Re: [find_orb] TNO and Find_Orb

Bill Gray Sep 28, 2013

Hi Alessandro, all,

On 09/28/2013 08:56 AM, alessandro_odasso@... wrote:
> the strange thing is that the orbital elements taken from MPC are very
> different:from those calculated by your Find_Orb and the difference
> between them is not so big:

Both objects have what are referred to as "very short arcs", or
"VSAs": so short that the motion is essentially linear, and you
can fit a wide range of possible distances to the target and radial
velocities, and still see small residuals.

In such cases, it's common to use a Vaisala orbit. If you look
at all four orbital elements, you'll see the mean anomaly is very
close to either zero or 180 degrees, i.e., near perihelion or
aphelion; that's usually the tell-tale sign that somebody is
using the Vaisala method. However, in using that method, you
have to supply a distance from the sun at the time of the
observations. You can try this with the "Vaisala" button in Find_Orb.

Take 2002 PJ153 as an example. If you select a distance of 2.3
AU (the sort of thing you'd normally do for a main-belt object),
you get a nearly parabolic orbit, but the mean residual is 2.35".
Try a distance of 3 AU, and the eccentricity jumps to 1.58,
which doesn't seem likely. And so on... try all sorts of
values, and you'll usually get either an orbit with lousy residuals
(if you're too close in) or a very hyperbolic orbit (if you're
further out).

But if you try a Vaisala orbit at 41.5 AU, you get good
residuals and a near-parabolic orbit. As you search out from that
value, you get decent residuals and a more circular orbit.
(Eventually, you get some unlikely orbits that are retrograde,
or would have the object fall in close to the sun... these are
actually quite possible, but don't seem too likely. Maybe
somebody will follow these objects up and prove me wrong, but
these objects probably have moderate eccentricity and prograde
orbits.) Finally, at 64.4 AU, you get a parabolic orbit that
is retrograde.

Anyway. When Find_Orb loads up astrometry for an object, it
tries dozens or hundreds of possible orbits, including those
found by the method of Gauss and a slew of Vaisala orbits at
assorted distances from the sun. Each orbit is given a "score"
based on how "likely" the orbit seems. High residuals, a
hyperbolic orbit, or an orbit that doesn't match the sort of
elements normally observed all result in a poor score. If the
arc is long enough, then the method of Herget and/or the "full
improvement" method result in improved scores. After all this,
the initial orbit shown by Find_Orb is the one with the best score.

I would be reasonably certain that the other people doing
automated orbit determination (MPC, JPL, AstDyS/NEODyS, and
Lowell) apply similar methods. However, the exact distances
tested for Vaisala orbits won't necessarily be the same, nor
will the "scoring" systems. So we'll all come up with reasonable
orbits, but for very short arcs, we won't come up with the
same orbits.

A few more words about the method of Vaisala, mostly about
some minor tricks to simplify and improve it :

http://www.projectpluto.com/vaisala.htm

-- Bill