With the change of subject, I take it that you're satisfied with the explanations for the difference between sidereal and solar days, why we see different stars at different times of year, and how the seasons work in the Heliocentric Model.
You're making this way harder than it actually is.
Maybe but now I have a new problem that seemingly shows Earth concave when calculating AU from Jupiter's Moons from Simulation software:
Imagine that. It seems like every time you misinterpret or miscalculate something, the only possible explanation for the result you see is "we're living inside a concave earth!"
(From This GooglePlus channel here on Sep 10th, 2014 (if you look at this post in the future): https://plus.google.com/u/0/103461383283161976782/posts look for his post about " You might like to know that I managed to get a confession out of +Sculelos, regarding the fact that they simply used software which employs calculations based on the non-geocentric model" (Which is correct as I was actually using a Celestial sphere model (with the heavens inside the earth aka Concave Earth theory based))
I actually was using a celestial sphere based model to calculate Jupiter's Jovian moons. Concave Earth uses a celestial sphere, but besides that huge point I ran into problems when using a heliocentric simulation, let me explain.
I'm not sure why we're invited to view the aftermath of an argument you had (and lost, if your synopsis above is accurate) with someone on Google+. I'm not a member of Google+ and see no reason to join, so I'll pass, thanks.
The simulation was ran by what angle we see Jupiter from North America Mountain Daylight Time so rotation and orbit of Earth literally doesn't matter.

Jupiter only moves about 8.31% of one degree in respect to the background stars every-day so every 12 days and 48 minutes it moves 1 degree West in the Sky.
When viewed from the sun that 0.083 degree/day sounds about right, but it's moving eastward in the sky, not west. From the earth it's not so simple. Because of parallax due to our different orbits, it varies quite a bit, even appearing to reverse directions for a while.
How, by the way, does a hollow earth with the universe inside it explain apparent retrograde motion of the planets? [Edit] On second thought, don't get distracted trying to answer this. Focus!
Right now Jupiter would be in the roughly 8:36 pm position when Earth is in the 12:00 am position. So they are about 42.35 degrees apart.
Is this a 24-hour clock or a 12-hour clock you are comparing these positions to? Since you're using AM/PM, it suggests a 12h clock, but 9 o'clock is 90 degrees from 12 o'clock on a 12h clock and 8:36 is more; on a 24h clock, 21:00 (9 PM) is 45 degrees from 00:00 (12:00 AM), but 20:36 (8:36 PM) is greater than 45 degrees, not less. Where are you getting 42.35 degrees?
What do these positions refer to, anyway? Is it the position of the planets in their orbits relative to the sun? If so, they're not right for times near now. If not (and I expect it isn't, since you aren't a Heliocentric kind of guy), what are they?
Jupiter's Moons in comparison would be around 6 degrees each from Jupiter in comparison this means Jupiter should be around 7 AU.
Where did that 6 degrees come from? I think the most distant of the Galilean moons, Callisto, appears at most about 1/6 degree from Jupiter when viewed from earth. The others are closer. How does this lead you to determine Jupiter is 7 AU, and from what?
In heliocentric theory this should be around 4.65 AU if we take Jupiter's average of 5.2 AU in demonstration and subtract 42 degrees.
How can you subtract an angle from a distance? Can you show the exact math you're using?
Then the question becomes why does heliocentric theory predict 4.65 AU when in reality we get 7 AU? Let's check this out with concave model: In concave model Earth is the edge of the entire universe and wraps in on itself. Thus we get a Sun that is 1 AU away from us. Jupiter being -42 degrees from Earth would mean it's 138 degrees from the Sun. 138 degrees is 1.5333% of 4.65 AU so we get about 7.13 AU according to the concave model where as the geocentric and heliocentric models both predict 4.65 AU. Flat Earth theory the whole Earth plane would be 90 degrees even so the Sun would only be 34.5 degrees of this plane which would translate to 4 AU. So it seems like Heliocentrism and Geocentrism both have the same prediction of 4.65 AU, Flat Earth theory predicts 4 AU and Concave Earth theory predicts 7 AU. Only one is correct.
Actually, none of these are correct. The question remains where did you get these numbers and what are they supposed to mean? It looks like you're again just slamming numbers together until you see a result you like. Then you take that result as proof of an inside-out universe.
Jupiter is currently just over 6 AU from earth since it's near the opposite side of the sun from us.