Orbits of moons of Saturn :(

[selden]

I hope I'm doing something wrong, but I fear not.

I'm trying to pin down some of the flybys of Cassini through the Saturnian system. The ESA claims that the very first one is of Phoebe at a distance of about 52,000 km 19 days before Saturn orbital insertion. (See http://esapub.esrin.esa.it/bulletin/bullet92/b92kohlh.htm) That'd be on the 12th of June, 2004.

Celestia's custom orbit for Phoebe puts it ~180 degrees away in its orbit from Cassini on the 12th. So I sighed and asked Horizons for Phoebe's elliptical elements referenced to Saturn's barycenter for that epoch. Celestia shows "Phoebe 2004" to be ~180 degrees away from Cassini on the 12th, too. But that orbit has quite a different orientation.

So I asked Horizons for the elements for the other way-out satellite, Iapetus. After all, we "know" it's being drawn right because its eclipses are happening at the right time. Using those elements, Celestia draws "Iapetus 2004" 180 degrees away from where it draws Iapetus using its custom orbit.

So then I asked Horizons for Phoebe's Heliocentric xyz coordinates for that epoch... lo and behold they show closest approach to be 2059km at 2004 06 11 19:30 UTC. While closer and (maybe) sooner than it should be, it does indicate that Cassini's in about the right place and the elliptical orbital elements for Phoebe and Iapetus are confused and confusing.

I'm feeling rather depressed right now.

[selden]

So just to see what would happen, I asked Horizons for the orbital parameters for Io. I figured if I was asking wrong and causing the orbital phases were all messed up for Saturn, surely they'd be messed up for Jupiter.

Io-2002 (at the time of the Amalthea encounter) is in the right location in its orbit. But the orbit is tipped about 20 degrees.

So it looks like I'm getting the satellite orbits referenced to Earth's equatorial plane and not the local planet's equatorial plane. arrgh.
Yup. it looks like i need to specify "ecliptic" and not "frame" as the reference system. With that, Io's current orbit is only tipped 2 instead of 25 degrees, although it's still not identical to the custom orbit calc.

Next to redo phoebe and friends.

[selden]

Well, the tilt of the orbit changed again (and still doesn't match that of the "custom orbit" -- presumably I have to subtract Saturn's axiial tilt), but the phase is unchanged. Phoebe is still 180 degrees away on the other side of Saturn from Cassini. And never the twain shall meet....

So I did Titan, just to see if it's consistant. Yup: It's 180 off, too.

sigh.
I'm gonna sleep on it.
I must be doing something really stupid, but it is not at all obvious to me..

[selden]

I give up.
I can't persuade Horizons to generate elliptical orbital elements for Saturn's moons in the coordinate system that Celestia is using

Celestia's own orbit for Phoebe is wrong by 180 degrees, since it places Phoebe on the wrong side of the planet during the Cassini flyby.

I've generated an xyz trajectory for one of Phoebe's orbits. It has 2 day samples +/- 1 year around the Cassini flyby, with 15 minute samples +/- 2 days around it.

I've also generated a version of Cassini's xyz trajectory that includes 15 minute samples +/- 2 days around the Phoebe flyby.

Both are available on my Web page of spacecraft orbits. http://www.lns.cornell.edu/~seb/celestia/spacecraft.html#3.4.1

[granthutchison]

Selden:
Looking at Horizons' prediction for RA&dec, Phoebe does seem to be 180 degrees out of sync - on the day in question; east of Saturn in Celestia, west in Horizons. Although Phoebe orbits in a correct retrograde manner in Celestia, I can't help but wonder if the 180 anomaly isn't due to some coordinate transformation error in creating the CustomOrbit.
But Titan and Iapetus do seem to be correct, making rough positional comparisons to Horizons for the Cassini date, and checking the current Titan position against the S&T chart. But you're saying that Titan and Iapetus are coming up wrong as well?

Grant

[granthutchison]

Selden:

it looks like i need to specify "ecliptic" and not "frame" as the reference system. With that, Io's current orbit is only tipped 2 instead of 25 degrees, although it's still not identical to the custom orbit calc.

That's about right - Jupiter's equator is tilted 2.22 degrees to the ecliptic (J2000.0).

Grant

[selden]

Grant,

I realized this morning that I was asking for the orbital parameters in the wrong coordinate system, relative to the barycenter (@6).

The closest I could get was to use Saturn's body centered coordinate system (@699). That gave an angular position for Phoebe that was almost, but not quite correct. It was maybe 20 degrees off in the counter-clockwise direction. The orbital inclination was still slightly wrong, too.

Unfortunately, it is not at all obvious to me how to ask for the correct coordinate system. For example, what's the correct reference plane? [eclip, frame, body] ?

sigh.

[selden]

Grant,

My question about the correct reference frame was more from frustration. As best I can tell, "eclip" yields elements relative to the plane of the earth's orbit, "frame" yields elements relative to the plane of the earth's equator, and I would have expected "body" to yield elements relative to the plane of the central body's equator: Saturn in this case. If that's what Horizons does, then that's not the plane that Celestia seems to be using for Saturn.

Perhaps the problem is that Horizons uses the right plane, but its "node" is not the one that Celestia uses. In particular, the returned data file says "Coordinate system: Body Mean Equator and Node of Date" -- "Node of Date" being the problem. I don't see any obvious way to tell it the right epoch for the "Node" (and which "Node" does it mean?), or, for that matter, how to determine what epoch Celestia is using for its reference. Presumably J2000, I'd guess, but how to be sure?

p.s. Well, OK, rereading Horizons' doc file, it's pretty clear:

Body mean equator and node of date

Reference epoch: "of date"
Reference plane: ICRF/J2000.0 or FK4/B1950.0
xy-plane: central-body mean equator plane at reference epoch
x-axis : out along the ascending node of the central-body mean equator
plane on the reference plane at the reference epoch
z-axis : along the central-body mean north pole at the reference epoch

So this suggests to me that Celestia may not be positioning the elements relative to the ascending node of Saturn's equator at the epoch specified in the elements, but rather somehow is still referencing back to the equator's ascending node at J2000. But that's just a guess, rationalizing from the fact that the positions are still wrong.

[granthutchison]

Selden:
The orbital position of the planetary moons in Celestia is measured relative to the parent planet's equatorial ascending node on the ecliptic plane, not the Earth's equatorial plane. So we need to add in an offset for the difference between these two nodes, unless you can persuade Horizons to provide the data in the relevant reference frame.
For Saturn, the ecliptic ascending node lies 39.98 degrees counter-clockwise along Saturn's equatorial plane from its Earth-equatorial ascending node (I've had to work this out already to get my prime meridian offsets right). So that number needs to be subtracted from the Horizons data for longitude of the ascending node, longitude of the pericentre and mean longitude (but not from argument of the pericentre or mean anomaly, if the data come in that form).
(Doesn't sound as if this solves your problem, though - the number doesn't fit with any of the offsets you've reported :( .)

I'm still seeing Phoebe 180 degrees out of place in Celestia compared to Horizons, BTW. On 12 June 2004, for instance, Horizons gives these coordinates:
Saturn RA 6 57 39 Dec +22 28 08
Phoebe RA 6 59 21 Dec +22 27 52

So Phoebe is east and a hair south of Saturn. Fire up Celestia for that date, and Phoebe is west and a hair north.

Grant

[selden]

Well, I have to admit that I can't get too enthused about finding exactly what the offset is between the various "misaligned" orbital parameter sets returned by Horizons and the xyz set which is "correct". I'd rather Chris fixed the code for Phoebe's CustomOrbit.

To that end: as seen from Saturn, the CustomOrbit for Phoebe puts it on the Celestial Grid at somewhat more than 2H (2.3?) and somewhat less than +15 degrees (13?). While the xyz position is near 15.5 Hours, -10 degrees. So the difference isn't exactly 180 degeres.

It's times like this I think it'd be really nice if the Celestial Grid had some options in resolution, units, origin, etc.... Oh, silly me.. of course: give saturn some *really* high non-moving "clouds." I suspect appropriate fiducials could be created that way. ... I'll go ahead and post this while I try to create an appropriate grid with alpha channel.

[chris]

Selden:
The orbital position of the planetary moons in Celestia is measured relative to the parent planet's equatorial ascending node on the ecliptic plane, not the Earth's equatorial plane. So we need to add in an offset for the difference between these two nodes, unless you can persuade Horizons to provide the data in the relevant reference frame.
For Saturn, the ecliptic ascending node lies 39.98 degrees counter-clockwise along Saturn's equatorial plane from its Earth-equatorial ascending node (I've had to work this out already to get my prime meridian offsets right). So that number needs to be subtracted from the Horizons data for longitude of the ascending node, longitude of the pericentre and mean longitude (but not from argument of the pericentre or mean anomaly, if the data come in that form).
(Doesn't sound as if this solves your problem, though - the number doesn't fit with any of the offsets you've reported .)

I'm still seeing Phoebe 180 degrees out of place in Celestia compared to Horizons, BTW. On 12 June 2004, for instance, Horizons gives these coordinates:
Saturn RA 6 57 39 Dec +22 28 08
Phoebe RA 6 59 21 Dec +22 27 52

So Phoebe is east and a hair south of Saturn. Fire up Celestia for that date, and Phoebe is west and a hair north.

Grant

The custom orbit for Phoebe was just an experiment, and I didn't really mean to distribute a solarsys.ssc with it enabled. Does it seem to be exactly 180 degrees off? If that's the case, maybe I did something right with it and I just need to add the correct . . . I'll look at it again tonight, but for now, my advice would be to just comment out the CustomOrbit line for Phoebe and use elliptical elements.

I'm pretty sure that at some point I generated oribital elements in Horizons that are usable with Celestia. What you want are elements referred to the equatorial plane of Saturn . . . The fact that it's using the Body Mean Equator and Node of Date isn't a big problem. In fact, it's desirable, though Celestia currently just uses fixed equatorial planes (J2000) for all the major planets.

I'll try and sort this out . . . Grant, are you certain that Horizons reports the elements of satellites relative to the parent planet's equatorial ascending node on Earth's equatorial plane? I thought it was the ascending node on the ecliptic plane.

--Chris

[selden]

Clearly the code for clouds wasn't written with this in mind.. with a hdight of 200,000km, they disappear overhead when viewed from Saturn's "surface" and are visible only near the horizon. Oh, well.

Chris, as mentioned in my previous post, the offset ibetween xyz and Custom sn't quite 180. The elliptical orbital parameters provided in solarsys.ssc for Phoebe are way off, too.

On June 11 at 21:00, Elliptical Phoebe is at slightly ore than 0H (~15'?) RA, and about -3 degress Dec. while the xyz positin is at about 14h30' RA and -12deg Dec when seen from Saturn. Those are just crude guestimates, but it seems I misread the xyz RA (in the wrong direction from the 15h position?) before. I'd suggest you look at them yourself. I'm obviously getting tired. It's fairly straight forward: Phoebe has no visible parallax.

[granthutchison]

Grant, are you certain that Horizons reports the elements of satellites relative to the parent planet's equatorial ascending node on Earth's equatorial plane? I thought it was the ascending node on the ecliptic plane.

Hmmm. No, I don't think I am certain, now you mention it.
I'm interpreting "equator and node of date" to indicate the ascending node of the planetary equator on some plane, and the equatorial node the Astronomical Almanac uses is in on the Earth's equatorial plane. But you're right, I've no evidence that's what Horizons is using, nor can I find a definition on the JPL site.
I've been messing with osculating elements for the Galileans, and certainly my coordinate conversion hasn't yet improved the hit rate for mutual phenomena.

Grant

[granthutchison]

No, no, hang on; I knew I'd read this somewhere recently. It's Selden's quotation from the Horizons documentation:

Body mean equator and node of date

Reference epoch: "of date"
Reference plane: ICRF/J2000.0 or FK4/B1950.0
xy-plane: central-body mean equator plane at reference epoch
x-axis : out along the ascending node of the central-body mean equator
plane on the reference plane at the reference epoch
z-axis : along the central-body mean north pole at the reference epoch

So it's from the J2000.0 equator, not the ecliptic. Yes?

Grant

[granthutchison]

Yes!
Chris, the problem with the mutual events of Jupiter's satellites, at least, seems to be that their CustomOrbits are plotted relative to Jupiter's equatorial ascending node on the Earth's equator (as are the Horizons data), whereas Celestia is using the ascending node on the ecliptic.
I've taken Horizons osculating elements for the Gallileans on 05 Dec 2002 at 20:10 UT and laid them into Celestia as they stand - very close to the Celestia CustomOrbit positions at the same date and time, as you might expect. But no occultation of Callisto by Ganymede.
Scoot the ascending node of the Horizons data anticlockwise by 20.453 degrees (the distance from the ecliptic node to the Earth-equatorial node of the plane of Jupiter's equator) and Bingo! an occultation occurs bang on schedule. Similarly with the Europa-on-Io eclipse later on the 5th December, the Europa-on-Io occultation of 06 December, and the Io-on-Callisto annular occultation on the 7th.
At dates farther from the precise date of the osculating elements the moon-on-moon position deteriorates, as you might expect, but the orbital positions are clearly near-correct each time - I think a simple rotation of the CustomOrbits is all that's required.

Selden: although your Cassini and Phoebe meet correctly, I'd be prepared to bet that they're out of orientation with the Sun, and Saturn's terminator, by about 40 degrees. The two Horizons datasets are bound to agree, but they'll be misplaced relative to the coordinate system used by Celestia.

Chris: I'll come back shortly with the ecliptic-to-Earth-equatorial node distance for the other planets.

Grant

[chris]

Yes!
Chris, the problem with the mutual events of Jupiter's satellites, at least, seems to be that their CustomOrbits are plotted relative to Jupiter's equatorial ascending node on the Earth's equator (as are the Horizons data), whereas Celestia is using the ascending node on the ecliptic.
I've taken Horizons osculating elements for the Gallileans on 05 Dec 2002 at 20:10 UT and laid them into Celestia as they stand - very close to the Celestia CustomOrbit positions at the same date and time, as you might expect. But no occultation of Callisto by Ganymede.
Scoot the ascending node of the Horizons data anticlockwise by 20.453 degrees (the distance from the ecliptic node to the Earth-equatorial node of the plane of Jupiter's equator) and Bingo! an occultation occurs bang on schedule. Similarly with the Europa-on-Io eclipse later on the 5th December, the Europa-on-Io occultation of 06 December, and the Io-on-Callisto annular occultation on the 7th.
At dates farther from the precise date of the osculating elements the moon-on-moon position deteriorates, as you might expect, but the orbital positions are clearly near-correct each time - I think a simple rotation of the CustomOrbits is all that's required.

Cool . . . I think you've solved a mystery that's been bugging me for quite some time. While the planet positions are in great shape, satellite positions have never been quite in agreement with what I get from Horizons. I think that the description of the coordinate system used by Horizons is somewhat misleading . . .

I don't want to change Celestia to use the ascending node on the Earth's equator instead of the ecliptic, as it doesn't make a lot of sense outside of the solar system. So, I guess that means adjusting the custom orbits . . . I believe that the orbits for the satellites of Uranus and Saturn (except Phoebe) are already referred to the ascending node on the ecliptic. The slight error in the positions of the Saturnian satellites is due to another issue. After work tonight, I'll try rotating the orbits of the Galilean moons by 20.453 degrees and report back.

--Chris

[granthutchison]

Here are the ecliptic node to Earth-equatorial node distances for the equatorial planes of the various planets with moons, measured counterclockwise as seen from the planet's north pole. So these numbers need to be added to the Horizons ascending node to give a correct Celestia ascending node. They are calculated for the J2000.0 pole position, and given to a perhaps-spurious six decimal places.

Mars -40.863031 degrees
Jupiter 20.453422 degrees
Saturn -39.977646 degrees
Uranus 5.013392 degrees (IAU north pole)
Uranus -5.013392 degrees (Celestia north pole)
Neptune -24.527368 degrees
Pluto -17.515689 degrees (IAU north pole)
Pluto 17.515689 degrees (Celestia north pole)

I'm not up to speed with Horizons and Celestia xyz coordinates, but there should be a transformation of the two equatorial-plane coordinates based on these angles and some simple trig.

Grant

[granthutchison]

I believe that the orbits for the satellites of Uranus and Saturn (except Phoebe) are already referred to the ascending node on the ecliptic.

If Phoebe is referred to the Earth-equatorial ascending node, it might explain Selden's observation - a 180-degree error that crept in because of the retrograde motion, coupled with a -40-degree nodal error, is pretty close to his eyeballed 150-degrees anomaly.

Grant

[selden]

Grant,

The xyz positions are supposed to be heliocentric.

If I understand what you're saying, Saturn's solar phase angle should be wrong when viewed from Cassini's xyz position, although I have to admit that I don't see how that follows, at least not with a large enough value that'd be visible.

Another way that occurs to me to check would be to look at the objects telescopically from a viewpoint at the Earth. I know Horizons can generate appropriate RA. Dec and time values for most observatory locations. Presumably I'll have to compare Cassini to the position of an appropriate "guide star". I don't think the "Celestial Grid" is going to be accurate enough -- it certainly doesn't have enough fiducial marks to keep me from messing up!

But Celestia uses xyz coordinates to place the stars, too. Hmmm.

I think it would be very useful if Celestia included a selection of adjustable telescopic graticules. (although I suppose mylar sheets with lines drawn on them would be a reasonable short-term hack -- just not very reproducable by others ) Then when binaries are implemented we can REALLY be pickey!

[granthutchison]

The xyz positions are supposed to be heliocentric.

Sorry. I gathered from your post containing the quote about body-centred xyz coordinates that you'd switched from heliocentric to Saturn-centred at some stage in your struggle. My mistake. (How much did we bet again? )
If you're fully heliocentric then no worries, you'll be correctly orientated relative to Saturn, of course. If you'd been using Horizons' xyz in the Saturn frame then both Cassini and Phoebe would have been screwed 40 degrees around Saturn when those figures went into Celestia - that would have made a noticeable difference to phase angles across the board for the Cassini encounters.

Grant