Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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PROPOSITIO VIII. THEOREMA VIII.
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DE MUNDI
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SYSTEMATE</
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Si Globorum duorum in ſe mutuo gravitantium materia undique,
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in regionibus quæ à centris æqualiter diſtant, homogenea ſit:
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erit pondus Globi alterutrius in alterum reciproce ut quadra
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tum diſtantiæ inter centra.
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>Poſtquam inveniſſem gravitatem in Planetam totum oriri &
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componi ex gravitatibus in partes; & eſſe in partes ſingulas reci
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proce proportionalem quadratis diſtantiarum a partibus: dubita
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bam an reciproca illa proportio duplicata obtineret accurate in vi
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tota ex viribus pluribus compoſita, an vero quam proxime. </
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fieri poſſet ut proportio, quæ in majoribus diſtantiis ſatis accu
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rate obtineret, prope ſuperficiem Planetæ ob inæquales particu
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larum diſtantias & ſitus diſſimiles, notabiliter erraret. </
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>Tandem
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vero, per Prop. LXXV. & LXXVI. Libri primi & ipſarum Corol
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laria, intellexi veritatem Propoſitionis de qua hic agitur.
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Corol.
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1. Hinc inveniri & inter ſe comparari poſſunt pondera
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corporum in diverſos Planetas. </
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lium circum Planetas in circulis revolventium ſunt (per Corol. 2.
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Prop. IV. Lib.I.) ut diametri circulorum directe & quadrata tem
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porum periodieorum inverſe; & pondera ad ſuperficies Planeta
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rum, aliaſve quaſvis a centro diſtantias, majora ſunt vel minora
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(per hanc Propoſitionem) in duplicata ratione diſtantiarum in
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verſa. Sic ex temporibus periodicis Veneris circum Solem die
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rum 224 & horarum 16 1/4, Satellitis extimi circumjovialis circum
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Jovem dierum 16 & horarum (16 1/15), Satellitis Hugeniani circum
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Saturnum dierum 15 & horarum 22 2/3, & Lunæ circum Terram
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dierum 27, hor. 7. min. 43, collatis cum diſtantia mediocri Vene
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ris a Sole & cum elongationibus maximis heliocentricis Satellitis
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extimi circumjovialis a centro Jovis 8′. 21 1/2″, Satellitis Hugeniani
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a centro Saturni 3′. 20″, & Lunæ a Terra 10′, computum ineundo
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inveni quod corporum æqualium & a Sole, Jove, Saturno ac Terra
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æqualiter diſtantium pondera in Solem, Jovem, Saturnum ac Ter
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ram forent ad invicem ut 1, (1/1033), (1/2411), & (1/227512) reſpective. </
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parallaxis Solis ex obſervationibus noviſſimis quaſi 10″, &
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Hal
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leius
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noſter per emerſiones Jovis & Satellitum e parte obſcura
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