Inclinations of Uranus' moons

[2552]

Is this right? Orbit MFD says Ariel's (and most of Uranus' moons) equatorial inclination to Uranus is 179.93 degrees. JPL Horizons also gives an equatorial inclination of 179.9638656407854 for Ariel. But Ariel isn't a retrograde moon, in fact JPL gives an equatorial value of 0.041 on this page, and Wikipedia gives 0.026. Which value is correct? I see that Uranus.cfg has a negative rotation period set so the moons will orbit in the same direction Uranus rotates, but why does JPL Horizons also give 179?

These are the settings I used in Horizons:

Ephemeris Type [change] : ELEMENTS
Target Body [change] : Ariel (UI) [701]
Center [change] : Uranus (body center) [500@799]
Time Span [change] : discrete time(s)=2451545
Table Settings [change] : reference plane=BODY EQUATOR
Display/Output [change] : default (formatted HTML)

 

[2552]

*after some googling*

Nevermind, they're both technically right. ~179 degrees if you set Uranus (as orbiter does) to 82.19 degrees of obliquity and retrograde rotation, and ~1 degree* if you set Uranus to 97.77 and prograde rotation. But if the inner moons orbit in the same direction as Uranus rotates, shoudn't their equatorial inclination in Orbit MFD be displayed as prograde (~1 degree)? Or is prograde in orbit around a planet considered to be east even if the planet rotates westward?

*Actually, I tried that just now and Orbit HUD displays Ariel's equatorial inclination as 164.45 degrees and Ariel's orbit appears tilted against Uranus's rings by probably 15.54 degrees. Edit: setting the obliquity to -1.7064078 (-97.77 degrees converted to radians) and the rotation as positive 62064 seems to work, Ariel's inc is shown as 0.07.

 

[tblaxland]

Thanks for the update.

With regards to the prograde question, a positive (what you are calling prograde) rotation is determined by the right hand grip rule. I that light, what you have described makes sense.