"Pseudo-MPEC" for Cassini

Created Fri Jan 30 12:56:47 2004 using Find_Orb

On 18 August 1999, Rob McNaught and Gordon Garradd were able to image the Cassini probe after it had flown by the Earth on its way to Jupiter (and thence to Saturn). With that data, plus some on the two following nights, we were able to get the orbits you see below (since recomputed to show uncertainties).

 Astrometry 
 Observing stations 

Using this data, you can see the short-period orbit before the flyby; the longer-period elliptical orbit after the flyby, with Cassini on its way to Jupiter; then Jovicentric elements during the flyby, indicating a perijove of 0.0662 AU, not far from the actual distance of 0.0681 AU. Next are Saturnicentric elements as it approaches Saturn in mid-2004. It shows Cassini missing Saturn by 0.028 AU. This is partly because we're extrapolating a short arc of a few days worth of data, and the close pass by Jupiter magnifies any errors in the starting orbit (you'll notice that the uncertainty in the perisaturn distance is more than a dozen times that of the uncertainty in the perijove distance). Also, Cassini probably maneuvered at least a small bit between these observations and its arrival at Saturn, five years later.

A little further checking reveals that the orbit can be run backward to show the previous flyby of Venus in June 1999! The accuracy isn't all that great, however, because any small error gets magnified as the orbit is run past the very close pass by the earth, and because maneuvers happened. The actual pass by Venus was about ten times closer than the "perivenus" distance indicated below.

 Venus-centric orbital elements (during the Venus flyby)
 Heliocentric orbital elements (before the Earth flyby)
 Geocentric orbital elements (during the flyby)
 Heliocentric orbital elements (during the Earth-to-Jupiter leg)
 Jovicentric orbital elements (during the Jupiter flyby)
 Saturnicentric orbital elements (during the approach to Saturn)
 Residuals 
 Ephemeris 

Astrometry:
     Cassini  C1999 08 18.51899 23 28 23.37 -05 04 56.9          16.2        422
     Cassini  C1999 08 18.52503 23 28 21.35 -05 04 57.3          16.7        422
     Cassini  C1999 08 18.54081 23 28 15.69 -05 04 56.6          16.5        422
     Cassini  C1999 08 18.57286 23 28 03.14 -05 04 51.7          17.0        422
     Cassini  C1999 08 18.58419 23 27 58.51 -05 04 48.9          16.4        422
     Cassini  C1999 08 18.59442 23 27 54.32 -05 04 45.8          16.7        422
     Cassini  C1999 08 19.72619 23 29 03.21 -05 01 06.4          19.0        422
     Cassini  C1999 08 19.73325 23 29 02.24 -05 01 04.8          19.2        422
     Cassini  C1999 08 19.74565 23 29 00.47 -05 01 02.1          19.0        422
     Cassini  C1999 08 19.77046 23 28 57.46 -05 00 56.8          19.1        422
     Cassini  C1999 08 19.77853 23 28 56.63 -05 00 55.2          19.1        422
     Cassini  C1999 08 20.66391 23 29 34.89 -05 00 47.0          19.1 R      413
     Cassini  C1999 08 20.66724 23 29 34.49 -05 00 47.2          19.4 R      413
     Cassini  C1999 08 20.67062 23 29 34.06 -05 00 47.0          19.4 R      413
     Cassini  C1999 08 20.69003 23 29 31.66 -05 00 46.5          19.4 R      413

Station data:
(413) Siding Spring Observatory (S31.2768 E149.0661).   Observer R. H.
    McNaught.  1.0m f/8 reflector + CCD.
(422) Loomberah  (S31.3347 E151.0461).   Observer G. J. Garradd.  0.45-m f/5.4
    reflector + CCD.

Orbital elements: (encounter at Venus)
Cassini
   Perivenus 1999 Jun 24.829416 +/- 0.0469 TT = 19:54:21 (JD 2451354.329416)
Epoch 1999 Jun 25.0 TT = JDT 2451354.5                        Gray
q147142.272 +/- 17158               (J2000 ecliptic)
H   27.5  G 0.15                    Peri.  289.72089 +/- 2.4
                                    Node   328.13750 +/- 2.7
e  39.7404533 +/- 4.65              Incl.   33.98757 +/- 3.7
From 15 observations 1999 Aug. 18-20; mean residual 0".220

Orbital elements: (Venus-Earth leg)
Cassini
   Perihelion 1999 Jun 29.537305 +/- 0.0258 TT = 12:53:43 (JD 2451359.037305)
Epoch 1999 Aug  1.0 TT = JDT 2451391.5   Earth MOID: 0.0000   Ve: 0.0001
M  14.84423 +/- 0.036               Ma: 0.0226                Gray
n   0.45727068 +/- 0.000763         Peri.  101.97847 +/- 0.034
a   1.66860603 +/- 0.00186          Node   144.77141 +/- 0.00042
e   0.5674026 +/- 0.000447          Incl.    1.08758 +/- 0.0018
P   2.16/787.26d           H 27.5   G  0.15   U  7.9
q 0.72183455 +/- 0.000102    Q 2.61537751 +/- 0.00365
From 15 observations 1999 Aug. 18-20; mean residual 0".220

Orbital elements: (encounter at Earth)
Cassini
   Perigee 1999 Aug 18.145552 +/- 0.000456 TT =  3:29:35 (JD 2451408.645552)
Epoch 1999 Aug 18.2 TT = JDT 2451408.7                        Gray
q  7547.78213 +/- 5.26              (J2000 equator)
H   27.5  G 0.15                    Peri.  248.47330 +/- 0.16
                                    Node     3.13379 +/- 0.16
e   5.8528767 +/- 0.00586           Incl.   25.43123 +/- 0.007
From 15 observations 1999 Aug. 18-20; mean residual 0".232
 
Orbital elements: (Earth-Jupiter leg)
Cassini
   Perihelion 1999 Jul 16.407386 +/- 0.00538 TT =  9:46:38 (JD 2451375.907386)
Epoch 1999 Aug 19.0 TT = JDT 2451409.5   Earth MOID: 0.0000   Ju: 0.0006
M   4.10568 +/- 0.014               Ma: 0.0252                Gray
n   0.12221979 +/- 0.000398         Peri.  131.94462 +/- 0.0018
a   4.02137902 +/- 0.00873          Node   144.74803 +/- 0.00041
e   0.7850050 +/- 0.000482          Incl.    0.71455 +/- 0.00028
P   8.06                   H 27.5   G  0.15   U  7.5
q 0.86457609 +/- 6.12e-5    Q 7.17818195 +/- 0.0175
From 15 observations 1999 Aug. 18-20; mean residual 0".220

Orbital elements: (encounter at Jupiter)
Cassini
   Perijove 2000 Dec 31.085092 +/- 0.806 TT =  2:02:31 (JD 2451909.585092)
Epoch 2001 Jan  1.0 TT = JDT 2451910.5                        Gray
q   0.06617887 +/- 0.000977         (J2000 ecliptic)
H   27.5  G 0.15                    Peri.  208.22450 +/- 2.1
                                    Node   100.96112 +/- 2.0
e   9.4590184 +/- 0.165             Incl.    2.01861 +/- 0.030
From 15 observations 1999 Aug. 18-20; mean residual 0".220

Orbital elements: (encounter at Saturn)
Cassini
   Perisaturn 2004 Jul 14.011380 +/- 6.88 TT =  0:16:23 (JD 2453200.511380)
Epoch 2004 Jul 14.0 TT = JDT 2453200.5                        Gray
q   0.02811291 +/- 0.0136           (J2000 ecliptic)
H   27.5  G 0.15                    Peri.  168.76891 +/- 14
                                    Node   151.67016 +/- 19
e   3.9816103 +/- 1.46              Incl.    4.56960 +/- 0.7
From 15 observations 1999 Aug. 18-20; mean residual 0".220


Residuals in arcseconds:
990818 422  .07+  .11+    990818 422  .05+  .13-    990819 422  .00   .13-
990818 422  .05+  .12-    990819 422  .39-  .32-    990820 413  .07+  .25+
990818 422  .20-  .10+    990819 422  .66+  .02-    990820 413  .29+  .03-
990818 422  .05+  .09+    990819 422  .06-  .25+    990820 413  .12+  .07+
990818 422  .02-  .06-    990819 422  .16-  .16+    990820 413  .55-  .21-

Ephemerides:
Da Mon Year HH:MM    RA              Dec         delta   r     elong mag
-- --- ---- -----  ------------   ------------  ------ ------ ----- ---
17 Aug 1999  0:00  10 18 24.962   +12 48 17.50  0.0106 1.0021   8.4 36.0
17 Aug 1999  2:00  10 18 30.831   +12 47 42.87  .00987 1.0028   8.4 35.9
17 Aug 1999  4:00  10 18 37.669   +12 47 02.44  .00909 1.0035   8.3 35.8
17 Aug 1999  6:00  10 18 45.746   +12 46 14.58  .00832 1.0043   8.3 35.7
17 Aug 1999  8:00  10 18 55.443   +12 45 17.00  .00755 1.0050   8.2 35.5
17 Aug 1999 10:00  10 19 07.315   +12 44 06.39  .00678 1.0058   8.2 35.3
17 Aug 1999 12:00  10 19 22.202   +12 42 37.70  .00601 1.0065   8.2 35.1
17 Aug 1999 14:00  10 19 41.438   +12 40 42.89  .00524 1.0073   8.2 34.8
17 Aug 1999 16:00  10 20 07.284   +12 38 08.35  .00446 1.0080   8.2 34.4
17 Aug 1999 18:00  10 20 43.889   +12 34 29.01  .00369 1.0088   8.3 33.9
17 Aug 1999 20:00  10 21 39.802   +12 28 53.06  .00292 1.0095   8.5 33.2
17 Aug 1999 22:00  10 23 15.895   +12 19 13.35  .00214 1.0103   8.8 32.1
18 Aug 1999  0:00  10 26 40.143   +11 58 31.75  .00137 1.0110   9.6 30.2
18 Aug 1999  2:00  10 38 54.718   +10 42 25.58  .00059 1.0118  12.7 25.5
18 Aug 1999  4:00  22 33 17.495   -11 17 03.82  .00022 1.0126 168.9  9.5
18 Aug 1999  6:00  23 17 42.511   -06 25 42.35  .00100 1.0133 157.1 13.2
18 Aug 1999  8:00  23 23 09.151   -05 48 18.30  .00178 1.0139 155.7 14.5
18 Aug 1999 10:00  23 25 17.109   -05 33 34.59  .00255 1.0146 155.2 15.3
18 Aug 1999 12:00  23 26 25.456   -05 25 41.58  .00332 1.0153 154.9 15.9
18 Aug 1999 14:00  23 27 07.993   -05 20 46.86  .00410 1.0160 154.8 16.3
18 Aug 1999 16:00  23 27 37.021   -05 17 25.59  .00487 1.0167 154.8 16.7
18 Aug 1999 18:00  23 27 58.090   -05 14 59.43  .00564 1.0173 154.7 17.0
18 Aug 1999 20:00  23 28 14.076   -05 13 08.48  .00641 1.0180 154.8 17.3
18 Aug 1999 22:00  23 28 26.615   -05 11 41.42  .00718 1.0187 154.8 17.5
19 Aug 1999  0:00  23 28 36.709   -05 10 31.31  .00795 1.0194 154.8 17.8
19 Aug 1999  2:00  23 28 45.004   -05 09 33.67  .00873 1.0201 154.9 18.0
19 Aug 1999  4:00  23 28 51.937   -05 08 45.47  .00950 1.0208 154.9 18.2
19 Aug 1999  6:00  23 28 57.812   -05 08 04.59  0.0103 1.0214 155.0 18.3
19 Aug 1999  8:00  23 29 02.851   -05 07 29.52  0.0110 1.0221 155.0 18.5
19 Aug 1999 10:00  23 29 07.214   -05 06 59.11  0.0118 1.0228 155.1 18.6
19 Aug 1999 12:00  23 29 11.025   -05 06 32.53  0.0126 1.0235 155.1 18.8
19 Aug 1999 14:00  23 29 14.378   -05 06 09.12  0.0134 1.0242 155.2 18.9
19 Aug 1999 16:00  23 29 17.347   -05 05 48.36  0.0141 1.0249 155.3 19.0
19 Aug 1999 18:00  23 29 19.989   -05 05 29.86  0.0149 1.0256 155.3 19.1
19 Aug 1999 20:00  23 29 22.352   -05 05 13.28  0.0157 1.0263 155.4 19.2
19 Aug 1999 22:00  23 29 24.474   -05 04 58.36  0.0164 1.0270 155.5 19.3
20 Aug 1999  0:00  23 29 26.386   -05 04 44.89  0.0172 1.0277 155.5 19.4
20 Aug 1999  2:00  23 29 28.114   -05 04 32.68  0.0180 1.0284 155.6 19.5
20 Aug 1999  4:00  23 29 29.680   -05 04 21.58  0.0188 1.0291 155.7 19.6
20 Aug 1999  6:00  23 29 31.102   -05 04 11.47  0.0195 1.0298 155.8 19.7
20 Aug 1999  8:00  23 29 32.395   -05 04 02.24  0.0203 1.0305 155.8 19.8
20 Aug 1999 10:00  23 29 33.573   -05 03 53.79  0.0211 1.0312 155.9 19.9
20 Aug 1999 12:00  23 29 34.647   -05 03 46.06  0.0218 1.0319 156.0 19.9
20 Aug 1999 14:00  23 29 35.626   -05 03 38.96  0.0226 1.0326 156.1 20.0
20 Aug 1999 16:00  23 29 36.520   -05 03 32.45  0.0234 1.0333 156.1 20.1
20 Aug 1999 18:00  23 29 37.336   -05 03 26.46  0.0242 1.0340 156.2 20.2
20 Aug 1999 20:00  23 29 38.080   -05 03 20.96  0.0249 1.0347 156.3 20.2
20 Aug 1999 22:00  23 29 38.758   -05 03 15.90  0.0257 1.0354 156.4 20.3
21 Aug 1999  0:00  23 29 39.375   -05 03 11.25  0.0265 1.0361 156.4 20.4
21 Aug 1999  2:00  23 29 39.935   -05 03 06.98  0.0272 1.0368 156.5 20.4