Last updated 2011 September 11
At present, making linkages in Find_Orb between widely separated arcs is usually quite difficult. If you're lucky, you can load the data, solve an orbit for one arc, and find that the residuals for the observations in the other arc are less than about ten degrees. If that happens, you can toggle one or more observations in the other arc and do a "full step" or two (or more), and gradually converge on a solution that includes both arcs. Then you can turn on all observations and do a "full step" to complete the process.
Often, this fails. In such cases, you can usually still persuade Find_Orb to link the arcs. But it needs some help. I'll describe a case where this can be done.
Alessandro Odasso brought up an example on MPML where he attempted a linkage for 2011 KS15 to three observations found on SkyMorph from 2003. So he was working with the following data. Alessandro gave the data as being for two different objects; since you can't (currently) tell Find_Orb, "Load up observations for both objects so I can see if they're the same object", I've converted the K11K15S designations in Alessandro's post to AAAAA.
AAAAA C2003 01 26.29531 07 57 14.06 +15 38 55.9 19.4 R 644
AAAAA C2003 01 26.36500 07 57 10.28 +15 38 52.5 19.4 R 644
AAAAA C2003 01 26.42778 07 57 06.85 +15 38 49.5 19.7 R 644
AAAAA * C2011 05 27.44795 23 01 10.56 +05 54 51.0 19.9 Vr~0WJO703
AAAAA C2011 05 27.45317 23 01 10.95 +05 54 56.4 19.5 Vr~0WJO703
AAAAA C2011 05 27.45843 23 01 11.20 +05 55 00.1 20.3 Vr~0WJO703
AAAAA C2011 05 27.46369 23 01 11.53 +05 55 03.9 19.8 Vr~0WJO703
AAAAA C2011 05 28.44639 23 02 10.68 +06 09 15.7 18.9 Ro~0WJOH01
AAAAA C2011 05 28.45173 23 02 11.01 +06 09 20.3 19.0 Ro~0WJOH01
AAAAA C2011 05 28.46033 23 02 11.52 +06 09 27.7 18.8 Ro~0WJOH01
AAAAA C2011 05 29.42273 23 03 08.76 +06 23 20.5 18.9 Ro~0WJOH01
AAAAA C2011 05 29.43457 23 03 09.45 +06 23 30.5 19.2 Ro~0WJOH01
AAAAA C2011 05 29.45480 23 03 10.64 +06 23 48.0 18.9 Ro~0WJOH01
Save this page as a text file, and you should be able to load it into Find_Orb and see the following result:
Orbital elements: AAAAA Perihelion 2011 Mar 28.910210 TT = 21:50:42 (JD 2455649.410210) Epoch 2011 May 28.0 TT = JDT 2455709.5 Sa: 0.0449 Find_Orb M 3.811070 (2000.0) P Q n 0.063422922 Peri. 19.812525 0.642709657 0.701903142 a 6.227377817 Node 291.515934 -0.739853015 0.464647241 e 0.57613826 Incl. 19.269277 -0.198851229 0.539847126 P 15.54 H 14.3 U 11.3 q 2.639547151 Q 9.815208483 From 10 observations 2011 May 27-29; mean residual 0".337.
If you click on "Full Step" a couple of times, you'll see that the (unincluded) 2003 observations have residuals of -24 degrees in RA and +13 degrees in declination. Also, the orbital period found is 19.9 years, which doesn't seem very likely.
It would be nice to try an orbit constrained to a more likely period, say four years. To do this, click on Settings, and then enter "P=4" in the Constraints box. Then click OK, and do a few 'full steps'. Find_Orb duly converges on a solution with a period of four years. The residuals are slightly worse than before (mean residual 0".358). But the 2003 data now have enormous residuals (-172 degrees in RA, i.e., completely wrong part of the sky.)
So we now try some other reasonable-seeming orbital periods. We go back into Settings and apply a constraint of P=5, which causes the 2003 data to have residuals of +41 and -15 degrees. Guessing P=6 gives residuals of -43 and +29 degrees.
Notice that those last two guesses are almost opposite one another. It would be reasonable to think that for some period between five and six years, we'd get low residuals for the 2003 observations. Going directly to the middle with P=5.5 years gives residuals for the 2003 observations of -12 degrees in RA and +454' (about +7.5 degrees) in declination.
At this point, things are just about at the point where we could stop hunting for a better orbital period. With the 2003 data having residuals of about ten degrees, we could toggle the three 2003 observations on, and do four "full steps". And we get:
Orbital elements: AAAAA Perihelion 2011 Jan 18.943231 TT; Constraint: P=5.5 Epoch 2011 May 28.0 TT = JDT 2455709.5 Find_Orb M 23.127387 (2000.0) P Q n 0.179203211 Peri. 0.006305 0.332846137 0.891286204 a 3.115818782 Node 289.435655 -0.865182584 0.158760437 e 0.23228144 Incl. 19.058902 -0.375063387 0.424739951 P 5.50 H 14.6 U 5.8 q 2.392071897 Q 3.839565668 From 13 observations 2003 Jan. 26-2011 May 29; mean residual 5".212.
Your first thought might be that a mean residual of 5".2 is really bad. And this is true. But you'll notice that the period is still still constrained to be 5.5 years. Go back into Settings and clear the "Constraint" field, click OK, and do more "full steps". At first, the mean residual balloons to over 8000 arcseconds; but another half dozen or so full steps brings the mean residual down to 0".458 arcseconds. But this is still without perturbers. Click "All Perturbers On" and do a "full step". Again, the immediate effect will be that the mean residual climbs up to over 1300 arcseconds. But with more "full steps", the solution again converges, this time to a mean residual of 0".330. And one has the following linked solution:
Orbital elements: AAAAA Perihelion 2011 Mar 12.045365 TT = 1:05:19 (JD 2455632.545365) Epoch 2011 May 28.0 TT = JDT 2455709.5 Find_Orb M 14.201943 (2000.0) P Q n 0.184549550 Peri. 16.509759 0.572776374 0.760239890 a 3.055348274 Node 289.458111 -0.784028168 0.398962368 e 0.18569346 Incl. 18.971703 -0.239221770 0.512702972 P 5.34 H 14.6 U 6.7 q 2.487990067 Q 3.622706482 From 13 observations 2003 Jan. 26-2011 May 29; mean residual 0".330.
However, you can't always get a linkage with ten-degree residuals. It's a good idea, normally, to attempt to refine your guess for the constrained period. In this case, P=5 gave us residuals for the 2003 observations of (+41, -15). P=5.5 gave us residuals of (-12, +7.5). It looks as if P=5.5 had residuals about one-third of those for P=5. So the "for-real" period ought to be about a quarter of the way from 5.5 to 5, which gives P=5.375. Go into Settings and apply that constraint, and the 2003 data have residuals of about -2 degrees in RA and +1.5 degrees in declination. With those residuals, one could proceed with greater confidence to a solution.