Gravitas (physica)

Gravitas,^[1]^[2] seu gravitatio,^[3] aliquando apud scriptores Romanos nutus appellata,^[4] est res physica quo pondus efficitur, omnia corpora inter se compelluntur, et omnes planetae in gyris circum solem tenentur. Vis gravitatis in physica est maxime imbecilla e quattuor viribus fundamentalibus.

Prima gravitatis theoria late patens ab Isaaco Newtono anno 1687 proposita est, qua fere omnia gyra planetarum systematis solaris nostri explicata sint. Tunc Albertus Einstein vim gravitatis secundum suam theoriam relativisticam anno 1923 redexplicavit. Secundum novam theoriam Einsteinianam, vis gravitatis fundamentaliter non est vis per se, sed effectum flectionis spatii temporisque, quam omnes massae efficiunt.

Quamquam theoria Newtoniana sola corpora massiva inter se compelli habebat, theoria Einsteiniana omnia corpora energiam cohibentia inter se compelli statuit.

Antiquitas

Qualis sit machinatio gravitatis a nonnullis philosophis antiquis exploratus est. In Graecia, Aristoteles credidit res in Terram decidisse quia Terra centrum universi erat, quod totam massam in universo attrahebat. Existimavit etiam celeritatem rei cadentis pondere suo augeri, sed haec coniectura postea a Galilaeo Galilaei falsa monstrata est.^[5] Plutarchus recte praedixit attractionem gravitatis non modo Terrae esse. Archimedes adeptus est ut barycentrum^(d) trianguli inveniret.^[6] Duobus post saeculis, Vitruvius architectus Romanus in libro De architectura contendit gravitatem non amplitudine ponderis substantiae, sed genere eius dependere.^[1]

Renascentia Europaea

Leonardus Vincius (1452–1519) 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 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.^[7] In hypotenusa, Leonardus notavit aequivalentiam duorum orthogonalium motuum, unum per gravitatem et alterum ab experimento propositam.^{[Latinitas dolet]}^[8]

Theoria Newtoniana

Traiectoriae duorum planetarum qui secundum Newtoni descriptionem ab vi gravitatis vinculati sunt. Motio planetarum sub vi gravitatis dicitur gravitatio.

Isaacus Newtonus formula gravitatis deduxit ab analysi legum Renati Cartesii, Galilaei Galilaei, imprimisque legum Ioannis Kepleri, quae proprietates gyrorum planetarum describunt. Formula quam Newtonus deduxit est:^[9]

{\vec {\mathbf {F} }}_{12}=-G{\frac {m_{1}m_{2}}{r^{2}}},\mathbf {\hat {r}} _{12}

ubi

${\vec {\mathbf {F} }}_{12}$ est vis attractus in corpus 1 ob corpus 2,
G est constans gravitatis quod valet vere ac 6.67 × 10^-11 Nm²/kg²,
m₁ et m₂ sunt massae corporum,
r est intervallum inter centra corporum, et
$\mathbf {\hat {r}} _{12}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {{\vec {\mathbf {r} }}_{1}-{\vec {\mathbf {r} }}_{2}}{\vert {\vec {\mathbf {r} }}_{1}-{\vec {\mathbf {r} }}_{2}\vert }}$ 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

Secundum theoriam gravitatis Newtonianam, pondus corporis super superficie Telluris correspondet vi gravitatis Telluricae in corpus. Pondus P in massam m, ut supra, igitur formula $P=mg$ datur ubi accelerationis magnitudo g est

g=G{\frac {m_{T}}{R_{T}^{2}}}\simeq 9.81

m/s²,

$m_{T}$ massa Telluris, $R_{T}$ 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 secundam legem Newtonianam vis aequat pondus

{\vec {F}}={\vec {P}}\rightarrow m{\vec {a}}=m{\vec {g}}\rightarrow {\vec {a}}={\vec {g}}

.

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." ^[13]^[14]

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 actiones trans distantias, autem, Newtonus nullas explicationes habebat in "Philosophiae Naturali Principia Mathematica".

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^[15]

Newtonus quoque sentiebat causam gravitatis quandam esse necessariam,^[16] sed nullae ideae de causa futurae erant trecentos annos.

Explicatio quam Einstein proposuit

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.^[17]

Tandem saeculo vicensimo, difficultas actionum trans distantias, quae theoriam Newtonianam tantum subruit, a Alberto Einstein superata est eius theoria 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 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";^[18] ^[19] et

Principiis mathematicis 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.^[17]

De natura spatii secundum Einstein

Diu physici praecipuam sentiebant materiam exsistere nomine aethere, quae omne spatium inter corpora complet. Imprimis Einstein, cum anno 1905 theoriam relativitatis specialis inveniret, aetherem exsistere negabat, sed iterum circum annum 1920 Einstein ipse invenit notionem aetheris necesse esse, ut una theoria relativitatis generalis satisfactoria sine actionibus trans distantias creetur.^[20] 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

Notae

↑ ^1.0 ^1.1 Vide Vitruviui De architectura, VII, 8, 3: "Ita non amplitudine ponderis sed genere singularum rerum gravitatem esse non est negandum." Pro editione impressa, vide Vitruvius, Marcus Pollio (1914). "7". In Alfred A. Howard. De Architectura libri decem. Herbert Langford Warren, Nelson Robinson (illus), Morris Hicky Morgan. Cantabrigiae in Re Publica Massachusettensi: Harvard University Press. p. 215
↑ 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).
↑ 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 corpori gravi subjecta, ab eodem premitur."
↑ Ciceronis, Tusculanae disputationes, 1.17: "terrena suopte nutu et suo pondere in terram ferri, &c."
↑ Edward Grant, The foundations of modern science in the Middle Ages pp. 60-61 (exemplar mutuabile apud Internet Archive).
↑ Reviel Neitz; William Noel (13 Octobris 2011). The Archimedes Codex: Revealing The Secrets of the World's Greatest Palimpsest. Hachette in Britanniarum Regno. p. 125. ISBN 978-1-78022-198-4
↑ Jennifer Ouellette, "Leonardo noted link between gravity and acceleration before Newton" (2023) apud Ars Technica.
↑ Morteza Gharib, Chris Roh, et Flavio Noca, "Leonardo da Vinci’s Visualization of Gravity as a Form of Acceleration" in Leonardo vol. 56 no. 1 (2023).
↑ Raymond A. Serway et John W. Jewett, Physics for Scientists and Engineers, ed. sexta (Brooks/Cole, 2004), ISBN 0-534-40842-7.
↑ De experimenta Galilei et versiones modernae.
↑ Rick Groleau. Galileo's Battle for the Heavens. July 2002.
↑ Phil Ball. Science history: setting the record straight. June 30, 2005.
↑ De experimenta NASA moderna Principum Aequivalentiae Galilei probans (Anglice).
↑ De experimenta in aëroplanis Principum Aequivalentiae Galilei probans^{[nexus deficit]}; Vide etiam http://eotvos.dm.unipi.it/documents/specificissues/aaaf.pdf .
↑ Scholium Generale: Philosophiae Naturalis Principia Mathematica, Secunda Editio, anno 1713
↑ 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 sito interretiali.
↑ ^17.0 ^17.1 Descriptio in Physical Review Focus; "Gravitational Red-Shift in Nuclear Resonance", R. V. Pound et G. A. Rebka Jr., Physical Review Letters 3: 439 (1959); "Apparent weight of photons", R. V. Pound et G. A. Rebka Jr., Physical Review Letters 4: 337 (1964).
↑ Primum dictum de Principio Aequivalentiae ad 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).
↑ 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: The Genesis of General Relativity.
↑ 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."

Bbliographia

Halliday, David; Robert Resnick; Kenneth S. Krane (2001). Physics v. 1. Novi Eboraci: John Wiley & Sons. ISBN 0471320579 .
Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (sexta ed.). Brooks/Cole. ISBN 0534408427 .
Thorne, Kip S.; Misner, Charles W.; Wheeler, John Archibald (1973). Gravitation. W. H. Freeman. ISBN 0716703440 .
Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (quinta ed.). W. H. Freeman. 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

Vide Gravitas (physica) in Victionario.

Vicimedia Communia plura habent quae ad gravitationem spectant.

Philosophiae Naturalis Principia Mathematica, a Newtono scripta (Latine)

[vitruvius-8-3-1] 1.0 ^1.1 Vide Vitruviui De architectura, VII, 8, 3: "Ita non amplitudine ponderis sed genere singularum rerum gravitatem esse non est negandum." Pro editione impressa, vide Vitruvius, Marcus Pollio (1914). "7". In Alfred A. Howard. De Architectura libri decem. Herbert Langford Warren, Nelson Robinson (illus), Morris Hicky Morgan. Cantabrigiae in Re Publica Massachusettensi: Harvard University Press. p. 215

[2] 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).

[3] 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 corpori gravi subjecta, ab eodem premitur."

[4] Ciceronis, Tusculanae disputationes, 1.17: "terrena suopte nutu et suo pondere in terram ferri, &c."

[5] Edward Grant, The foundations of modern science in the Middle Ages pp. 60-61 (exemplar mutuabile apud Internet Archive).

[6] Reviel Neitz; William Noel (13 Octobris 2011). The Archimedes Codex: Revealing The Secrets of the World's Greatest Palimpsest. Hachette in Britanniarum Regno. p. 125. ISBN 978-1-78022-198-4

[7] Jennifer Ouellette, "Leonardo noted link between gravity and acceleration before Newton" (2023) apud Ars Technica.

[8] Morteza Gharib, Chris Roh, et Flavio Noca, "Leonardo da Vinci’s Visualization of Gravity as a Form of Acceleration" in Leonardo vol. 56 no. 1 (2023).

[9] Raymond A. Serway et John W. Jewett, Physics for Scientists and Engineers, ed. sexta (Brooks/Cole, 2004), ISBN 0-534-40842-7.

[10] De experimenta Galilei et versiones modernae.

[11] Rick Groleau. Galileo's Battle for the Heavens. July 2002.

[12] Phil Ball. Science history: setting the record straight. June 30, 2005.

[13] De experimenta NASA moderna Principum Aequivalentiae Galilei probans (Anglice).

[14] De experimenta in aëroplanis Principum Aequivalentiae Galilei probans^{[nexus deficit]}; Vide etiam http://eotvos.dm.unipi.it/documents/specificissues/aaaf.pdf .

[15] Scholium Generale: Philosophiae Naturalis Principia Mathematica, Secunda Editio, anno 1713

[16] 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 sito interretiali.

[rebka-17] 17.0 ^17.1 Descriptio in Physical Review Focus; "Gravitational Red-Shift in Nuclear Resonance", R. V. Pound et G. A. Rebka Jr., Physical Review Letters 3: 439 (1959); "Apparent weight of photons", R. V. Pound et G. A. Rebka Jr., Physical Review Letters 4: 337 (1964).

[18] Primum dictum de Principio Aequivalentiae ad 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).

[19] 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: The Genesis of General Relativity.

[20] 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."

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