Four Mistakes in the Original Paper of Einstein in 1915 to Calculate the Precession of Mercury’s Perihelion

Volume 7, Issue 2, April 2022     |     PP. 41-56      |     PDF (1770 K)    |     Pub. Date: April 14, 2022
DOI: 10.54647/physics14418    98 Downloads     5321 Views  

Author(s)

Mei Xiaochun, Department of Theoretical Physics and Pure Mathematics, Institute of Innovative Physics in Fuzhou, Fuzhou, China

Abstract
Based on the gravitational field equations of general relativity, Einstein proposed a formula to calculate the precession of Mercury’s perihelion in 1915. It is pointed out in this paper that there were four mistakes in Einstein's original paper. The first was the mistake of integral calculation discovered by Huadi in 2015. If this mistake did not exist, the precession value of Mercury’s perihelion was 71.7” a century. The second was the mistake of the expansion coefficient of integral function. If this mistake did not exist, the precession value of Mercury’s perihelion was 14.3” a century.The third was to treat the perihelion and aphelion of Mercury’s elliptical orbit as poles of integrand expansion, resulted in that the correction term of general relativity should be equal to zero. The fourth was Einstein’s assumption that the constant terms in the formula to calculate the precession of Mercury’s perihelion was equal to those in the Newton’s formula of gravity. However, by precise calculations based on the Schwarzschild metric and the geodesic equation of Riemann geometric, this constant term must be equal to zero. The result means that general relativity can only describe the parabolic orbits (with minor corrections) of planets in the solar system. It can not describe the elliptical and hyperbolic orbits of celestial bodies. So Einstein did not prove that general relativity could explain the precession of Mercury's perihelion with the value of 43” a century. Since the fourth mistake was fatal which made the equations of planetary motion of general relativity untenable, Einstein's gravity theory of curved space-time does not hold.

Keywords
General relativity, Newton's theory of gravity, Mercury's perihelion precession, Riemann geometry, Geodesic equation, Parabolic orbits, Elliptical orbit, Hyperbolic orbit

Cite this paper
Mei Xiaochun, Four Mistakes in the Original Paper of Einstein in 1915 to Calculate the Precession of Mercury’s Perihelion , SCIREA Journal of Physics. Volume 7, Issue 2, April 2022 | PP. 41-56. 10.54647/physics14418

References

[ 1 ] Ji Hao, Problems and Challenges in the Theory of General Relativity, Huaxia Culture Publishing Co., p.329.
[ 2 ] Wadi, The problem of Mercury precession proved that Einstein's general theory of relativity is wrong, http://blog.sina.com.cn/s/blog_49905be30102wclr.html.
[ 3 ] Mei Xiaochun，The Precise Calculations of the Constant Terms in the Equations of Motions of Planetsand light of General Relativity, Physics Essays，2021, 34 (2), p.183 ~ 192.https://www.researchgate.net/publication/351730530_The_precise_calculations_of_the_constant_terms_in_the_equations_of_motions_of_planets_and_photons_of_general_relativity.
[ 4 ] Einstein, Explaining Mercury's Perihelion Precession with General Relativity, Commercial Press, Einstein Papers, Vol. 2, p.268.
[ 5 ] Anatoli Andrei Vankov，Einstein’s Paper: “Explanation of the Perihelion Motion of Mercury from General Relativity Theory”, IPPE, Obninsk, Russia; Bethany College, KS, USA.
[ 6 ] Liu Liao, Zhao Zheng, General Relativity (2nd edition), Higher Education Press, 2004, p.158.
[ 7 ] Feng Linbao, Liu Xuecheng, Liu Mingcheng, General Relativity, Jilin Science and Technology Press, 1995，p. 112.
[ 8 ] S. Weinberg, Theory of Gravity and Cosmology, Science Press, 1984, p. 208, 211, 228.
[ 9 ] Zhang Yongli, Introduction to Relativity, Yunnan People's Publishing House, 1980, p. 414.
[ 10 ] Zhou Yanbai, Theoretical Mechanics, Jiangsu Science Jiangsu Press, 1961, p. 117.
[ 11 ] Mei Xiachun, The Precise Inner Solutions of Gravity Field Equations of Hollow and Solid Spheres and the Theorem of Singularity, International Journal of Astronomy and Astrophysics, 2011, 1, 109-116.
[ 12 ] Mei Xiachun, The Singularities of Gravitational Fields of Static Thin Loop and Double Spheres Reveal the Impossibility of Singularity Black Holes Journal of Modern Physics, 2013, 4, 974-982.
[ 13 ] Mei Xiachun, The Calculations of General Relativity on Massive Celestial Bodies Collapsing into Singular Black Holes Are Wrong, International Journal of Astronomy and Astrophysics, 4, 656-667.
[ 14 ] Mei Xiaochun, The R-W Metric Has No Constant Curvature When Scalar Factor R(t) Changes with Time —Influence of Space Curvature on the Densities of Dark Material and Dark Energy, International Journal of Astronomy and Astrophysics, 2011, 1, 177-182 .
[ 15 ] Mei Xiachun, Yu Ping, Cosmology Should Directly Use the Doppler’s Formula to Calculate the Red Shift of Ia Supernova — The Proofs That Metric Red Shift Is Inapplicable and Dark Energy Does Not Exist, International Journal of Astronomy and Astrophysics, 2013, 3, 303-317.