Calculation of the Cosmological Constant for the Planetary System in Schwarzschild’s Cosmological Model

Abstract

In this work, the static cosmological model of the Schwarzschild solution for the solar system is proposed taking into account the cosmological constant in the equation of the general theory of relativity (GTR) proposed by A. Einstein. We found the nonlinear differential equation that describes the behavior of the planets around the Sun; this is solved exactly by the Jacobi and Weierstrass elliptic functions. The obtained solution allows for us to estimate the value of the cosmological constant knowing the perihelion of the different planets and from different mathematical approaches; that is, the inverse problem is solved. From the obtained results, the Schwarzschild static cosmological model for the solar system is proposed, establishing the Schwarzschild cosmological radius and the curvature limit of the solar system. From the curvature limit, different regions are proposed for the planets, exoplanets, and a region is predicted where the existence of new planets and exoplanets belonging to the solar system is possible. The proposed theory of the static Schwarzschild cosmological model may be of great interest to astronomers, cosmologists, and all those interested in the study of the universe.