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$$\begin{array}{cc} \text{fundamental relations}\\\hline v^2=\mu\left(\frac{2}{r}-\frac{1}{a}\right)\stackrel\odot=\frac{\mu}{r}\\ \frac{v^2}{2}-\frac{\mu}{r}=-\frac{\mu}{2a}=\epsilon<0\\ v_\text{esc}^2\stackrel\odot=\frac{2\mu}{r}\\ r=\frac{p}{1+e\cos\theta}\\ h^2=p\mu\\ r_p=\frac{p}{1+e}\\ r_a=\frac{p}{1-e}\\ a=\frac{r_p+r_a}{2}\\ p=a(1-e^2)\\ T=2\pi\sqrt\frac{a^3}{\mu}\\ M=E-e\sin E\\ \tan\frac{\theta}{2}=\sqrt{\frac{1+e}{1-e}}\tan\frac{E}{2}\\ M=n(t-t_p)\\ \end{array}$$ $$\begin{array}{cc} \text{constants}\\\hline \mu_\text{earth}=398600.4418(8)\text{ km}^3\text{ s}^{-2}\\ \mu_\text{moon}=4.9048695(9)\cdot 10^3\text{ km}^3\text{ s}^{-2}\\ \mu_\text{sun}=1.32712440018(9)\cdot 10^{11}\text{ km}^3\text{ s}^{-2}\\ \end{array}$$