Classical Derivation of the Total Solar Deflection of Light
International Journal of Applied Mathematics and Theoretical Physics
Volume 2, Issue 4, October 2016, Pages: 52-56
Received: Aug. 7, 2016; Accepted: Sep. 23, 2016; Published: Oct. 19, 2016
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Steven D. Deines, Donatech Corporation, Inc., Fairfield, Iowa, USA
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It has been held that the total solar deflection of light could only be derived correctly by Einstein’s general theory of relativity. This paper provides a new classical derivation for the total gravitational deflection of light as a photon passes by the Sun. Newton, Cavendish, Einstein and others discussed or calculated how gravity may bend the paths of light. In particular, von Soldner published an incomplete classical derivation to predict a solar deflection that was half of the later observed value, since he assumed a light wave was deflected by a stationary Sun. Einstein’s earliest derivation used his equivalence principle of a homogeneous gravity field and a constant dynamical acceleration, which predicted half of the observed solar deflection angle, because he was then unaware of all the first-order space-time contributions. Einstein’s general relativity theory predicted the full solar deflection. Assuming the photon has a mass via Einstein’s mass-energy equation, this classical derivation uses Newton’s mechanical laws and his law of gravitation for the photon’s and the Sun’s hyperbolic paths about their mutual barycenter. Both the Sun and photon deflect each other about their barycenter with an infinite lever. This Newtonian derivation obtains the prediction of 1.75 against the celestial sphere for the full gravitational deflection of light relative to the Sun.
Photon Deflection, Solar Deflection, General Relativity
To cite this article
Steven D. Deines, Classical Derivation of the Total Solar Deflection of Light, International Journal of Applied Mathematics and Theoretical Physics. Vol. 2, No. 4, 2016, pp. 52-56. doi: 10.11648/j.ijamtp.20160204.15
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Newton, I., Philosophiae Naturalis Principia Mathematica, (1726), English Translation by Alexandre Koyr (1833) with variant readings as assembled and edited by Alexandre Koyr, Vol. 1, Harvard University Press, Cambridge Mass.
Michell, J. “On the means of discovering the distance, magnitude of the fixed stars ...”, Philosophical Transactions of the Royal Society, p. 35-57, and Tab III (1784).
Will, C.M. “Henry Cavendish, Johann von Soldner, and the deflection of light”, Am. J. Phys., 56, p. 413–415, (1988).
von Soldner, J. G. (1801), English translation “Johann Georg von Soldner and the gravitational bending of light” in Foundations of Physics, 8, p. 927-950, (1978).
Einstein, A. "Relativitätsprinzip und die aus demselben gezogenen Folgerungen (On the Relativity Principle and the Conclusions Drawn from It)", Jahrbuch der Radioaktivität (Yearbook of Radioactivity), 4: pp. 411–462. See page 454 (1908).
Einstein, A. “The effect of gravity on light” (1911), translated and reprinted in The Principle of Relativity, by Davis, F. A., Dover Publications (1928).
Nelson, R. A. “Post-Newtonian approximation for an accelerated, rotating frame of reference”, General Relativity and Gravitation, 22, Issue 4, p. 431-449 (1990).
Einstein, A. “Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity”, Preussische Akademie der Wissenschaften, Sitzungsberichte, (part 2), p. 831–839 (1915).
Will, C. M. “The Confrontation of General Relativity and Experiment”, Living Reviews of Relativity, 9 (3), p. 39, (2006).
Einstein, A. “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt (trans. On a Heuristic Viewpoint Concerning the Production and Transformation of Light)”, Annalen der Physik, 17 (6), p. 132–148 (1905).
Einstein, A. “Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? (trans. Does the Inertia of a Body Depend Upon Its Energy Content?)”, Annalen der Physik, 18 (13), p. 639–641 (1905).
Renn, J., [Ed.] Albert Einstein-Chief Engineer of the Universe: One Hundred Authors for Einstein, Wiley-VCH, Berlin, p. 178-187 (2005).
Seidelmann, P. K. [Ed.] Explanatory Supplement to the Astronomical Almanac, U.S. Naval Observatory, University Science Books (1992).
Kaplan, M. H. Modern Spacecraft Dynamics and Control, John Wiley & Sons, New York, p. 300-304 (1976).
Shapiro, S. S., Davis, J. L., Lebach, D. E., and Gregory, J. S. “Measurement of the Solar Gravitational Deflection of Radio Waves using Geodetic Very-Long-Baseline Interferometry Data, 1979-1999”, Physical Review Letters, 92, No. 12, p. 121101-1 to 4 (2004).
Serway, R. A. and Jewett Jr., J. W., Physics for Scientists and Engineers, Cengage Learning, 9th ed. (2014).
Walton, F. R. “The Library of History of Diodorus Siculus”, pub. in Loeb Classical Library, Vol. XI (1957).
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