-3dc97f3d182b6b0ed3d-437a 20221010191122488 hyperscienceij@gmail.com:rcrl hyperscienceij@gmail.com WEB-FORM Hyperscience International Journals HIJ 28213300 09 2022 2 3 Department of Physics, Islamic Azad University (IAU)-Varamin-Pishva Branch, Varamin, Iran Bijan Nikouravan https://orcid.org/0000-0003-4308-1632 Misha Nikouravan https://orcid.org/0000-0003-1976-8848 Department of Engineering, Sharif University, Tehran, Iran Lagrangian method applied as well as tensor method, for a linear transformed geodesic line element of Schwarzschild-like The ‎Lagrangian method was applied for a linearly transformed geodesic line element of a Schwarzschild-like solution instead of ‎the tensor method. The solution shows that it is not only valid for spherical objects but also it is more comprehensive for ‎elliptical celestial objects. Two types of kinetic and potential energy are the basis of the calculation. Hamiltonian and ‎Lagrangian equality show that the problem has no potential energy. With this transformed geodesic line element, we obtained ‎a new coefficient for the meridional advance of an experimental particle in Schwarzschild spacetime in terms of period, ‎eccentricity, and mean distance. This new perigee equation is not only valid for the Schwarzschild metric (for a spherical ‎object), but also more accurate for the Schwarzschild-like metric (for elliptical objects).‎ 09 2022 209 216 10.55672/hij2022pp209-216 https://hscience.org/index.php/hij/article/view/59