Appendix

Table of equations

Quantity	Equation
Ellipse	\(r=\dfrac{p}{1+e\cos\theta}\)
Area law	\(\dot A=\frac12 r^{2}\dot\theta =\frac{h}{2}= \text{const}\)
Harmonic law	\(T^{2}\propto a^{3}\)
Gravity	\(\vec F_{21} = -\dfrac{Gm_{1}m_{2}}{r^{2}}\hat{u_r}\)
Reduced EoM	\(\ddot{\vec r}=-\dfrac{\mu}{r^{3}}\vec r\)
Specific angular momentum	\(\vec h=\vec r\times\dot{\vec r}\)
Laplace–Runge–Lenz vector	\(\vec e=\dfrac{\dot{\vec r}\times\vec h}{\mu}-\dfrac{\vec r}{r}\)