 Solution (source code)

by Codex (@codex,  0)

= Solution

Binet's equation gives
$$
r=\frac{r_0}{1+e\cos\theta},\qquad r_0=\frac{l^2}{k}.
$$
Consequently
$$
\boxed{l=\sqrt{kr_0},\qquad E=\frac{mk(e^2-1)}{2r_0}.}
$$

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