Kepler, Newton and Einstein

Volume 8, Issue 1, February 2023     |     PP. 10-38      |     PDF (11639 K)    |     Pub. Date: February 9, 2023
DOI: 10.54647/mathematics110381    84 Downloads     4539 Views  

Author(s)

Christer Oscar Kiselman, Uppsala University, Department of Mathematics, P. O. Box 480, SE-751 06 Uppsala, Sweden

Abstract
This essay describes orbits of particles passing near the sun, first according to Newton’s celestial mechanics and then according to Einstein’s general theory of relativity. Attempts to verify the latter by observing the deflection of light during total solar eclipses are mentioned. Confirmation also comes from mea- surements of the delay in the arrival of reflected light, as well as from the use of Very Long Baseline Interferometry (VLBI). A comparison of explanations of these phenomena reveals contradicting statements.

Keywords
Celestial mechanics · gravitation · the general theory of relativity · deflection of light rays · delay in the arrival of reflected light · Kepler · Newton · Einstein

Cite this paper
Christer Oscar Kiselman, Kepler, Newton and Einstein , SCIREA Journal of Mathematics. Volume 8, Issue 1, February 2023 | PP. 10-38. 10.54647/mathematics110381

References

[ 1 ] Bertotti, B.; Iess, L.; Tortora, P. 2003. “A test of general relativity using radio links with the Cassini spacecraft.” Nature 425, 374–376.
[ 2 ] Callahan, James J. 2001. The Geometry of Spacetime. An Introduction to Special and General Relativity, vxi + 451 pages. New York, NY, et al.: Springer-Verlag.
[ 3 ] Droste, J[ohannes]. 1916. “The field of a single centre in Einstein’s theory of gravitation, and the motion of a particle in that field.” Koninklijke Akademie van Wetenschappen te Amsterdam. Proceedings of the Section of Sciences 19 (1), 197–215.
[ 4 ] Earman, John; Glymour, Clark. 1980. “Relativity and eclipses: The British eclipse expeditions of 1919 and their predecessors.” Historical Studies in the Physical Sciences, 11, No. 1, 49–85.
[ 5 ] Earman, John; Janssen, Michel; Norton, John D., Eds. 1993. The Attraction of Gravitation; New Studies in the History of General Relativity, xii + 432 pages. Boston et al.: Birkhäuser.
[ 6 ] Eddington, A[rthur] S[tanley]. 1920. Space Time and Gravitation: An Outline of the General Rela- tivity Theory, vii + 218 pages. Cambridge: At the University Press.
[ 7 ] Einstein, A[lbert]. 1911. “Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes.” Annalen der Physik (ser. 4), 35, 898–908.
[ 8 ] Einstein, A[lbert]. 1914. “Prinzipielles zur verallgemeinerten Relativitätstheorie und Gravitations- theorie.” Physikalische Zeitschrift 15, 176–180. [Not in (Kox et al., Eds., 1996.)]
[ 9 ] Einstein, A[lbert]. 1915. “Die Feldgleichungen der Gravitation.” Sitzungsberichte der Könich Preußischen Akademie der Wissenschaften zu Berlin, 1915 November 25, 844–847. [Reprinted in (Kox et al., Eds., 1996: Document 25, pages 244–249).]
[ 10 ] Einstein, A[lbert]. 1916a. “Die Grundlage der allgemeinen Relativitätstheorie.” Annalen der Physik (ser. 4), 49, 769–822. [Reprinted in (Kox et al., Eds., 1996: Document 30, pages 283–339).]
[ 11 ] Einstein, A[lbert]. 1916b. Die Grundlage der allgemeinen Relativitätstheorie, 64 pages. Sonderdruck aus den ,,Annalen des Physik“, Band 49, 1916 = (1916a). Leipzig: Verlag von Johan Ambrosius Barth.
[ 12 ] Einstein, A[lbert]. 1916c. “Näherungsweise Integration der Feldgleichungen de Graviation.” Sitzungs- berichte der Könich Preußischen Akademie der Wissenschaften zu Berlin, 1916 June 22, 688–696. [Reprinted in (Kox et al., Eds., 1996: Document 32, pages 347–357).]
[ 13 ] Einstein, A[lbert]. 1917. “Über die spezielle und die allgemeine Relativitätstheorie (Gemeinver- ständlich).” Braunschweig: Verlag von Friedr. Vieweg & Sohn. [Reprinted in (Kox et al., Eds., 1996: Document 42, pages 420–539).]
[ 14 ] Einstein, A[lbret]. 1918. “Über Gravitationswellen.” Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften, 1918 January 31, 154–167. [Reprinted in Janssen et al., Eds., 2002: Document 1, pages 189–196.]
[ 15 ] Einstein, Albert. 1920. Relativity: the Special & the General Theory. A Popular Exposition. Author- ized translation [of (1917)] by Robert W. Lawson. With three new appendices. London: Methuen & Co. Ltd. Available at www.f.waseda.jp > sidoli > Einstein Relativity (retrieved on 2020-09-18).
[ 16 ] Einstein, Albert. 1970. “Remarks concerning the essays brought together in this co-operative volume.” Translated (from the German typescript) by Paul Arthur Schillp. In: (Schillp, Ed., 1970:665– 688).
[ 17 ] Einstein, A[lbert]. 1973a. “On the effect of gravitation on the propagation of light.” In: (Kilmister 1973:128–139).
[ 18 ] Einstein, A[lbert]. 1973b. “The foundation of general relativity theory.” In: (Kilmister 1973:140–172). Translation of a part of (Einstein 1916a).
[ 19 ] Einstein, Albert. 1987. The Meaning of Relativity, xiv + 161 pages. Sixth edition. First published in 1922. London: Chapman and Hall.
[ 20 ] Eisenhart, L. P. 1923. “Einstein and Soldner.” Science, New Series, 58, No. 1512, 516–517 (1923 December 21).
[ 21 ] Feferman, Solomon, Editor-in-chief. 1990. Kurt Gödel; Collected Works. Volume II. Publications 1938–1974. New York, NY; Oxford: Oxford University Press.
[ 22 ] Gilmore, Gerard; Tausch-Pebody, Gudrun. 2020. “The 1919 eclipse results that verified general relativity and their later detractors: A story re-told.” Notes and Records. The Royal Society Journal of the History of Science. Published online on 2020 October 21.
[ 23 ] Gödel, Kurt. 1949. “An example of a new type of cosmological solutions of Einstein’s field equations of gravitation.” Rev. Modern Physics 21, 447–450. [Reprinted in (Feferman, Editor-in-chief, 1990:150–198).]
[ 24 ] Gödel, Kurt. 1952. “Rotating universes in general relativity theory.” Proceedings of the International Congress of Mathematicians, Cambridge, MA, 1950, volume 1, pages 175–181. Providence, RI: Amer. Math. Soc. [Reprinted in (Feferman, Editor-in-chief, 1990:208–216).]
[ 25 ] Goenner, Hubert. 1993. “The Reaction to Relativity Theory in Germany, III. ‘A Hundred Authors against Einstein’. ” In: (Earman et al., Eds., 1993:248–273).
[ 26 ] Goldstein, Rebecca. 2005. Incompleteness. The Proof and Paradox of Kurt Gödel, 296 pages. New York, NY; London: W. W. Norton & Company.
[ 27 ] Henriksson, Göran. 2017. “The acceleration of the Moon and the Universe the mass of the graviton.” Advances in Astrophysics, 2, No. 3, 184–196.
[ 28 ] Henriksson, Göran. 2020, ms. The mass of the graviton. Manuscript, 12 pages. Uppsala University, Department of Physics and Astronomy.
[ 29 ] International Astronomical Union. 2012. Resolution B2 on the re-definition of the astronomical unit of length, 2 pages.
[ 30 ] International Astronomical Union. 2015. Resolution B3 on recommended nominal conversion con- stants for selected solar and planetary properties, 6 pages.
[ 31 ] Janssen, Michel; Schulman, Robert; Illy, József; Lehner, Christoph; Kormos Buchwald, Diana, Eds. 2002. The Collected Papers of Albert Einstein, Volume 7, The Berlin Years: Writings, 1918–1921, xlviii + 689 pages. Princeton, NJ: Princeton University Press.
[ 32 ] Kilmister, C[live] W[illiam]. 1973. General Theory of Relativity, ix + 365 pages. Oxford et al.: Pergamon Press.
[ 33 ] Kox, A[nne] J.; Klein, Martin J.; Schulmann; Robert, Eds. 1996. The Collected Papers of Albert Einstein, Volume 6, The Berlin Years: Writings, 1914–1917, xxv + 626 pages. Princeton, NJ: Princeton University Press.
[ 34 ] Landau, L. D.; Lifshitz, E. M. 1975. The Classical Theory of Fields, xi + 402 pages. Fourth revised English edition, translated from the Russian by Morton Hamermesh. Oxford et al.: Pergamon Press.
[ 35 ] Lebach, D. E.; Corey, B. E.; Shapiro, I. I.; Ratner, M. I.; Webber, J. C.; Rogers, A. E. E.; Davis, J. L.; Herring, T. A. 1995. “Measurement of the solar gravitational deflection of radio waves using very-long-baseline interferometry.” Phys. Rev. Lett. 75, 1439–1442.
[ 36 ] Lemos, José P. S. 2019. Shadow of the Moon and general relativity: Einstein, Dyson, Eddington and the 1919 light deflection, 63 pages. Avaiblable at https://arXiv.org.pdf/1912.05587.pdf (accessed 2020-05-23).
[ 37 ] Lemos, José P. S.; Herdeiro, Carlos A. R.; Cardoso, Vitor. 2019. Einstein and Eddington and the eclipse in Principe: Celebration and science 100 years after, 12 pages. Available at https://arXiv.org/pdf/1912.08354.pdf (accessed 2020-05-23).
[ 38 ] Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archbald. 2002. Gravitation, xxvi + 1279 pages. New York, NY: W. H. Freeman and Company.
[ 39 ] Møller, C. (1952, 1955), 1957. The Theory of Relativity. Oxford: The Clarendon Press.
[ 40 ] Pais, Abraham. 1982. ‘Subtle is the Lord . . . ’. The Science and Life of Albert Einstein, xvi + 552 pages. Oxford et al.: Oxford University Press.
[ 41 ] Poor, Charles Lane. 1927. “The relativity deflection of light.” The Journal of the Royal Astronomical Society of Canada, XXI, No. 6, 225–238.
[ 42 ] Robertson, D. S.; Carter, W. E.; Dillinger, W. H. 1991. “New measurement of solar gravitational deflection of radio signals using VLBI.” Nature 349, 768–770.
[ 43 ] Schillp, Paul Arthur, Ed. 1970. Albert Einstein: Philosopher–Scientist, xviii + 781 pages. London: Cambridge University Press.
[ 44 ] Schwarzschild, K[arl]. 1916. “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie.” Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften, 189–196.
[ 45 ] Schwinger, Julian. 1986. Einstein’s Legacy. The Unity of Space and Time, xii + 250 pages. New York, NY: Scientific American Books, Inc.
[ 46 ] Shapiro, I. I.; Reasenberg, R. D.; MacNeil, P. E.; Goldstein, R. B.; Brenkle, J. P.; Cain, D. L.; Komarek, T.; Zygielbaum, A. I.; Cuddihy, W. F.; Michael, W. H., Jr. 1977. “The Viking relativity experiment.” Journal of Geophysical Research, 82, Issue B28, 4329–4334.
[ 47 ] Shapiro, S. S.; Davis, J. L.; Lebach, D. E.; Gregory, J. S. 2004. “Measurement of the solar gravitational deflection of radio waves using geodetic very-long-baseline interferometry data, 1979–1999.” Phys. Rev. Lett. 92, 121101-1–121101-4.
[ 48 ] Shapiro, Steven S.; Shapiro, Irwin L. 2010. “Gravitational deflection of light.” In: Einstein Online, Band 04, 03-1003.
[ 49 ] Soffel, Michael H. 1989. Relativity in Astrometry, Celestial Mechanics and Geodesy. Berlin: Springer- Verlag.
[ 50 ] von Soldner, J. G. 1801–1804. “On the deflection of a light ray from its rectilinear motion, by the attraction of a celestial body at which it nearly passes by.” Berliner Astronomisches Jahrbuch, pages 161–172. [Title probably translated from the German original.]
[ 51 ] von Soldner, J. 1921. (Lenard, P.): “Über die Ablenkung eines Lichtstrahls von seiner geradlinigen Bewegung durch die Attraktion eines Weltkörpers, an welchem er nahe vorbeigeht; von J. Soldner, 1801.” Annalen der Physik 65(15), 593–604.
[ 52 ] von Soldner, Johann Georg (1776–1833). Wikipedia.
[ 53 ] Sternberg, Shlomo. 2012. Curvature in Mathematics and Physics, 405 pages. Mineola, NY: Dover Publications, Inc.
[ 54 ] Titov, O.; Girdiuk, A.; Lambert; S. B.; Lovell; J.; McCallum; J.; Shabala, S.; McCallum, L.; Mayer, D.; Schartner, M; de Witt, A.; Shu, F.; Melnikov, A.; Ivanov, D.; Mikhailov, A.; Yi, S.; Soja, B.; Xia, B.; Jiang, T. 2018. “Testing general relativity with geodetic VLBI. What a single, specially designed experiment can teach us.” Astronomy & Astrophysics 618, article A8.
[ 55 ] Wazeck, Milena. 2009. Einsteins Gegner. Die öffentliche Kontroverse um die Relativitätstheorie in den 1920er Jahren, 429 pages. Frankfurt/Main; New York, NY: Campus Verlag.
[ 56 ] Wazeck, Milena. 2014. Einstein’s Opponents: The Public Controversy about the Theory of Relativity in the 1920s. Cambridge: Cambridge University Press.
[ 57 ] Weber, J[oseph]. 1964. “Gravitation and light.” In: Chiu, Hong-Yee; Hoffmann, William F., Eds., pages 231–240. Gravitation and Relativity, xxxv + 353. New York, NY; Amsterdam: W. A. Benjamin, Inc.
[ 58 ] Will, Clifford M. 2017. “Did Einstein get it right? A centennial assessment.” Proceedings of the American Philosophical Society 161, No. 1, 18–30.
[ 59 ] Wright, Edward L. 2004. Deflection and delay of light. Available at www.astro.ucla.edu/˜wright/deflection-delay.html (accessed 2020-05-06).
[ 60 ] Xu, Feng. 2002. “Light deflection near the Sun’s limb: refraction by the solar atmosphere.” Solar physics 206, 243–248.