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16

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 ...


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 ...


5

"All earth orbiting satellites should have the same velocity" is not true. Kepler's Laws merely state that an object in a circular orbit at a particular altitude must have a particular speed. Not all objects in orbit are in a circular orbit. Non-circular (elliptical) orbital paths can cross one another as the object's altitude varies. Also, speed ...


3

According to Kepler laws all earth orbiting satellites should have the same velocity. This is not correct. It is not even close to correct. Mercury orbits the Sun at a much higher speed than does Pluto. Just as bad, you are conflating speed with velocity, which are two very different things. By way of analogy, consider the case of a person who mistakenly ...


3

The Milky Way's outer halo has many globular clusters with a retrograde orbit (about 40% of all clusters in Milky Way). One of the more prominent example include Kapteyn's star which is highly retrograde due to it being ripped from a dwarf galaxy and merging with the Milky Way. However, the structure of the halo is a topic of an ongoing debate. Several ...


2

You can do this without having to know or derive the vis-viva equation, just by applying conservation of energy and angular momentum. At perihelion and aphelion the velocities are purely tangential, so conservation of angular momentum yields $$ r_p v_p = r_a v_a\ ,$$ $$ a(1-e)v_p = a(1+e)v_a\ .$$ Conservation of energy (potential plus kinetic) then gives $$ -...


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