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So I've been having fun with trying to determine where the perihelia of different planets are (using JPL Horizons).

And by the time I got to Saturn, something weird started happening. I've noticed that at some moments true anomaly (that I've used to track perihelion time) started falling rather than rising. I've also noticed that it seems to be only a slight effect, which also demonstrated ~ 17 days period. So I though: perhaps that's the effect of Titan, right? Problem solved.

Yet now I look at Neptune's true anomaly (see the last column on the picture) and have absolutely no idea what's going on. Can somebody explain, please? How is something like that even possible? It's like the planet decided to go backwards for a change.

My settings are:

Ephemeris Type [change] : OBSERVER

Target Body [change] : Neptune [899]

Observer Location [change] : Sun (body center) [500@10]

Time Span [change] : Start=1900-01-01, Stop=2100-12-01, Step=1 Y

Table Settings [change] : QUANTITIES=18,41

Display/Output [change] : default (formatted HTML)

enter image description here

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    $\begingroup$ barrycarter's answer is right. You can read more about osculating elements and why you should use them carefuly or not at all in these answers: 1, 2, 3 $\endgroup$ – uhoh Dec 11 '18 at 8:18
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Short answer: because Neptune's argument of the perifocus, the reference point for the true and mean anomalies jumps around a lot because Neptune's orbit is nearly circular.

If you run HORIZONS w/ the following parameters:

enter image description here

you'll notice Neptune's mean anomaly also decreases at times.

Both of these occur because Neptune's argument of the perifocus (from which both anomalies are measured) is itself jumping around quite a bit.

Except when Neptune is actually at perihelion, the argument of the perifocus is a theoretically computed point, not representing any actual physical quantity.

The function NASA uses to calculate the argument of the perifocus is oscelt, and specifically notes:

6) If the eccentricy of the orbit is very close to but not equal to zero, the argument of periapse may not be accurately determined.

To summarize, using the true anomaly to determine's Neptune's position is a bad idea, unless you also account for the changing argument of the perifocus.

As you note, Neptune's ecliptic longitude behaves much better, because the zero point of the ecliptic, which, while based on the Earth's precession and thus not completely fixed, nonetheless moves very slowly, much slower than Neptune's orbit.

Of course, the "best" coordinate system to use is something like ICRF, which is unchanging with respect to the fixed stars.

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