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Both ellipticity $f$ (also called flattening) and eccentricity $e$ are measures of how elongated an ellipse is, based on the semi-major axis $a$ and the semi-minor axis $b$ (figure from wikipedia). They are defined respectively as $$f=\frac{a-b}{a}$$ and $$e=\sqrt{1-\frac{b^2}{a^2}}$$ For a circle, $a=b$, which implies that $f=e=0$. In modern orbital ...


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Ellipses have a "long radius" called the "semi-major-axis" which is the length from the centre to the ellipse measured along the long axis. And a "semi-minor-axis" which is measured along the short axis. Call the semi-major-axis "a" and the semi-minor-axis "b". Ellipses also have foci: which is where the ...


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There are two types of angular momentum of each planet: orbital angular momentum of the planet around the Sun, and rotational angular momentum of the planet around its rotational axis. Orbital angular momentum $L_{orb}$ is typically calculated at perihelion or aphelion as $L_{orb}=mvr$, where $m$ is the mass of the planet, $v$ is the instantaneous orbital ...


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You are doing many things wrong. You are computing the eccentricity of one body with respect to the center of mass. You need to compute the eccentricity of one body with respect to the other. You are using reduced mass in np.cross(Ve, Le, axis=0) / mred - Xe / np.sqrt(np.sum(np.square(Xe), axis=0)) This is wrong for multiple reasons. First off, look at the ...


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ANSWER I would put the massive object at the origin. Then, I would calculate the velocity at periapsis, when $r=a(1-e)$ as $$v = \sqrt{GM\frac{1}{a}\left(\frac{1+e}{1-e}\right)}$$ (stolen from Uhoh's answer to Calculating object velocity at perihelion ). Put the periapsis on the positive y axis. Then the velocity vector at periapsis is $\vec{v}=[v,0]$. If ...


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