"Pseudo-MPEC" for Saturn

Created 2015 Jun 4 14:02:44 UT using Find_Orb

Based on VLBA "astrometry" from here (see page 12 for the astrometry). The full precision of the RA/decs and times was used, relying on Find_Orb specific extensions to the MPC format. That helped to ensure that, for example, the time is really given to an exact UTC second, dec to a microarcsecond, etc. You'll see that the format for residuals is also a little different from that used by the MPC.

Similarly, the sigmas in RA and declination are specified using a Find_Orb extension, in the columns 57-65 of each MPC-formatted observation (those columns are usually all blanks). For clarity, I've also shown the uncertainties in a separate line above each observation.

The original sigmas in RA, by the way, were in microseconds (i.e, units of time) only; the angular version, multiplied by 15 cos(dec), was added by me.

The positions are "packed", but still in base-60. Thus, the RAs are good to a millionth of a second in time, or 15 microarcseconds at the equator; the declinations are good to 10 microarcseconds. That way, they fit in the fields usually given for RA and dec, but provide the much greater precision required for VLBA data. For example, the first observation was at RA=07h43m57.853971s, dec=+21° 06' 11.47271" degrees.

Even allowing for the odd sigmas, the result still ought to be a little better than it is; most observations are not within one sigma. I'm still trying to figure out why that's so. I suspect we've hit a point where Find_Orb's physical model may need some embellishments, though I don't know what those would be... possibly relativistic light-bending, or something similarly exotic. I'll probably just have to add some effects that I think of as "so small they couldn't possibly matter", until I find one that, it turns out, really does matter.

Astrometry:
Sigmas 73µsec = 1022 µas, 510 µas
     Saturn    K040908:180000000074357853971+210611472711022 510u            500
Sigmas 10µsec = 140 µas, 200 µas
     Saturn    K041020:140000000075552671889+20382056170 140 200u            500
Sigmas 23µsec = 334 µas, 820 µas
     Saturn    K061011:170000000093954457138+14575539356 334 820u            500
Sigmas 16µsec = 230 µas, 440 µas
     Saturn    K070301:070000000093140709323+16024954185 230 440u            500
Sigmas 16µsec = 230 µas, 490 µas
     Saturn    K070608:000000000093140531546+15590693837 230 490u            500
Sigmas  9µsec = 133 µas, 310 µas
     Saturn    K080112:100000000104100869118+10114598668 133 310u            500
Sigmas 12µsec = 176 µas, 280 µas
     Saturn    K080614:000000000102229258277+11590178156 176 280u            500
Sigmas  9µsec = 133 µas, 220 µas
     Saturn    K080801:220000000104007840689+10124968911 133 220u            500
Sigmas 11µsec = 164 µas, 230 µas
     Saturn    K081111:170000000112407553620+05513499254 164 230u            500
Sigmas  9µsec = 135 µas, 140 µas
     Saturn    K090211:140000000112715292862+05563739980 135 140u            500
Sigmas 11µsec = 164 µas, 370 µas
     Saturn    K090424:060000000110902825608+07525801088 164 370u            500
Sigmas 13µsec = 195 µas, 410 µas
     Saturn    K110221:130000000130444278204-04015303571 195 410u            500
Sigmas 22µsec = 322 µas, 770 µas
     Saturn    K130331:110000000143346748638-12172206923 322 770u            500
Sigmas 12µsec = 177 µas, 240 µas
     Saturn    K130614:070000000141441930107-10470754163 177 240u            500
Sigmas 13µsec = 188 µas, 490 µas
     Saturn    K140106:180000000151519189132-15483831563 188 490u            500

Station data:
(500) Geocentric.

Orbital elements:  Saturn
   Perihelion 2003 May 1.749030 +/- 0.000529 TT = 17:58:36 (JD 2452761.249030)
Epoch 2011 Feb 21.0 TT = JDT 2455613.5   Sa: 0.0004           Find_Orb
M  95.69052 +/- 0.000021
n   0.03354912 +/- 1.2e-9           Peri.  336.85745 +/- 0.000020
a   9.52098582 +/- 2.27e-7          Node   113.62245 +/- 0.0000019
e   0.0546028 +/- 5.7e-9            Incl.    2.48772 +/- 0.00000007
P  29.38              U -0.9
q 9.00111264 +/- 1.66e-7    Q 10.0408590 +/- 2.9e-7
From 15 observations 2004 Sept. 8-2014 Jan. 6; mean residual 7".8e-04
Residuals in arcseconds:
040908 500 1.7m- 2.1m-    080112 500 1.1m+ 162µ-    090424 500 186µ- 223µ+
041020 500  22µ- 245µ-    080614 500 433µ- 477µ+    110221 500 1.0m- 596µ+
061011 500 982µ+ 348µ-    080801 500 465µ- 461µ+    130331 500 237µ+ 1.1m+
070301 500 344µ+  67µ+    081111 500 355µ- 123µ-    130614 500 1.0m+ 703µ-
070608 500 273µ- 422µ+    090211 500 141µ+ 265µ-    140106 500 1.7m-  51µ-

Ephemerides (geocentric):
Date (UT)    RA              Dec         delta   r     elong  " sig PA
---- -- --  ------------   ------------  ------ ------ -----  ---- ---
2015 04 17  16 08 58.500   -18 46 48.53  9.1567 9.9725 142.6  0.0 102
2015 04 18  16 08 45.710   -18 46 08.58  9.1467 9.9727 143.6  0.0 102
2015 04 19  16 08 32.617   -18 45 27.97  9.1369 9.9729 144.6  0.0 102
2015 04 20  16 08 19.230   -18 44 46.69  9.1274 9.9730 145.7  0.0 102
2015 04 21  16 08 05.555   -18 44 04.77  9.1181 9.9732 146.7  0.0 102
2015 04 22  16 07 51.600   -18 43 22.23  9.1091 9.9734 147.7  0.0 102
2015 04 23  16 07 37.373   -18 42 39.09  9.1003 9.9735 148.8  0.0 102
2015 04 24  16 07 22.882   -18 41 55.37  9.0918 9.9737 149.8  0.0 102
2015 04 25  16 07 08.135   -18 41 11.09  9.0836 9.9739 150.8  0.0 102
2015 04 26  16 06 53.140   -18 40 26.26  9.0756 9.9740 151.9  0.0 102
2015 04 27  16 06 37.904   -18 39 40.92  9.0679 9.9742 152.9  0.0 102
2015 04 28  16 06 22.435   -18 38 55.08  9.0604 9.9744 153.9  0.0 102
2015 04 29  16 06 06.742   -18 38 08.76  9.0532 9.9745 155.0  0.0 102
2015 04 30  16 05 50.832   -18 37 21.98  9.0463 9.9747 156.0  0.0 102
2015 05 01  16 05 34.714   -18 36 34.77  9.0397 9.9748 157.0  0.0 102
2015 05 02  16 05 18.395   -18 35 47.14  9.0333 9.9750 158.0  0.0 102
2015 05 03  16 05 01.884   -18 34 59.13  9.0273 9.9752 159.1  0.0 102
2015 05 04  16 04 45.189   -18 34 10.74  9.0215 9.9753 160.1  0.0 102
2015 05 05  16 04 28.318   -18 33 22.00  9.0160 9.9755 161.1  0.0 102
2015 05 06  16 04 11.279   -18 32 32.94  9.0107 9.9757 162.2  0.0 102