Tomado de arXiv
``1. INTRODUCTION
The motion of a planet around a star can be understood in the context of the two-body problem, where two bodies exert a mutual gravitational effect on each other. The solution to the problem was first presented by Isaac Newton (1687) in his Principia. He was able to show that the observed elliptical path of a planet and the empirical laws of planetary motion derived by Kepler (1609, 1619) were a natural consequence of an inverse square law of force acting between a planet and the Sun. According to Newton’s universal law of gravitation, the magnitude of the force between any two masses $m_1$ and $m_2$ separated by a distance $r$ is given by
$F = G \frac{m_1m_2}{ r^2}$ (1)
where $G = 6.67260 \times 10^{-11}Nm^2 kg^{-2}$ is the universal gravitational constant. The law is applicable in a wide variety of circumstances. For example, the two bodies could be a moon orbiting a planet or a planet orbiting a star. Newton’s achievement was to show that motion in an ellipse is the natural consequence of such a law.''
