/http://funphysics.jpl.nasa.gov/technical/grp/lunar-laser.html | archive-date=28 November 2016 | url-status=dead }}</ref><ref>{{cite journal |last1=Viswanathan |first1=V |last2=Fienga |first2=A |last3=Minazzoli |first3=O |last4=Bernus |first4=L |last5=Laskar |first5=J |last6=Gastineau |first6=M |title=The new lunar ephemeris INPOP17a and its application to fundamental physics |journal=Monthly Notices of the Royal Astronomical Society |date=May 2018 |volume=476 |issue=2 |pages=1877–1888 |doi=10.1093/mnras/sty096|doi-access=free |arxiv=1710.09167 |bibcode=2018MNRAS.476.1877V |s2cid=119454879 }}</ref> Up to the limit of one part in 10<sup>13</sup> there is no Nordtvedt effect.

A tight bound on the effect of nearby gravitational fields on the strong equivalence principle comes from modeling the orbits of binary stars and comparing the results to [[pulsar]] timing data.<ref name=Will2014/>{{rp|49}} In 2014, astronomers discovered a stellar triple system containing a millisecond pulsar [[PSR J0337+1715]] and two [[white dwarf]]s orbiting it. The system provided them a chance to test the strong equivalence principle in a strong gravitational field with high accuracy.<ref>{{cite journal |url=http://www.nature.com/nature/journal/vaop/ncurrent/full/nature12917.html#ref7 |title=A millisecond pulsar in a stellar triple system |first1=Scott M. |last1=Ransom |display-authors=etal |journal=Nature |year=2014|doi=10.1038/nature12917 |arxiv = 1401.0535 |bibcode = 2014Natur.505..520R |volume=505 |issue=7484 |pages=520–524 |pmid=24390352|s2cid=4468698 }}</ref><ref>{{cite journal|title=Universality of free fall from the orbital motion of a pulsar in a stellar triple system|author=Anne M. Archibald|author-link=Anne Archibald|display-authors=etal |journal=Nature|volume=559 |issue=7712|pages=73–76 |date=4 July 2018|doi=10.1038/s41586-018-0265-1|pmid=29973733 |arxiv=1807.02059 | bibcode=2018Natur.559...73A|s2cid=49578025}}</ref><ref>{{cite news|title=Even Phenomenally Dense Neutron Stars Fall like a Feather – Einstein Gets It Right Again|url=https://public.nrao.edu/news/neutron-stars-fall/ |publisher=NRAO|date=4 July 2018 |work=Charles Blue, Paul Vosteen}}</ref> If there is any departure from the strong equivalence principle, it is no more than two [[parts per million]].<ref>{{Cite journal|last1=Voisin|first1=G. |last2=Cognard|first2=I. |last3=Freire|first3=P. C. C.|last4=Wex|first4=N. |last5=Guillemot|first5=L. |last6=Desvignes|first6=G. |last7=Kramer|first7=M. |last8=Theureau|first8=G. |date=2020-06-01|title=An improved test of the strong equivalence principle with the pulsar in a triple star system |url=https://www.aanda.org/articles/aa/abs/2020/06/aa38104-20/aa38104-20.html |journal=Astronomy & Astrophysics|language=en |volume=638 |pages=A24 |arxiv=2005.01388|doi=10.1051/0004-6361/202038104|bibcode=2020A&A...638A..24V|s2cid=218486794 |issn=0004-6361}}</ref>

Most alternative theories of gravity predict a change in the gravity constant over time.  Studies of [[Big Bang nucleosynthesis]], analysis of pulsars, and the lunar laser ranging data have shown that ''G'' cannot have varied by more than 10% since the creation of the universe. The best data comes from studies of the [[ephemeris]] of Mars, based on three successive NASA missions, [[Mars Global Surveyor]], [[Mars Odyssey]], and [[Mars Reconnaissance Orbiter]].<ref name=Will2014/>{{rp|50}}