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 ...
"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 ...
It takes a spot "bump" half the rotation period to traverse from the blue side of the line profile to the red.
You can see that the bump has maybe moved across 20% of the profile in one night, so the rotation period would be estimated as $\sim 10$ days.
Looking up the period of Sigma Gem - it is 19.6 days. So my method is not very accurate by eye, ...
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
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 ...
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 ...