# Comparative Study Of Generalized Newton Dynamical Gravitational Scalar Potential With The Golden Riemanian Dynamical Gravitational Scalar Potential

## DOI:

https://doi.org/10.60787/jnamp.vol68no1.432## Keywords:

Gravitational scalar potential, Taylor series, Golden Riemanian scalar potential, Spherical massive bodies Additional correction terms## Abstract

Over the years, there has been a growing need to generalize both Newton’s dynamical theory of gravitation and Einstein’s geometrical theory of gravitation to achieve better consistency with all physical theories. In this article, a Taylor series expansion approach was utilized to extend Newton’s dynamical gravitational field, resulting in the construction of a generalized dynamical gravitational field equation. This generalized equation was then applied to static, homogeneous spherical massive bodies to derive generalized exterior gravitational scalar potentials. The generalized dynamical gravitational scalar potential was utilized to analyze the motion of planets within the solar system. The findings reveal that this potential is enhanced by additional correction terms of all orders of ????−2 which are not present in Newton’s dynamical equation of motion. Additionally, the generalized dynamical gravitational scalar potential includes a ????−4 postNewtonian correction term. These results were compared with those obtained using the Golden Riemannian dynamical gravitational scalar.

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Okpara, P. A., Umahi, E. A. and Oboma, D. N. (2018). Generalized Dynamical gravitational scalar potential for static homogeneous spherical distribution of mass using Taylor series approach. Journal of the Nigeria Association of Mathematical Physics, vol 48, 243-246.

Nura, Y., Howusu, S. X. K, Nwagbara, O. and Nuhu, I. (2017). Solution of Newton gravitational field equation of a static homogeneous prolate spheoidal massive body. International Journal of Engineering Science and Innovation Technology (IJESIT) 6(1), 67-76.

Ebenezer, N. I. (2012). Gravitational fields Exterior to homogeneous spheroidal masses. The Abraham Zelmanov Journal, vol 5, 1-67.

Howusu, S. X. K. (2004). Einstein’s equation of motion in the gravitational field of an oblate speroidal body. Journal of the Nigerian Association of Mathematical Physics, 8(1), 251-260.

Chifu, E.N., Usman, A. and Meludu, O. C. (2010). Gravitational time dilation and length contraction in fields exterior to static oblate spheroidal Mass distributions. Journal of the Nigerian Association of Mathematical Physics, vol. 15, 247-252

Lumbi, W. L. and HOwusu, S. X. K. (2014). Generalized Dynamical Equation of motion for particles of non-zero mass for static Homogeneous spherical. Journal of the Nigerian Association of Mathematical Physics, 27(7), 365-368

Maisalatee, A. U., Lumbi, W. L. Ewa, I. I., Mohammed, M. and Kaika, Y. K. (2020). Generalization of Quantum Mechanical Wave Equation in Spherical coordinate using Great Metric Tensors and a Variable Gravitational Scalar Potential. Journal of the Nigerian Association of Mathematical Physics, 2(1), 139-147.

Lumbi, W. L., Howusu, S. X. K., Nwagbara, O. and Gurku, U. M. (2016). Generalization of Newton’s Dynamical Gravitational Scalar Potential for Static Homogeneous Spherical Distribution of Mass using Golden Laplacian Operator. International Journal of pure and

Applied Sciences. 6(1), 105-111

Lumbi, W. L., Nwagbara, O. Ewa, I .I., Yakubu, N. and Hassanu, M. (2017). A Generalization of Newton’s Planetary Gravitational Equation of Motion for Static Homogeneous Spherical Massive Bodies. International Journal of Theoretical and Mathematical Physics. 7(1), 1-3

Mungan, C. E. (2009). Three Important Taylor Series for Introductory physics. Lat. Am. J. Phys. Educ. 3(3):535-538

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*The Journals of the Nigerian Association of Mathematical Physics*,

*68*, 157-162. https://doi.org/10.60787/jnamp.vol68no1.432