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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 ...


10

It has a low eccentricity, but there may not be a particular reason. Image by Kheider on wikipeda using Gravity Simulator by Trevor Dunn In a simulation of the solar system, both Earth and Venus had orbital eccentricities that were much below those of Mars and Mercury (note the two axes. Mars and Mercury are on a scale that is 10 times bigger). But in ...


9

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 ...


6

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 ...


5

Sirius is a binary system, composed of a main sequence star (Sirius A) and a white dwarf (Sirius B). The two orbit each other with a period of about 50 years, and the eccentricity given on Wikipedia is the eccentricity of the stars' orbits around one another. The inclination, according to Bond et al. 2017 - the paper Wikipedia references for both numbers - ...


5

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 ...


2

My answer won't be complete, from lack of time and resources, but I still wanted to share some interesting aspects here that could be helpful. The difficulty in aswering this question revolves around the complex and irregular shapes involved here. Also, finding a "best-fit" ellipse for comparison is not as easy as it seems, because it depends on what and ...


1

One uses the so called eccentricity vector, also called (up to a factor) Laplace-Runge-Lenz vector. Given the position $$\vec{r} = \begin{bmatrix}x\\ y\\ z\end{bmatrix}$$ of the object at given time $t$ and its velocity $$\vec{v} = \begin{bmatrix}u\\ v\\ w\end{bmatrix}$$ both with respect to an inertial coordinate system cantered at the origin of the ...


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