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
For a circle, $a=b$, which implies that $f=e=0$. In modern orbital ...
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 ...
"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 ...
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 ...
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 ...
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