Galileo-Amalthea revisited

[granthutchison]

Two threads of discussion have just come together for me.
Here
http://www.celestiaproject.net/forum/viewtopic.php?t=1422
I've been correcting the axial orientation of the planets in solarsys.ssc.
Here
http://www.celestiaproject.net/forum/viewtopic ... 9&start=15
we've been talking about the difficulty resolving Celestia's coordinate system with imported coordinate systems, and in the process I misunderstood something Selden had been doing with the Cassini-Phoebe encounter.

This led me to wonder about Galileo-Amalthea, which looked so nice in the latest pre of Celestia. If I'd just rearranged Jupiter's axis, and if the imported coordinate system for Amalthea was wrong anyway, how could that encounter have been so precise (particularly since it had taken Selden a day or so to get Cassini to pass near Phoebe).
So I looked at Galileo-Amalthea using my revised solarsys.ssc, and found that the encounter had been destroyed by my correction of Jupiter's axis .
But then I corrected Amalthea's ascending node in the light of our recent discussions about coordinate system conversion, and the encounter came back! One problem had cancelled the other, in a way I don't understand at all.
So I'm hoping to persuade Selden to tweak the version of solarsys.ssc I have lodged on his website, so that the file reflects the proper Galileo-Amalthea encounter.
But meanwhile here is the corrected definition for Jupiter and Amalthea:

Code: Select all

"Jupiter" "Sol"
{
   Texture "jupiter.jpg"
   #Texture "westgrid.jpg" #added IAU grid texture map
   HazeColor [ 0.4 0.45 0.5 ]
   HazeDensity 0.3

   Radius 71398
   Oblateness 0.064

   CustomOrbit "vsop87-jupiter"
   EllipticalOrbit
   {
   Period           11.8622
   SemiMajorAxis     5.2034
   Eccentricity      0.0484
   Inclination       1.3053
   AscendingNode   100.556
   LongOfPericenter 14.7539
        MeanLongitude    34.404
   }

   RotationPeriod    9.924920 #revised value: System III - magnetic field
   Obliquity   2.22 #revised value
   EquatorAscendingNode   337.77 #revised value

   RotationOffset 305.40 #correct orientation for map with central prime meridian

   Albedo            0.51
}


"Amalthea" "Sol/Jupiter"
{
   Texture "asteroid.jpg"
   #Texture "westgridmirror.jpg" #added IAU grid texture map
   BlendTexture true
   Color   [ 0.5 0.12 0.16 ]
   Mesh "amalthea.3ds"
   Radius    124

   EllipticalOrbit
   {
   Epoch         2452583.763194445 #2002 Nov 05.26
   Period          0.501637511
   SemiMajorAxis   181994.98
   Eccentricity    0.0046637841
   Inclination     0.39217201
   AscendingNode   224.4139186 #revised value
   ArgOfPericenter 293.4707817
   MeanAnomaly     319.3794140
   }
   
   Obliquity   0.4 #axis normal to orbit
   EquatorAscendingNode 224.41 #correct orientation for given ascending node
   RotationOffset   344.91 #correct orientation for given orbital parameters

   Albedo          0.06
}


Grant

[selden]

The updated solarsys.ssc and newtextures.zip are now avaiable at
http://www.lns.cornell.edu/~seb/celestia/hutchison/index.html

Note: these are just interim updates until Chris has had a chance to make approprite changes to the Celestia distribution.

[chris]

But then I corrected Amalthea's ascending node in the light of our recent discussions about coordinate system conversion, and the encounter came back! One problem had cancelled the other, in a way I don't understand at all.

I completely fudged Jupiter's obliquity and equatorial ascending node to make the Amalthea encounter work out. The positions of the Galilean satellites are (I think) in the same coordinate system as the Amalthea data from Horizons, so my change also helped there positions. Your listed values for the orientation of Jupiter are exactly the ones I get when I run my RA/dec to obliquity/eq. ascending node utility . . . The correction required to the ascending node of Amalthea explains why these values didn't work. In fact, the fudged value for the equatorial ascending node of Jupiter in the current solarsys.ssc is off by about 20 degrees from the correct value! It all makes sense now . . .

I'm in the process of fixing solarsys.ssc and the custom orbits.

--Chris

[chris]

So . . . I modified Jupiter so that it's pole is pointing in the right direction. Galileo now passes within 1200km of Amalthea--a bit off the 160km distance, but reasonably close. There are several possible sources of error . . . Storing only single precision coordinates for the trajectory of Galileo can give errors of ~100km. Interpolation error could also be part of the problem. Grant, how close an approach are you getting?

I modified the custom orbits for the Galilean satellites, but I'm still not able to get all of the mutual events right. I've been testing events from this list:

http://skyandtelescope.com/observing/ob ... _771_3.asp

I don't see the eclipses, and while the occultations are mostly there, the timing is off by a bit, even when I account for light time delay.

--Chris

[granthutchison]

Grant, how close an approach are you getting?

With the definition for Jupiter and Amalthea I posted above, ~750km.

Grant

[selden]

Clearly some more work is needed on the elliptical coordinate system :)
But it's getting closer!

Using Horizons' heliocentric xyz coordinates for both Galileo and Amalthea for within a minute of the time of the encounter, I get a minimum altitude of 5.242 km at 6:19:41 GMT. Since Celestia uses a radius of 124km, that's a distance of 129.242 km. (NASA claimed 160km at 6:18:28)

Presumably part of the xyz error is the linear interpolation. I don't know how much is due to inaccuracies in Horizons' database. I'm sure a lot of people have looked at this particular flyby, so I'm guessing they've tried to make it as accurate as possible. But maybe not.

FWIW the earlier flyby of Io at 2:57gmt isn't very accurate when using Io's custom orbit, but that's to be expected right now.

[granthutchison]

Clearly some more work is needed on the elliptical coordinate system

The problem isn't with the elliptical coordinate system - it's with the CustomOrbit of Jupiter, and the fact that the Galileo coordinates are heliocentric. On 5th November 2002 at 6:19:41, the Celestia Jupiter is passing ~800km ecliptic north of the position given for Jupiter by Horizons, so Galileo's relationship with the Jovian system is offset by that amount.
With a dummy Jupiter sitting at the right spot, and Amalthea in the defined orbit around it, I'm seeing an altitude of 8km at the critical time. In fact, a pretty damn good confirmation of the pole and orbit adjustments!

So the question is, will the CustomOrbit ever be tight enough to model such close approaches in a heliocentric coordinate system - we're talking about a 0.0001% error.

Grant

[selden]

Grant,

Sorry, I wrote ambiguously. I was thinking about both the Elliptical and Custom coordinate systems and their offsets relative to the heliocentric xyz coordinates.

In principle, I don't see why the Custom orbits can't be arbitrarily accurate, although keeping Celestia's frame refresh rate reasonably fast will put constraints on how much computation can be done. There's always the time/space tradeoff. Chebyshev polynomials with appropriate (but very large) lookup tables can be faster than the vsop calculations. One discussion is at http://www.ctv.es/USERS/aramirez/cielos/

Perhaps some "future major release" could provide various tradeoff options between "small fast" and "large slow accurate".

[granthutchison]

I modified the custom orbits for the Galilean satellites, but I'm still not able to get all of the mutual events right.

They seem to be very tightly dependent on the orbit specification. I've just tried meaning the osculating elements for the Galileans across a couple of months, to see if I could get a series of mutual events to play out. Instead, it wrecked almost all the events .

Grant