Physics textbooks generally present the equation for universal gravitation as if it sprang fully formed from the head of Isaac Newton, which it most certainly did not. This analysis traces the development of Classical/Newtonian gravity as it evolved from Aristotle to Copernicus to Kepler, Horrocks, Roberval, Boulliau, Baliani, Borelli, Hooke, Halley, Wren, Newton, and Cavendish, and then finally on to C. V. Boys and J. H. Poynting. By focusing on the evolution of the underlying physics, we unfold a fascinating story that has never quite been told before, one we hope will provide insights useful in the classroom.
REFERENCES
1.
Peter
Dear
, European Knowledge in Transition, 1500–1700
, 3rd ed. (
Princeton U. P
.,
Princeton
, 2019
).2.
Marshall
Clagett
, The Science of Mechanics in the Middle Ages
(
University of Wisconsin Press
,
Madison
, 1959
), p. 94
.See also
David C.
Lindberg
, “
Science and the early christian church
,” Isis
74
, 509
–530
(1983
).3.
L. M.
Celnikier
, “
Towards an impressionist picture of the history of astronomy
,” Am. J. Phys.
49
, 473
–476
(1981
);see also
Douglas R.
Martin
, “
Status of the Copernican theory before Kepler, Galileo, and Newton
,” Am. J. Phys.
52
, 982
–986
(1984
);4.
Nicolaus
Copernicus
, “
On the revolutions of the heavenly spheres
,” in Great Books of the Western World
(
Encyclopedia Britannica
,
Chicago
, 1948
), p. 521
.5.
Johannes
Kepler
, Mysterium Cosmographicum
, translated by
A. M.
Duncan
(
Abaris Books
,
NY
, 1981
).6.
Gerald
Holton
, “
Johannes Kepler's universe: Its physics and metaphysics
,” Am. J. Phys.
24
, 340
–351
(1956
).7.
Johannes
Kepler
, Astronomia Nova
, translated by
William
Donahue
(
Green Lion Press
,
NM
, 2015
), p. 300
, ch. 38. Online in Latin at <e-rara.ch/zut/content/zoom/87684> also at <https://archive.org/details/den-kbd-pil-20008609-001>.8.
9.
Johannes
Kepler
, Gesammelte Werke
, edited by
C. H.
Beck
(H. Becksche Verlagsbuchhandlung
, Munich, Germany
, 1938
), Vol.
13
, Letter 91.See also,
Aviva
Rothman
, “
Johannes Kepler's pursuit of harmony
,” Phys. Today
73
(1
), 36
–42
(2020
).10.
Max
Jammer
, Concepts of Mass in Classical and Modern Physics
(
Dover Pub
.,
Mineola, NY
, 1997
), pp. 37
–48
.11.
12.
Reference 2, p.
522
. See also Buridan and the theory of impetus: <http://faculty.fordham.edu/klima/Blackwell-proofs/MP_C23.pdf>.13.
Reference 10, p.
56
, translation slightly modified for additional clarity.14.
Joannis
Kepleri
, Opera Omnia, Mysterium Cosmographicum
, edited by
C.
Frisch
(
Francofurti a. M. et Erlangae, Heyder & Zimmer
, Erlangen
, 1858
), Vol.
1
, Chap. 16, p. 161
, author's notes 1621, my translation. Online in Latin at <https://archive.org/details/joanniskepleria27frisgoog/page/n15/mode/1up>.15.
Reference 10, p.
9
, In Jammer's words, “
It is important to note that the Latin moles is often synonymous with [the Latin] massa, as for example in Pliny, both terms denoting matter which occupies a certain volume.
”16.
Johannes
Kepler
, Epitome of Copernican Astronomy & Harmonies of the World
(1618–1621), translated by
Charles
Wallis
(
Prometheus Books
,
NY
, 1995
), p. 65
.17.
Reference 16, p.
90
.18.
Natural philosophers writing in English in the early 1700s favored the term quantity of matter and that was occasionally true even into the mid-19
th century. The alternative English physics term mass.
(or masse
) became commonplace by the late 1700s. Nonetheless, the phrase quantity of matter, albeit now scientifically meaningless,
can still be found in modern schoolbooks.19.
Eugene
Hecht
, “
Kepler and the origins of the theory of gravity
,” Am. J. Phys.
87
, 176
–185
(2019
).20.
Max
Casper
, Johannes Kepler Gesammelte Werke
(
C.H. Beck'sche Verlagsbuchhandlung
,
München
, 1990
), Vol.
III
, p. 24
. “Punctum mathematicum, sive centrum mundi sit sive non, nequit movere gravia neque effective neque objective; ut ad se accedant,” online in Latin at <http://publikationen.badw.de/de/002334739/pdf/CC%20BY>. My translation. “The true doctrine” can be found in English in several texts including, William Donahue, Selections From Kepler's Astronomia Nova (Green Cat Books, NM, 2008), p. 12. Alternatively see Ref. 7, p. 24, Kepler's Introduction.21.
Reference 14, Vol. III, p.
150
. Online at <https://archive.org/details/joanniskepleria14frisgoog/page/n8/mode/1up>. “
Gravitas est affectio corporea, mutual inter cognata corpora ad unitionem seu conjunctionem (quo rerum ordine est et facultas Magnetica)
,”My translation. Other versions can be found in
Alexandre
Koyré
, Newtonian Studies
(
Harvard U. P.
,
Cambridge, MA
, 1965), p. 174
;Angus
Armitage
, “
Borelli's hypothesis and the rise of celestial mechanics
,” Ann. Sci.
6
(3
), 268
–282
(1950
); Ref. 7, p. 24.22.
D. T.
Whiteside
, “
The prehistory of the Principia from 1664 to 1686
,” Notes Records R. Soc. London
45
, 11
–61
(1991
).23.
Reference 20, Vol. III. My translation. Online at <https://archive.org/details/joanniskepleria14frisgoog/page/n8/mode/1up>. For an alternative translation and the original Latin, see Ref. 10, p.
54
.24.
Eugene
Hecht
, “
Kepler and the origins of pre-Newtonian mass
,” Am. J. Phys.
85
, 115
–123
(2017
).25.
Johannes
Kepler
, Optics
, translated by
William
Donahue
(
Green Lion Press
,
NM
, 2000
), p. 141
. Online in Latin at <https://www.e-rara.ch/zut/content/zoom/87654>.26.
Conversation with the Sidereal Messenger, translated by
Edward
Rosen
(1610
), p. 83
. Online at: <http://digitalcollections.library.cmu.edu/awweb/awarchive?type=file&item=393654>.27.
Reference 16, pp. 51 and 98. Books I to III online in Latin at <https://books.google.com/books?id=KUE1AAAAcAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false>. Also in Latin at <http://kepler.badw.de/kepler-digital.html>, where it appears in Vol. VII.
29.
Reference 7, pp. 25–26. Translations are slightly modified for additional clarity. Online in Latin at <https://archive.org/details/den-kbd-pil-20008609-001/page/n33/mode/1up> (manuscript p. 4). See also Ref. 20, Selections from Kepler's Astronomia Nova, p. 15. The idea that the orb of the attractive power of the Earth is greater than that of the Moon, no doubt because of its greater size and hence greater mass, suggests what we would call its gravitational field.
30.
Edward
Rosen
, Kepler's Somnium
(
University of Wisconsin Press
,
Madison
, 1967
), Note 76, p. 73
. Online in Latin at <https://archive.org/stream/joanniskepleria00frisgoog#page/n8/mode/2up>.31.
Dorothea W.
Singer
, Giordano Bruno, His Life and Thought
(
Abeard-Schuman Inc
.,
NY
, 1950
), third dialogue, p. 303
.32.
Reference 16, p.
92
. Slightly modified for additional clarity.33.
Reference 16, p.
130
.34.
“
Lettre d'Étienne pascal et roberval à fermat, samedi 16 août 1636
,” in Oeuvers de Fermat
, edited by
P.
Tannery
and
C.
Henry
(
Gauthier-Villars
,
Paris
, 1894
), Vol.
2
, p. 36
.35.
Kokiti
Hara
, “
Roberval
,” Dictionary of Scientific Biography
, edited by
Charles
Gillispie
(
Scribner's Sons
,
New York
, 1975
), Vol.
XI
, pp. 486
–491
.36.
H. A. M.
Snelders
, “
Christiaan Huygens and Newton's theory of gravitation
,” Notes Records R. Soc. London
43
, 209
–222
(1989
).37.
Robert
Brickel
, The transits of Venus, 1639–1874; or a chapter of romance in science; In memoriam Horroccii
(
Henry Oakey, Preston, England
, 1874
), partly reprinted in 1998 to commemorate the building of the Brickel Vestry, p. 23
. Available from St. Michael's Church
, Hoole
.38.
A. B.
Whatton
, The transit of Venus across the Sun: A translation of the celebrated discourse thereupon, by the Rev. Jeremiah Horrox
(
William Macintosh
,
London
, 1859
). Online at <https://archive.org/details/transitofvenusac00horr>.39.
Danilo
Capecchi
, “
Experiments, mathematics and principles of natural philosophy in the epistemology of Giovanni Battista Baliani
,” Adv. Hist. Stud.
6
(2
), 78
–94
(2017
). Online at <https://www.researchgate.net/publication/317731714_Experiments_Mathematics_and_Principles_of_Natural_Philosophy_in_the_Epistemology_of_Giovanni_Battista_Baliani>. Translation slightly modified for additional clarity.40.
Ismail
Bullialdus
, Astronomia Philolaica
(
Piget
,
Paris
, 1645
). Online in Latin at <http://diglib.hab.de/drucke/2-1-4-astron-2f-1/start.htm?image=00005)>. See Ref. 8, pp. 467–527. See also Robert Hatch, Boulliau Planetary Theory, online at <http://users.clas.ufl.edu/ufhatch/pages/11-ResearchProjects/boulliau/conical-hypothesis/06rp-b-planet5.htm>.41.
Translation of the Latin quote from Bullialdus's Astronomia Philolaica, online at <http://www-history.mcs.st-and.ac.uk/Biographies/Boulliau.html>. See also, Robert Hatch, Boulliau Planetary Theory, online at <http://users.clas.ufl.edu/ufhatch/pages/11-ResearchProjects/boulliau/conical-hypothesis/06rp-b-planet4.htm>.
42.
Domenico B.
Meli
, “
Shadows and deception: From Borelli's ‘Theoricae’ to the ‘Saggi’ of the Cimento
,” BJHS
31
, 383
–402
(1998
).43.
Giovanni Alfonso
Borelli
, Theoricæ Mediceorum Planetarum ex Causis Physicis Deducta.
Online in Latin at <https://archive.org/details/bub_gb_-a1tAxwj5lcC/page/n6>.44.
45.
EL/N1/55, Royal Society Library, London, UK. Online at <http://www.newtonproject.ox.ac.uk/view/texts/diplomatic/NATP00325>.
46.
M.
Nauenberg
, “
Hooke, orbital motion and Newton's Principia
,” Am. J. Phys.
62
, 331
–350
(1994
).47.
Thomas
Birch
, The History of the Royal Society of London for the Improving of Nature
(
A. Millar in the Strand
,
London
, MDCCLVI), Vol.
1
, p. 163
. Online at <https://play.google.com/books/reader?id=RSpAAQAAMAAJ&hl=en&pg=GBS.PA59>.48.
Reference 47, Vol. 1, p.
507
.49.
Reference 47, Vol. 2, p.
66
. Online at <https://lensonleeuwenhoek.net/sites/default/files/pdf/birch_1756_history_royal_society_II.pdf>.50.
Reference 49, Vol. 2, p.
70
.51.
Reference 46. See also
Robert
Hooke
, “
Cometa or, remarks about comets, 1682
,” in The Cutler Lectures of Robert Hooke
, edited by
Robert T.
Gunther
(
Early science in Oxford
,
Oxford
, 1931
), Vol.
VIII
, pp. 217
–271
, and 252.52.
Robert
Hooke
, The Posthumous Works of Robert Hooke
(
Royal Society
,
London
, 1705
), p. 175
. Online at: <http://www.babordnum.fr/items/show/160>.53.
Reference 52, p. 176. Also,
Robert D.
Purrington
, The First Professional Scientist
(
Birkhäuser
,
Basel
, 2009
), p. 175
. Online at <https://books.google.com/books?id=tJu97S3BtGIC&pg=PA168>.54.
Gribbin
John
and
Gribbin
Mary
, Out of the Shadow of a Giant
(
Yale U. P
.,
New Haven
, 2017
), p. 144
.56.
W. W.
Rouse Ball
, An Essay on Newton's Principia
(
Macmillan and co
.,
NY
, 1893
), p. 162
.57.
George E.
Smith
, “
Newton's numerator in 1685: A year of gestation
,” Stud. Hist. Philos. Mod. Phys.
68
, 163
–177
(2019
).58.
Craig
Fox
, “
The Newtonian equivalence principle: How the relativity of acceleration led Newton to the equivalence of inertial and gravitational mass
,” Philos. Sci.
83
, 1027
–1038
(2016
). Quoting Fox: “The word he [Newton] had been using was moles … It is not entirely clear why Newton abandoned moles, which I [Fox] call the mechanical quantity of matter …”59.
C.
Vernon Boys
, “
On the Newtonian constant of gravitation
,” Nature
50
, 330
–333
(1894
).See also,
J. H.
Poynting
, “
On a determination of the mean density of the earth and the gravitation constant by means of the common balance
,” Philos. Trans.
clxxxii
, 565
–656
(1891
). Online at <https://archive.org/details/meandensityofear00poynuoft>. It should be mentioned that A. Cornu and J. Baille (1873) published a version of Eq. (1) wherein the gravitational constant was given as f rather than G.60.
and
A.
Wilmer Duff
, A Text–Book of Physics
(
P. Blakiston's Son & Co.
,
Philadelphia
, 1909
), p. 109
. These are the earliest appearances that I have found in textbooks in English.© 2021 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2021
Author(s)
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.