Alessandro Jan 29, 2011
--- In find_orb@yahoogroups.com, Bill J Gray <pluto@...> wrote:
>
> Hi Alessandro,
>
> (Side note: this discussion appears to be continuing on both the
> Find_Orb and MPML lists. Fortunately, both are open to viewing by
> non-members.)
>
> With the short arc you have here (two hours long), you can get
> an astonishing variety of orbits. That's basically standard
> procedure for very short arcs, except in some unusual situations
> (mostly involving objects that are really close to us). We can
> say, though, with confidence, that the object isn't more than
> .447 AU away. If it were, the orbit would have to be hyperbolic,
> and nobody has seen that happen (yet). That upper distance limit
> is just about the only constraint on the orbit right now.
>
> Within .447 AU, there is a huge range of orbits. Find_Orb
> looks through a broad sample of them and picks one that looks most
> "reasonable", given what we know about the distribution of orbits
> among observed objects. Usually, that leads to a main-belt
> solution. (This is the approach that says, "When you hear
> hoofbeats, expect horses, not zebras".)
>
> In this case, Find_Orb's default orbit has i=27, q=.13, Q=1.53.
> That's a pretty weird orbit. Find_Orb should have looked further
> (i.e., tried out some more possible orbits). With some searching,
> I found one with i=4, q=.57, Q=1.89, though the residuals are
> a bit high (rms error = .705 arcseconds).
>
> One _could_ just look for the orbit with the lowest residuals.
> In this case, with only three observations, the lowest residuals
> would be exactly zero. As has been pointed out in this thread,
> that leads to a somewhat exotic orbit with i=55, q=.09.
>
> There are a couple of problems with doing this. For one thing,
> with a very short arc like this, it's common for the lowest-residual
> orbit to be something _really_ exotic, like a Warp 9 orbit out past
> Alpha Centauri. Sometimes, it diverges completely. Or, it
> converges on something pretty weird.
>
> The usual way to tackle this sort of very short arc problem
> would be with statistical ranging. SR says: We compute a slew
> of possible orbits at various ranges and radial velocities, and
> keep those with non-hyperbolic orbits. We also add in some "noise"
> that reflects our guess as to how exact our observations are. All
> the resulting "virtual asteroids" are at least _possible_ places
> the object could be. (Though if both main-belt solutions and
> exotic solutions appear, it'll probably be a main-belter: again,
> expect horses, not zebras.)
>
> This is the approach used for the NEOCP uncertainty charts: each
> of triangle in the chart represents a possible orbit that fits the
> observations tolerably well. Dave Tholen's KNOBS software, I gather,
> does the same thing, and I think OrbFit and CODES have this
> capability. As does Find_Orb... except %$!*^ it, I tried it on this
> object and got three orbits, and then it failed. I'll have to check
> that out. (I only added SR recently; it's a "work in progress".)
>
> -- Bill
>