jbriggs444 said:
What is the difference between those two quantities?
You mean the "angular velocity of the Earth [about the sun] with respect to the fixed stars", perhaps? If so then no, you would not want to add those two quantities together.
That's probably not the best way to describe it, but if you let
wf = Earth's rotation relative to the fixed stars
ws = Earth's rotation relative to it's orbit around the sun
we = rotation perceived on earth
Then we + ws = wf
Probably, a better way to describe it is that relative to the fixed stars the rotation of the Earth about its axis is 366 / yr
The perceived rotation on Earth is 365 / yr.
The difference is due to the Earth in its orbit is rotating from east to west at 1 rotation /yr or, in
other words, if the Earth had no rotation about its axis, an observer on Earth would see the sun
rise once in the west and set once in the east per year effectively losing a day
from the 366 rotations about its axis per year.
Phileas Fogg learned this in his journey of "80 Days Around the World".
Since he traveled from west to east he saw the sun rise 80 times while his
companions in London only observed 79 sunrises.
(The Earth under him rotated one time from east to west during his journey)