Proof of Kepler's Laws through the Lens of Newtonian Dynamics

Authors

  • Amitabh Kumar Veer Kunwar Singh University

DOI:

https://doi.org/10.59890/ijsas.v2i8.2316

Keywords:

Kepler's Laws, Newtonian Dynamics, Celestial Mechanics, Planetary Motion, Gravitational Forces

Abstract

At the beginning of the 17th century, Johannes Kepler developed the laws of planetary motion, which became fundamental to understanding the motion of celestial bodies. These principles have been crucial in forming our knowledge of the solar system and help us comprehend how planets orbit the Sun in elliptical orbits. Although Kepler's laws were derived from empirical observations, Isaac Newton's laws of motion and universal gravitation provided a solid theoretical foundation. This research article examines the evidence for Kepler's laws from a Newtonian dynamics perspective, highlighting the harmonious relationship between Kepler's observational discoveries and Newton's mathematical principles.

References

Landau, L., & Lifshitz, E. (1969). Mechanics. Pergamon Press.

Arnold, V. (1978). Mathematical methods of classical mechanics. Springer.

Bertrand, J. (1873). Théorème relatif au mouvement d’un point attiré vers un centre fixe. C. R. Académie des Sciences, 77, 849–853.

Bacry, H., Ruegg, H., & Souriau, J.-M. (1966). Dynamical groups and spherical potentials in classical mechanics. Communications in Mathematical Physics, 3(5), 323–333.

Goldstein, H. (1975). Prehistory of the “Runge-Lenz” vector. American Journal of Physics, 43(8), 737–738.

Goldstein, H. (1976). More on the prehistory of the Laplace or Runge-Lenz vector. American Journal of Physics, 44(11), 1123–1124.

Hill, E. (1951). Hamilton’s principle and the conservation theorems of mathematical physics. Reviews of Modern Physics, 23(3), 253.

Lévý-Leblond, J.-M. (1971). Conservation laws for gauge-variant Lagrangians in classical mechanics. American Journal of Physics, 39(5), 502–506.

Gonzalez-Gascon, F. (1977). Notes on the symmetries of systems of differential equations. Journal of Mathematical Physics, 18(9), 1763–1767.

Schweiger, F. (1964). Bemerkungen zum Laplace-Lenzschen Vektor. Acta Physica Austriaca, 17, 343–346.

Sexl, R. (1966). On classical systems with internal symmetry groups. Acta Physica Austriaca, 22, 159.

Stiefel, E., & Scheifele, G. (1971). Linear and regular celestial mechanics. Springer.

Rogers, H. (1973). Symmetry transformations of the classical Kepler problem. Journal of Mathematical Physics, 14, 1125.

Prince, G., & Eliezer, C. (1981). On the Lie symmetries of the classical Kepler problem. Journal of Physics A: Mathematical and General, 14, 587.

Nucci, M. (1996). The complete Kepler group can be derived by Lie group analysis. Journal of Mathematical Physics, 37, 1772–1775.

Krause, J. (1994). On the complete symmetry group of the classical Kepler system. Journal of Mathematical Physics, 35, 5734–5748.

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Published

2024-08-31

How to Cite

Amitabh Kumar. (2024). Proof of Kepler’s Laws through the Lens of Newtonian Dynamics. International Journal of Sustainable Applied Sciences, 2(8), 847–856. https://doi.org/10.59890/ijsas.v2i8.2316

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Section

Articles