I recently got an inquiry about how to compute an orbit and ephemeris for WT1190F in Find_Orb. I wrote the following reply, and then thought it might be of use to others.

Your first step should be to get the current, in-development version of Find_Orb :

```
http://www.projectpluto.com/pluto/devel/find_orb.htm  ```

This is partly because it turns out the existing version didn't show the impact coordinates for this object. (There was so much text for the orbital elements that things got cut off at the bottom.) But in addition, the new version is a bit faster, shows the impact latitude/longitude and time, and gives a more reliable solution when you include solar radiation pressure. (There was a bug in the earlier version that caused the orbit to shift slightly when you did a 'full step' including solar radiation pressure.) Also, the update can generate ephemerides showing the ground track and the object's speed. So it's a good idea all around.

Also, make sure you are using JPL DE ephemerides in Find_Orb. (When you start up Find_Orb, it should mention which version you're using at the bottom of the dialog.) The program will be very slow on this object without it.

I would suggest you click here for a list of observations made in 2015 of WT1190F, and save it in the folder with Find_Orb. (I left out the 2013 and 2009 data, because that linkage is quite tricky. I did it with a modified version of the Linux console version of Find_Orb; the modifications are not really ready to be posted.) When you first load 'short.txt' in the updated Find_Orb, the elements will look like this :

```Orbital elements:  UDA34A3 = UW8551D = WT1190F
Perigee 2015 Nov 13.276733 +/- 1.31e-5 TT =  6:38:29 (JD 2457339.776733)
Epoch 2015 Nov  8.0 TT = JDT 2457334.5                        Find_Orb
M 264.49896 +/- 0.00017             (J2000 equatorial)
n  18.09851555 +/- 1.12e-5          Peri.  195.15247 +/- 0.000036
a310104.595 +/- 0.128               Node    68.75737 +/- 0.000038
e   0.9777706 +/- 4.33e-8           Incl.   11.03177 +/- 0.0000057
P  19.89d                  H 31.4   G  0.15   U  5.1
q 6893.41178 +/- 0.011    Q 613315.779 +/- 0.265
1074 of 1145 observations 2015 Oct. 22-Nov. 8; mean residual 0".32```

Which isn't quite right. It doesn't say anything about an impact, and there are a couple of other things we need to do.

• The epoch is for the time of the most recent observation. Change '2015 Nov 8' to read '2015 Nov 13.2', just before re-entry.

• Only the earth and moon are included as perturbers. Find_Orb is bright enough to realize that the object is close enough to require those (and the sun), but not bright enough to realize that other planets might matter in this case as well. Rather than attempt to sort out which planets have a meaningful effect, I'd just click on "All Perturbers Off", then again on that button to turn "All Perturbers On".

• You keep hearing about the importance of solar radiation pressure on this object, but Find_Orb isn't taking it into account. Go into the Settings dialog, and look for the 'Physical Model' box. Change it from 'Standard' to 'Include SRP', and click OK.

• A lot of observations are excluded, including those from before October 22. You can use those if you want to model the object's orbit for dates back then. But they'll throw things off, very slightly, if you attempt to use them for the object's motion in November.

Now that you've got things set up properly, click on "Full Step". If you do this three or four times, the numbers will converge :

```Orbital elements:  UDA34A3 = UW8551D = WT1190F
Perigee 2015 Nov 13.268037 +/- 1.34e-5 TT =  6:25:58 (JD 2457339.768037)
Epoch 2015 Nov 13.2 TT; AMR 0.011467 +/- 0.00012 m^2/kg       Find_Orb
M 358.74839 +/- 0.00024             (J2000 equatorial)
n  18.39596210 +/- 1.9e-5           Peri.  191.86156 +/- 0.00025
a306752.776 +/- 0.211               Node    72.94932 +/- 0.00026
e   0.9813153 +/- 1.09e-7           Incl.   13.24811 +/- 0.000055
P  19.57d                  H 31.4   G  0.15   U  5.4
q 5731.55910 +/- 0.0368    Q 607773.993 +/- 0.391
1074 of 1145 observations 2015 Oct. 22-Nov. 8; mean residual 0".25
IMPACT at  13 Nov 2015  6:19:08.25 lat  +5.63176 lon E81.45326 ```

The mean residual drops from 0".32 to 0".25, reflecting the fact that your physical model (now that it includes other planets and SRP) reflects the real motion of this object. Impact coordinates will appear, and in the correct place.

At this point, you can generate an ephemeris. I would recommend that you click on "Ephemeris" (of course!), then the "MPC code" radio button, and enter the code WT1 in the box to the right of that button. I've added a new "MPC station" that is directly at the point where Find_Orb thinks the object will hit.

Except that I just realized that it's the location where WT1190F would hit, if the earth had no atmosphere. To fix this, edit the file rovers.txt and look for a line starting with WT1. Before starting Find_Orb, change the longitude/latitude on that line to read :

`WT1  80.9004 +05.5488  0      WT1190F nominal impact point`

If you generate ephemerides with a small step size, you will see the distance to the object decrease to about ten meters at closest approach, at 2015 November 13 06:21:52. (Of course, the actual object will probably turn to small bits in the upper atmosphere. So this is really a mathematical example!) You can also tick the 'ground track' and 'speed' boxes to have those quantities shown in the ephemerides. The 'speed', in particular, shows how the object accelerates as it comes in toward the earth, reaching a maximum of 11 km/s. Then it hits the upper atmosphere and decelerates very quickly (over 100 gs, more than a kilometer/second/second) for a few seconds.

The actual object is also shifting around from solar radiation forces. I'll be trying to get people to observe this object starting November 8, when it's reasonably bright again, in hopes of getting a lot of data close to impact. With that, the incoming trajectory should be nicely determined.