I am attempting to create a "top-down view" of the Saturnian System, using the Keplerian Elements + Rates provided here: https://ssd.jpl.nasa.gov/?sat_elem#saturn
To verify the validity of my simulation, I am using this NASA simulator: https://space.jpl.nasa.gov/
When I compare my findings with the NASA simulation, I realize that I am doing something wrong:
- JAN 1, 2000 (EPOCH): Simulation matches NASA simulation
- JAN 1, 2002: Simulation needs to be rotated 30 degrees to match NASA simulation
- JAN 1, 2004: Simulation needs to be rotated 60 degrees to match NASA simulation
So as time passes from the EPOCH I need to adjust my simulation by roughly 15 degrees per year to continue to have it match.
Why is this? Is this due to the changing angle between Saturn and the Earth, or am I not understanding the "Laplace Plane"?
NOTE: I am using the same logic I used to create a simulation for the 8 planets in our solar system and this simulation does not have this issue.
NOTE2: To calculate the "Longitude rate" for the moons, I multiple the value for "n" found on the JPL webpage by 36525 Julian Days (e.g. 381.9944948 degrees/day x 36525).
Below I add additional information based on the feedback from uhoh.
1) HOW I DO MY SIMULATION
First I used the elements & rates from the following JPL table: I noticed that the table does not give me "MEAN LONGITUDE" and "LONGITUDE OF PERIHELION". So I calculate them using the following formula:
- LONG. PERIHELION(W) = ARG. PERIHELION(w) + LONG. ASC. NODE(☊)
- MEAN LONGITUDE(L) = LONG. ASC. NODE(☊) + ARG. PERIHELION(w) + MEAN
Next to that, I realize I am missing the following rates:
So I set those all to 0 degrees per century. I know this is not ideal, but I can't imagine these rates would amount to a 30 degree mismatch after 2 years.
Finally, I calculate the "LONGITUDE RATE" using this formula: LONGITUDE RATE = n * 36,525 JULIAN DAYS
Since the position of moons match with the NASA simulation @J2000, I would think I am making a calculation mistake with this "LONGITUDE RATE"...
2) ROTATION AFTER SHORTER TIME PERIODS (6 MONTHS + 1 YEAR)
- JUL 1, 2000: Simulation needs to be rotated 10 degrees clockwise to match NASA simulation
- JAN 1, 2001: Simulation needs to be rotated 20 degrees clockwise to match NASA simulation
So it doesn't look it is 360 + 30...
ADDITIONAL INFORMATION PART II
Find here the complete JS source code for the Saturnian Simulation for reference with the issue described here: