We start with a simpler case first, the Earth-Sun system in two dimensions only. The gravitational force \( F_G \) is $$ F=\frac{GM_{\odot}M_E}{r^2}, $$ where \( G \) is the gravitational constant, $$ M_E=6\times 10^{24}\mathrm{Kg}, $$ the mass of Earth, $$ M_{\odot}=2\times 10^{30}\mathrm{Kg}, $$ the mass of the Sun and $$ r=1.5\times 10^{11}\mathrm{m}, $$ is the distance between Earth and the Sun. The latter defines what we call an astronomical unit AU. From Newton's second law we have then for the \( x \) direction $$ \frac{d^2x}{dt^2}=\frac{F_{x}}{M_E}, $$ and $$ \frac{d^2y}{dt^2}=\frac{F_{y}}{M_E}, $$ for the \( y \) direction.