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.

中文翻译：

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史瓦西宇宙模型中行星系统宇宙常数的计算

在这项工作中，考虑到爱因斯坦提出的广义相对论（GTR）方程中的宇宙学常数，提出了太阳系史瓦西解的静态宇宙学模型。我们发现了描述太阳周围行星行为的非线性微分方程；这完全由 Jacobi 和 Weierstrass 椭圆函数解决。获得的解决方案使我们能够根据不同行星的近日点和不同的数学方法来估计宇宙学常数的值；也就是解决了逆问题。根据所得结果，提出了太阳系史瓦西静态宇宙学模型，建立了史瓦西宇宙学半径和太阳系曲率极限。从曲率极限，为行星、系外行星提出了不同的区域，并预测了一个可能存在属于太阳系的新行星和系外行星的区域。提出的静态史瓦西宇宙学模型理论可能会引起天文学家、宇宙学家和所有对宇宙研究感兴趣的人的极大兴趣。