Fontem paginae Gravitas (physica) inspicere

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[[Fasciculus:Spacetime_curvature.png|upright=1.5|thumb|Secundum theoriam gravitatis Einsteinianam, materia ipsa [[natura]] [[spatium]] et [[tempus]] flectit, unde [[vis gravitatis]] oritur. Difficile est animo fictu flexio [[dimensio]]num trium, difficilius quattuor, ergo haec imago modo monstrat flexionem duarum.]]

'''Gravitas,'''<ref name="vitruvius-8-3">Vide [[Marcus Vitruvius Pollio|Vitruviui]] ''[[De architectura (Vitruvius)|De architectura]]'', {{Vf|De architectura/Liber VII|Caput Octavum|VII, 8, 3}}: "Ita non amplitudine ponderis sed genere singularum rerum gravitatem esse non est negandum." Pro editione [[impressio|impressa]], vide {{Cite book
	| last = Vitruvius
	| first = Marcus Pollio
	| author-link = Marcus Vitruvius Pollio
	| editor = Alfred A. Howard
	| title = De Architectura libri decem
	| trans-title = Ten Books on Architecture
	| place = Cantabrigiae in Re Publica Massachusettensi
	| publisher = Harvard University Press
	| date = [[1914]]
	| chapter = 7
	| page = 215 
	| chapter-url = http://www.gutenberg.org/files/20239/20239-h/29239-h.htm#Page_215
	| others = Herbert Langford Warren, Nelson Robinson (illus), Morris Hicky Morgan
	| work = VII
}}</ref><ref>Isaacus Newtonus ipse solus dicit ''vim gravitatis'' et verba similia et numquam dicit ''gravitatio'' (''Philosophia Naturalis Principia Mathematica,'' prima editio anno [[1687]], secunda editio anno [[1713]]).</ref> seu '''gravitatio,'''<ref>[http://www.xs4all.nl/~adcs/beeckman/suppl/Descartes.html Isaacus Beekmann] novum sensum de gravitationis verbo explicat anno 1618: "Secundo, ut quid significet verbum gravitare intelligatur, fingendum est corpus quod gravitare dicitur deorsum moveri, et illud in primo instanti motus considerandum est. Vis enim qua in primo instanti impellitur motus, ea est quae gravitatio vocatur, non illa quae illud in toto motu fert deorsum, quae a prima valde distincta esse potest. Dicemus igitur gravitationem esse vim qua proxima superficies [[corpus|corpori]] gravi subjecta, ab eodem premitur."</ref> aliquando apud [[scriptor]]es [[Romani|Romanos]] '''nutus''' appellata,<ref>[[Cicero|Ciceronis]], [[Tusculanae disputationes]], 1.17: "terrena suopte nutu et suo pondere in terram ferri, &c."</ref> est [[res]] physica quo [[pondus]] efficitur, omnia [[corpus|corpora]] inter se compelluntur, et omnes [[planeta]]e in gyris circum solem tenentur. [[Vis]] gravitatis in [[physica]] est maxime imbecilla e quattuor [[vis fundamentalis|viribus fundamentalibus]].
[[Fasciculus:Portrait of Sir Isaac Newton, 1689.jpg|thumb|upright=0.6|left|[[Isaacus Newtonus]] Eques, [[physicus]] [[Anglia|Anglicus]] (1642–1727).]]

Prima gravitatis [[theoria]] late patens ab [[Isaacus Newtonus|Isaaco Newtono]] anno [[1687]] proposita est, qua fere omnia gyra [[planeta]]rum [[systema solare|systematis solaris nostri]] explicata sint. Tunc [[Albertus Einstein]] vim gravitatis secundum suam [[relativitas generalis|theoriam relativisticam]] anno [[1923]] redexplicavit. Secundum novam theoriam Einsteinianam, vis gravitatis fundamentaliter non est vis per se, sed effectum flectionis [[spatium|spatii]]  [[tempus|temporisque]], quam omnes [[massa]]e efficiunt. 

Quamquam theoria Newtoniana sola corpora [[massa|massiva]] inter se compelli habebat, theoria Einsteiniana omnia corpora [[energia]]m cohibentia inter se compelli statuit.

== Antiquitas ==
Qualis sit machinatio gravitatis a nonnullis [[philosophus|philosophis]] [[antiquitas|antiquis]] exploratus est. In [[Graecia]], [[Aristoteles]] credidit res in [[Tellus (planeta)|Terram]] decidisse quia Terra centrum [[universum|universi]] erat, quod totam [[massa]]m in universo attrahebat. Existimavit etiam [[celeritas|celeritatem]] rei cadentis [[pondus|pondere]] suo augeri, sed haec [[coniectura]] postea a [[Galilaeus Galilaei|Galilaeo Galilaei]] falsa monstrata est.<ref>Edward Grant, ''The foundations of modern science in the Middle Ages'' [https://archive.org/details/foundationsofmod0000gran/page/60/mode/2up pp. 60-61] (exemplar mutuabile apud ''Internet Archive'').</ref> [[Plutarchus]] recte praedixit attractionem gravitatis non modo Terrae esse. [[Archimedes]] adeptus est ut {{Creanda|d|Q2945123|barycentrum}} [[triangulum|trianguli]] inveniret.<ref>{{cite book
	| author1 = Reviel Neitz
	| author2 = William Noel
	| url = https://books.google.com/books?id=ZC1MOaAkKnsC&pg=PT125
	| title = The Archimedes Codex: Revealing The Secrets of the World's Greatest Palimpsest
	| date = [[13 Octobris]] [[2011]]
	| publisher = Hachette in Britanniarum Regno
	| isbn = 978-1-78022-198-4
	| page = 125
	| access-date = 10 April 2019
	| archive-url = https://web.archive.org/web/20200107004958/https://books.google.com/books?id=ZC1MOaAkKnsC&pg=PT125
	| archive-date = 7 Ianuarii 2020
	| url-status = live
}}</ref> Duobus post [[saeculum|saeculis]], [[Marcus Vitruvius Pollio|Vitruvius]] [[architectus]] Romanus in [[liber (litterae)|libro]] ''De architectura'' contendit gravitatem non amplitudine ponderis [[substantia]]e, sed genere eius dependere.<ref name="vitruvius-8-3" />

== Renascentia Europaea ==
[[Leonardus Vincius]] (1452–1519) {{Latinitas dolet|delineationem fecit accelerationem rerum cadentium. Scripsit "matrem et originem gravitatis" esse industriam. Duo paria virium physicorum describit, quae a metaphysica oriuntur, et effectum habent in omnibus: vim et motum, ac gravitatem et resistentiam abundantiam. Gravitatem sociat cum elementis classicis, aqua et terra frigidis, et industriam suam infinitam appellat. In [[Codex Arundel|codice Arundel]] Leonardus memoratur, si vas aquae fundens transversaliter moveatur, simulans trajectoriam obiecti verticalis cadentis; triangulum rectum cum paribus cruris longitudinis, ex materia caduca composita hypotenusam et vas trajectorium unum crurum efformans.<ref>Jennifer Ouellette, "[https://arstechnica.com/science/2023/02/leonardo-noted-link-between-gravity-and-acceleration-centuries-before-einstein/ Leonardo noted link between gravity and acceleration before Newton]" (2023) apud ''Ars Technica.''</ref> In hypotenusa, Leonardus notavit aequivalentiam duorum orthogonalium motuum, unum per gravitatem et alterum ab experimento propositam.}}<ref>Morteza Gharib, Chris Roh, et Flavio Noca, "[https://direct.mit.edu/leon/article-abstract/56/1/21/113863/Leonardo-da-Vinci-s-Visualization-of-Gravity-as-a Leonardo da Vinci’s Visualization of Gravity as a Form of Acceleration]" in ''Leonardo'' vol. 56 no. 1 (2023).</ref>

== Theoria Newtoniana ==
[[Fasciculus:Orbit5.gif|thumb|[[Traiectoria planetarum|Traiectoriae]] duorum planetarum qui secundum [[Isaacus Newtonus|Newtoni]] descriptionem ab vi gravitatis vinculati sunt. Motio planetarum sub vi gravitatis dicitur gravitatio.]]
[[Isaacus Newtonus]] formula gravitatis deduxit ab analysi legum [[Renatus Cartesius|Renati Cartesii]], [[Galilaeus Galilaei|Galilaei Galilaei]], imprimisque legum [[Iohannes Keplerus|Ioannis Kepleri]], quae proprietates gyrorum planetarum describunt. Formula quam Newtonus deduxit est:<ref>Raymond A. Serway et John W. Jewett, ''Physics for Scientists and Engineers,'' ed. sexta (Brooks/Cole, 2004), ISBN 0-534-40842-7.</ref>

:::<math>\vec \mathbf{F}_{12} =  - G \frac{m_1 m_2}{r^2}, \mathbf{\hat{r}}_{12}</math>

ubi 

* <math>\vec \mathbf{F}_{12}</math> est vis attractus in corpus 1 ob corpus 2,
* ''G'' est [[constans gravitatis]] quod valet vere ac 6.67 × 10<sup>-11</sup> Nm²/kg²,
* ''m''<sub>1</sub> et ''m''<sub>2</sub> sunt massae corporum,
* ''r'' est intervallum inter centra corporum, et
* <math> \mathbf{\hat{r}}_{12} \ \stackrel{\mathrm{def}}{=}\  \frac{\vec \mathbf{r}_1 - \vec \mathbf{r}_2}{\vert \vec \mathbf{r}_1 - \vec \mathbf{r}_2\vert} </math> est directio ad corpus 1 a corpore 2.

Plane, quia omnia dividuntur a quadrata potestate intervalli, corpora quae ulterius ab se distant, minus inter se tractantur. Eodem modo, corpora massiviora magis compelluntur.

=== De natura ponderis secundum Newtonum ===
[[Fasciculus:Leaning tower of pisa 2.jpg|thumb|250px|Turris [[Pisae|Pisarum]] [[Italia]]e ubi [[Galilaeus Galilaei|Galileo]] dicitur [[saeculum 16|saeculo sexto decimo]] pilas massis discrepantibus iecisse, ut demonstretur omnia corpora vi gravitatis cadere adaeque.<ref>[http://science.nasa.gov/headlines/y2004/06may_lunarranging.htm De experimenta Galilei et versiones modernae.]</ref><ref>Rick Groleau. [http://www.pbs.org/wgbh/nova/galileo/experiments.html Galileo's Battle for the Heavens]. July 2002.</ref><ref>Phil Ball. [http://www.hindu.com/seta/2005/06/30/stories/2005063000351500.htm Science history: setting the record straight.] June 30, 2005.</ref> Secundum Newtonum, hoc experimentum et similia comprobant aequivalentiam inter massam gravitatis et massam inertialis. ]]
Secundum theoriam gravitatis Newtonianam, pondus corporis super superficie [[Tellus|Telluris]] correspondet vi gravitatis Telluricae in corpus. Pondus ''P'' in [[massa]]m ''m'', ut supra, igitur formula <math>P = mg</math> datur ubi [[acceleratio]]nis magnitudo ''g'' est
:::<math>g =  G \frac{m_{T}}{R_T^2}\simeq 9.81</math> m/s²,
<math>m_{T}</math> massa Telluris, <math>R_{T}</math> radius superficiei Telluris, et ''G'' constans gravitatis.

Ut consequentia huius formulae, eadem acceleratio ''g'' est omnibus corporibus in statu libere cadendi (id est, si contra gravitatis vim non fulciatur). Omnia corpora igitur in vacuo cadunt adaeque, etsi massas distinctas habent, quod secundum [[Leges motus Newtoni|secundam legem Newtonianam]] vis aequat pondus

:::<math> \vec F = \vec P \rightarrow m\vec a = m \vec g \rightarrow \vec a = \vec g</math>.

Haec conclusio, quam multa experimenta Galilei diu comprobaverunt, multum pendet in aequivalentia massae inventae in lege gravitatis et massae inertialis inventae in secunda lege Newtoniana. Haec aequivalentia, quae tam maximi momenti physicae Newtonianae est, saepe appellatur "Principium Aequivalentiae Galilei." <ref>[https://web.archive.org/web/20081022174402/http://science.nasa.gov/headlines/y2007/18may_equivalenceprinciple.htm De experimenta NASA moderna Principum Aequivalentiae Galilei probans (Anglice).]</ref><ref>[http://www.iop.org/EJ/abstract/0264-9381/13/11A/028 De experimenta in aëroplanis Principum Aequivalentiae Galilei probans]{{Nexus deficitur|date=October 2022 |bot=InternetArchiveBot |fix-attempted=yes }}; Vide etiam http://eotvos.dm.unipi.it/documents/specificissues/aaaf.pdf .</ref>

=== De sententia quam Newtonus de sua formula habebat ===
Newtonus ipse suam formulam credidit imperfectam, quod, secundum eam, vires gravitationales sine ulla mora per [[spatium]] translatae sunt. De hoc phaenomeno, quod hodie dicitur [[actio trans distantiam|actiones trans distantias]], autem, Newtonus nullas explicationes habebat in "[[Philosophiae Naturalis Principia Mathematica|Philosophiae Naturali Principia Mathematica]]".

{{Citatio|Rationem vero harum gravitatis proprietatum ex phaenomenis nondum potui deducere, et hypotheses non fingo. Quicquid enim ex phaenomenis non deducitur, hypothesis vocanda est; et hypotheses seu metaphysicae, seu physicae, seu qualitatum occultarum, seu mechanicae, in philosophia experimentali locum non habent. In hac philosophia propositiones deducuntur ex phaenomenis, et redduntur generales per inductionem. Sic impenetrabilitas, mobilitas, impetus corporum, et leges motuum et gravitatis innotuerunt. Et satis est quod Gravitas revera existat, et agat secundum leges a nobis expositas, et ad corporum caelestium et maris nostri motus omnes sufﬁciat."|Isaacus Newtonus<ref>Scholium Generale: [[Philosophiae Naturalis Principia Mathematica]], Secunda Editio, anno [[1713]] </ref>}}

Newtonus quoque sentiebat causam gravitatis quandam esse necessariam,<ref>Secundum chartam ad Dr Bentley 25 Februarii [[1693]] (I B Cohen, Isaac Newton's papers and letters on natural philosophy and related documents (Cambridge, 1958), p. 302): "It is inconceivable that inanimate brute matter should, without the mediation of something else, which is not material, operate upon, and effect other matter without mutual contact, as it must be if gravitation in the sense of Epicurus be essential and inherent in it. And this is one reason why I desired you would not ascribe innate gravity to me. That gravity should be innate, inherent and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me a great absurdity, and I believe that no man who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial I have left to the consideration of my reader"; capta e [https://web.archive.org/web/20080116131732/http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Gravitation.html sito interretiali].</ref> sed nullae [[idea]]e de causa futurae erant trecentos annos.

== Explicatio quam Einstein proposuit ==
[[Fasciculus:JeffersonLeft.jpg|thumb|upright=0.8|[[Turris]] laeva Laboratorii Jeffersonis Universitatis Harvardianae, ubi [[Robertus Pound]] et [[Glen Rebka]] experimenta celebra annis inter [[1959]] et [[1964]] fecerunt effectum dilatationis temporis necessarium ad gratitationem explicandam secundum principia Einsteiniana confirmantes.<ref name="rebka"> [http://focus.aps.org/story/v16/st1 Descriptio in Physical Review Focus]; [http://prola.aps.org/abstract/PRL/v3/i9/p439_1 "Gravitational Red-Shift in Nuclear Resonance"], R. V. Pound et G. A. Rebka Jr., ''Physical Review Letters'' 3: 439 (1959); [http://prola.aps.org/abstract/PRL/v4/i7/p337_1 "Apparent weight of photons"], R. V. Pound et G. A. Rebka Jr., ''Physical Review Letters'' 4: 337 (1964).</ref>]]

Tandem [[saeculum 20|saeculo vicensimo]], difficultas [[actio trans distantiam|actionum trans distantias]], quae theoriam Newtonianam tantum subruit, a Alberto Einstein superata est eius theoria [[Relativitas generalis|relativitatis generalis]], quod in theoria Einsteiniana omnes effectus, illique gravitationales inclusi, celeritate lucis movent. Secundum Einstein, virum gravitatis causa est flectio spatii temporisque. Einstein, ad suam theoriam relativisticam commentam, magnopere confisus est:

* Principio Immutabilis [[celeritas luminis|Celeritatis Lucis]], quod dixit lucem esse eadem maxima celeritate aeque ubique in universo;

* Principio Aequivalentiae Einstein, quod dixit a perspectiva systematum coordinatarum: "Non possumus distinguere effectum gravitatis a effecto accelerationis in systemate coordinatarum";<ref> Primum dictum de Principio Aequivalentiae ad [[Anglice|linguam Anglicam]] ab Anna Beck versum, Albertus Einstein anno [[1907]]: "we . . . assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system"; "Über das Relativitätsprinzip und die aus demselben gezogene Folgerungen," ''Jahrbuch der Radioaktivitaet und Elektronik'' 4 (1907); in "On the relativity principle and the conclusions drawn from it," in The collected papers of Albert Einstein. Vol. 2 : The Swiss years: writings, 1900–1909 (Princeton University Press, Princeton, NJ, 1989).</ref> <ref>Albertus Einstein, "Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes," ''Annalen der Physik'' 35 (1911); ad linguam Anglicam ab Anna Beck versum: "On the Influence of Gravitation on the Propagation of Light" in ''The collected papers of Albert Einstein. Vol. 3 : The Swiss years: writings, 1909–1911'' (Princeton University Press, Princeton, NJ, 1994), et in ''The Principle of Relativity,'' (Dover, 1924), pp 99–108, W. Perrett and G. B. Jeffery translators, ISBN 0-486-60081-5; Vide etiam situm interretialem Anglice: [http://www1.kcn.ne.jp/~h-uchii/gen.GR.html The Genesis of General Relativity].</ref> et

* Principiis mathematicis [[geometria differentialis|geometriae differentialis]], quibus nobis licet flectionem spatialum temporumque dicere secundum leges mathematicales.

Ut omnia haec principia simul honorata sint, Einstein deduxit prope corpora massiva, sicut Tellurem, tempus segnius spatiumque brevius necesse esse. Einstein tunc hypothesim fecit, ut gravitatio deflectio traiectoriarum sit ob hanc flexionem spatii temporisque. 

Postea multa experimenta observationesque hanc flexionem a Einstein predictam confirmaverunt. Inter eorum celeberrima fuit experimenta a Pound et Rebka annis ab [[1959]] ad [[1964]] facta, quae modo quantitativo confirmaverunt effectum dilatationis temporis necessarium ad gravitationem explicandam secundum principia relativitatis Einsteiniana.<ref name="rebka"> [http://focus.aps.org/story/v16/st1 Descriptio in Physical Review Focus]; [http://prola.aps.org/abstract/PRL/v3/i9/p439_1 "Gravitational Red-Shift in Nuclear Resonance"], R. V. Pound et G. A. Rebka Jr., ''Physical Review Letters'' 3: 439 (1959); [http://prola.aps.org/abstract/PRL/v4/i7/p337_1 "Apparent weight of photons"], R. V. Pound et G. A. Rebka Jr., ''Physical Review Letters'' 4: 337 (1964).</ref>

=== De natura spatii secundum Einstein ===
Diu physici praecipuam sentiebant materiam exsistere nomine ''aethere,'' quae omne [[spatium]] inter [[corpus|corpora]] complet. Imprimis Einstein, cum anno [[1905]] theoriam [[relativitas specialis|relativitatis specialis]] inveniret, aetherem exsistere negabat, sed iterum circum annum [[1920]] Einstein ipse invenit notionem aetheris necesse esse, ut una [[relativitas generalis|theoria relativitatis generalis]] satisfactoria sine [[actiones trans distantias|actionibus trans distantias]] creetur.<ref>[https://web.archive.org/web/20070419024649/http://www.tu-harburg.de/rzt/rzt/it/Ether.html A. Einstein, "Aether and the theory of Relativity" (University of Leyden, 1920).] Anglice: "Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only wonld be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable inedia, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it."</ref> Novus autem aether Alberto Einstein non erat ex materia corporeali antiqua, nec ex partibus positiones distinctas habentibus; novus aether simpliciter erat sedes campi electromagnetici gravitatisque. In omni loco spatii temporisque, aether particulis corporibusque communicaturus est quantum et quo modo flexum est spatium tempusque.

== Nexus interni==
* [[Antigravitas]]
* [[Constans gravitatis]]
* [[Fluctus gravitatis]]
* [[Particula subatomica]]
* [[Relativitas generalis]]
* [[Relativitas specialis]]
* [[Spatium Calabi-Yau]]
* [[Vis aestualis]]

== Notae ==
<references />

== Bbliographia ==
* {{cite book | last = Halliday | first = David | author2 = Robert Resnick | author3 = Kenneth S. Krane | title = Physics v. 1 | location = Novi Eboraci | publisher = John Wiley & Sons | date = [[2001]] | isbn = 0471320579}}.
* {{cite book | last = Serway | first = Raymond A. | author2 = Jewett, John W. | title = Physics for Scientists and Engineers | edition = sexta | publisher = Brooks/Cole | date = [[2004]] | isbn = 0534408427}}.
* {{cite book |author=Thorne, Kip S. |author2=Misner, Charles W. |author3=Wheeler, John Archibald |title=Gravitation |publisher=W. H. Freeman |date=[[1973]] |isbn=0716703440}}.
* {{cite book | last = Tipler | first = Paul | title = Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics | edition = quinta | publisher = W. H. Freeman | date = [[2004]] | isbn = 0716708094}}.
*Wald, Robert M. [[1994]]. ''Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics.'' Sicagi: Chicago University Press. ISBN 0-226-87027-8.

== Nexus externi ==
{{wiktionary}}
{{CommuniaCat|Gravitation|gravitationem}}
* [http://books.google.com/books?id=WqaGuP1HqE0C&printsec=titlepage Philosophiae Naturalis Principia Mathematica, a Newtono scripta] {{Ling|Latine}}

[[Categoria:Acceleratio]]
[[Categoria:Mechanica caelestis]]
[[Categoria:Notiones in physica]]
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