When we have sidereal periods of a celestial body, we are told that it is a measure of the orbit in relation to a "distant star".
What is this distant start that everything is being compared to? I've been searching and searching, both through NASA's site as well as journals (and even sites like the Astronomy StackExchange), and have not found an explanation of what this "distant star" is!
Then, this further leads into how are they coming up with heliocentric longitudes? These seem to be based on the vernal point as a point of reference — thus, they have precession built in already. I'm inclined to believe these heliocentric longitudes are being found based off of geocentric observations done in right ascension, and then they are just using equations to convert them into heliocentric.
The only thing I've come across so far that has been a little help is this 1932 article by William H. Pickering entitled Planet U, and the Orbits of Saturn and Jupiter. On page 73, first paragraph, he states:
He, however, does not detail more beyond that. The number that current heliocentric ephemerides gives up for July 1872 for Saturn is off by a couple of degrees. I don't know if it's because our current ephemerides have precession already built in, or if it was because there was some error in their former readings.We feel that we may therefore safely use the longitude of the minimum of 1872.6 taken from the table number III published with the curve of Figure 1 in 1929. The corresponding heliocentric longitude for the former date, and not corrected for precession, is 289ª.8.
If current heliocentric longitudes do indeed have precession built in, what would be the equation to correct for this? I'm assuming the equation would also have to consider the tilt of the various orbits to one another.
For some of the things I'm investigating in the Gann thread, I'd need to know these parameters. One of the things I'm curious is whether or not the heliocentric position in relation to the stars (and NOT the vernal point) has any influence on the patterns we see.