Solving Kepler's equation via Smale's $\alpha$-theory

Martin Avendano, Verónica Martín-Molina, Jorge Ortigas-Galindo

We obtain an approximate solution $\tilde{E}=\tilde{E}(e,M)$ of Kepler's equation $E-e\sin (E)=M$ for any $e\in [0,1)$ and $M\in [0,\pi ]$. Our solution is guaranteed, via Smale's $\alpha$-th…