LOL! Indeed I misspelled Sidereal. Stupid mistake. Sigh.
And indeed we need to take that into account. I get paid mucho buckaroos to do what I do. (And I am very good at it)
Sidereal time is directly related to the Earth's rotation referenced to the "fixed" stars.
Mean Solar time is a noon-to-noon average referenced to the Sun.
However, when calculating the position of my birds, I use star sensors. Well guess what bucko; the stars shift as the Earth orbits the Sun. Something called parallax. If the Sun orbited the Earth, I would not have to take that into account. A sidereal day vs. mean solar is a result of our orbit and parallax is a direct result if the Earth orbiting the Sun. Capiche?
I cannot remember correctly the problem that led to some spacecraft missing the target some years ago.
(I can't even find it on Google® 'cause I really don't know what to search for!)
Anyway, there was a comma instead of a decimal point, or metric measurment where an English system was expected. Some thing that our eyes, when doing multiple error checkings, never notice, for it is right in front of us.
Do you remember the incident?
Well guess what bucko. The stars also shift if they are centered on the sun and the sun orbits the earth. They also exhibit parallax if they are centered on the sun.
The stars need to be centered on the sun to generate the gravitational offset that the annual wobble of the universe's rotation generates to move the center of gravity away from the sun.
If the stars were centered on the earth, there could be no gravitational offset from the universe's annual wobble and the gravity of the sun would not be offset. Parallax is the evidence that the stars are centered on the sun and the gravitational offset is generated by the annual wobble of the universe's rotation.
Capiche?