Update posted to fix natural satellite problems
Bill Gray Jun 5, 2017
Hello all,
I had a couple of inquiries from people trying to get orbits for
the two newly-discovered satellites of Jupiter, who found that they
were getting some pretty strange angles. The eccentricity, major
axis, perijove, and time of perijove were right, but the
inclination, ascending node, and argument of perijove were weird.
The problem was that a while back, I'd set up Find_Orb to
generate "body frame" elements for natural satellites. In this
system, an object orbiting in the same plane as the planet's
equator has zero inclination. It's a good fit for inner satellites,
but isn't usually used for distant, irregular satellites such as
the two new guys on the block.
I've posted updates to all flavors of Find_Orb (source code, the
online version, and the Windows 32-bit and 64-bit versions) that
follow MPC's behavior: use J2000 equatorial elements for objects
orbiting the earth, and J2000 ecliptic elements for everything else.
If you look in 'environ.def', you'll see that it's possible to get
whatever frame you want, though I doubt anybody will do that. (Except
me, when computing orbits for inner satellites of other planets.)
Incidentally, S/2017 J 1 will load up and generate the right
orbit automatically. (You can just cut-and-paste astrometry from
the discovery MPEC into the on-line Find_Orb and it'll compute the
correct orbit.) S/2016 J 1 is a tougher case, as sometimes happens
with these objects. Find_Orb does get a solution, but it's the
wrong one, and it only fits the first couple of months of data.
My usual method with "problem" irregulars is to start with an arc
covering a few months, i.e., part of a full orbit. I run some
Vaisala orbits that will put them near the gas giant they're actually
orbiting. That's wrong, but if you then do some Herget steps followed
by some full steps, it will often converge on the correct orbit; you
can then toggle on some additional observations and do full steps to
get the entire arc included. It usually takes a bit of trial and
error with different Vaisala distances before you get it right.
In this case, I loaded up S/2016 J 1 and got a pretty bad orbit
(e=.78, i=71, and high residuals). So I tried Vaisala orbits at 5.2
and 5.1 AU, following each with Herget steps, then full steps. In
both cases, it converged to the same (wrong) answer.
But if you try a Vaisala orbit at 5.3 AU, then about half a dozen
Herget steps, then several full steps, the residuals drop and the
orbit looks like a "normal" outer Jovian orbit, and the residuals for
the next year's observations are about half an arcminute. (Which is
to say that when the discoverers did their follow-up, they didn't
have a big area to search.) Turn those four observations on and do
some more full steps, and you have the orbit.
To get a result passably close to MPC's, you'll need to reset
the epoch to match that used by MPC, then do full steps again.
There are still some small differences, probably because we aren't
assuming exactly the same uncertainties for the observations, and I
dunno what MPC does for debiasing or over-observing.
-- Bill