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AAS 05-312

CASSINI DETERMINATION PERFORMANCE DURING THE FIRST EIGHT OF THE SATELLITE TOUR

P.G. Antreasian, J.J. Bordi, K.E. Criddle, R. Ionasescu, R.A. Jacobson, J.B. Jones, R.A. MacKenzie, M.C. Meek, F.J. Pelletier, D.C. Roth, I.M. Roundhill, and J. Stauch∗

From June 2004 through July 2005, the Cassini/Huygens spacecraft has executed nine successful close-targeted encounters by three of the major satellites (Phoebe, Titan, and Enceladus) of the Saturnian system. During the third orbit the Huy- gens probe was precisely targeted for a successful descent to Titan’s surface. Current results show that orbit determination has met design requirements for targeting encounters, Huygens descent, and predicting science instrument point- ing for targeted satellite encounters. This paper compares actual target disper- sions against the predicted tour covariance analyses. To assess orbit determina- tion performance, post-flyby results are compared to OD predictions. Prediction accuracy of the satellite is a key challenge for successful navigation. The improvement of this ephemeris through the orbit determination process is discussed.

INTRODUCTION

The Cassini/Huygens spacecraft entered into orbit around Saturn on July 1, 2004. From June 2004 through July 2005, the orbiter has performed nine successful close-targeted encounters by three of the major satellites of the Saturnian system. Six of these flybys specifically targeted Saturn’s largest Titan, two were with the icy moon Enceladus, Saturn’s second closest, and one tar- geted Saturn’s distant moon, Phoebe, during the final approach to Saturn orbit insertion (SOI). During the third orbit and third Titan encounter the European Space Agency’s (ESA) Huygens probe was precisely targeted for a successful descent to Titan’s surface. While the first year of the Mission’s designed four-year Saturn satellite tour has been completed, there are over 40 remaining encounters to navigate before the end of the prime mission. Consistent, accurate, and efficient orbit determination (OD) processes are important elements to successful satellite tour navigation. Cur- rent results show that orbit determination has met design requirements for targeting encounters, the Huygens descent, and predicting science instrument pointing for targeted satellite encounters. The nine satellite encounters covered in this report are listed in Table 1 with corresponding orbit characteristics. The achieved times of closest approach (TCA) and achieved altitudes are shown. The satellite encounters occur on either the inbound approach to Saturn periapsis or outbound from periapsis. The Titan-4 (T4) and Titan-5 (T5) encounters are the only flybys thus far to occur after Saturn periapsis.

THE CASSINI/HUYGENS MISSION

Cassini was launched in 1997 aboard a Titan IV launch vehicle. After gravity assists by in April 1998 and June 1999, in August 1999 and in Dec 2000, the Cassini spacecraft has

∗Members of the Engineering Staff in the Guidance, Navigation and Control Section, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109

1 Table 1 The first nine encounters of the Cassini’s Saturn satellite tour. ‡ Encounter Achieved TCA Achieved Altitude In V∞ Orbit Inc Rev TCA† Error Altitude Error or Period‡ No. (UTC) (sec) (km) (km) Out§ (km/s) (days) (deg) Phoebe Ph 11-Jun-2004 +0.2 2070.9 +70.9 I 6.35 N.A. 17.2 0 19:33:37.2 Titan-A Ta 26-Oct-2004 −4.2 1174.1 −25.9 I 5.65 47.2 13.8 1(a) 15:30:04.6 Titan-B Tb 13-Dec-2004 +2.4 1192.3 −7.7 I 5.64 32.0 8.5 2(b) 11:38:15.4 Titan-C Tc 14-Jan-2005 +3.0 60003.3 +3.3 I 5.37 33.3 5.2 3(c) 11:11:58.8 Titan-3 T3 15-Feb-2005 +0.3 1579.0 +2.3 I 5.58 20.7 0.4 4 06:57:53.1 Enceladus-1 E1 09-Mar-2005 +1.5 501.8 +1.8 I 6.60 20.2 0.21 5 09:08:02.4 Titan-4 T4 31-Mar-2005 +0.2 2403.5 +3.5 O 5.61 16.1 7.5 6 20:05:16.0 Titan-5 T5 16-Apr-2005 +0.1 1027.4 +2.4 O 5.63 18.1 21.6 7 19:11:45.9 Enceladus-2 E2 14-Jul-2005 -0.4 172.6 −2.4 I 8.18 18.3 21.8 12 19:55:21.4 † S/C event time ‡ Conditions after encounter, inclination is wrt Saturn Mean Equator § Encounter occurs before (In) or after (Out) Saturn periapsis reached its final destination, Saturn, following the completion of the SOI burn on July 1, 2004. The science objectives of Cassini’s four year tour of the Saturnian system are to determine the composi- tion, structure and dynamical processes of Saturn’s atmosphere, magnetosphere, rings, and satellites. These are important since the dynamical processes shaping the Saturnian system are believed to be similar to those which created our . In addition, it is believed that Titan’s atmosphere is much like that of the primordial Earth and so observations of Titan’s atmosphere and morphology could provide insight to Earth’s evolution. In conjunction with the Cassini orbiter observations, the Huygens probe objectives are to determine Titan’s atmospheric structure and constituents as well as Titan’s surface topography.

Since the successful Phoebe flyby (June 11, 2004) and SOI (July 1, 2004), science instruments onboard Cassini/Huygens have returned a wealth of data. In addition to Cassini’s remote sensing during close flyby’s, the Titan atmospheric descent and landing of Huygens probe have sampled unprecedented in situ data of Titan’s atmosphere and soil and has also sent back phenomenal images from Titan’s surface. Scientists have already made several new interesting discoveries: Phoebe being a captured moon, volcanism on Titan, evidence for liquid methane, land and drainage systems on Titan, several new minor , and moon-ring interactions.

CASSINI OD BACKGROUND

After a targeted flyby, the first two tracking passes of radio-metric data help to precisely determine the flyby conditions and the targeted satellite’s ephemeris state at that orbital longitude. These post-encounter data also help improve the satellite’s orbit significantly. The flyby conditions are then compared to the pre-encounter control or OD prediction to compute an overall 3-dimensional position error measurement. These measurements are shown later for the nine encounters, and this provides a basis to assess the overall performance of the orbit determination or navigation processes. Satellite ephemeris errors were the major navigation error source prior to Saturn orbit insertion. Improvements in the estimates of the satellite ephemeris, Saturn and satellite masses, Saturn zonal harmonics, and Saturn pole vector through the orbit determination process are important for nav- igating the tour. This paper exhibits the improvements made to the satellite ephemeris and the resultant satellite position uncertainties are compared to predictions given in the Cassini Satellite

2 Tour Navigation Plan (Nav Plan).1 This paper also compares the predicted tour covariance analysis as specified in the Nav Plan to the rev-by-rev high-fidelity covariance analyses, which are generally performed one and one half orbit revolutions before each encounter using the latest tracking sched- ules, updated dynamic models, and latest OD filter assumptions. Actual errors are then continuously compared to these covariance analyses for tracking the OD convergence of orbit errors leading up to encounters.

The OD results of Cassini’s interplanetary journey are reported in papers Roth, et al[2], Guman, et al[3],Roth, et al[4]. Roth, et al[5]describe the orbit determination results during the final approach to Saturn which encompasses the Phoebe flyby. Roundhill, et al [6] report the OD results for the first orbit in the Saturnian system after SOI leading up to the first Titan encounter (Titan-A or Ta) on October 27, 2004. Stauch, et al[7] summarize the next encounter, Titan-B (Tb) OD results and strategies leading up to the Huygens probe mission in December 2004. Bordi, et al[8] explain in detail the OD strategy, and results which led to the successful landing of the Huygens probe on Titan during January 14, 2005. The Titan-C orbit, which involved the probe mission, was unique and the details involving the probe will not be discussed in this paper.

ORBIT DETERMINATION OBJECTIVES

During the prime mission, the Navigation Team’s (Nav) main objective is to keep Cassini on the designed satellite tour trajectory.1 Three Orbit Trim Maneuvers (OTMs) are generally planned per targeted encounter: the apoapsis maneuver targets the trajectory to maintain the designed upcoming encounter flyby conditions, the approach maneuver at -3 to -6 days before the encounter to correct the trajectory from maneuver and OD dispersions, and the encounter +3 day (or more) clean-up maneuver to compensate for flyby errors. Details of the maneuver design strategy are described in the Nav Plan and the performance of the maneuvers (including the OD reconstruction estimates) to date is given by Wagner, et al[9]. OTMs are performed on either the S/C’s 445 N bi-propellant Main Engine (ME) or on the four 0.9 N (co-aligned with the ME) monopropellant Control System thrusters.9

Three main objectives of the Orbit Determination (OD) Team are: 1) to perform covariance studies for trajectory designs or redesigns in order to determine navigational capabilities of meeting requirements, 2) to routinely estimate and improve the predictions of the spacecraft (S/C) trajectory as well as the ephemerides of Saturn and the major Saturnian satellites (in order of distance from Saturn, these include the nine moons, Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion, Iapetus and Phoebe), 3) to reconstruct the S/C, Saturn and the satellite ephemerides after the fact.

The predicted S/C, Saturn and satellite ephemerides are provided to the project, Deep Space Network, Science and Nav Teams for designing OTMs, computing tracking antenna frequency pre- dicts, or planning sequence updates. Occasionally, these predictions are used to update the tour reference trajectory such as the recent tour modification to accommodate a unique close flyby of Tethys prior to the planned Hyperion flyby in September of 2005.10 In order to verify the feasibility of these reference updates a covariance study like that described in ref[11]is performed.

Generally, five days prior to encountering the target satellite a final approach maneuver is de- signed to correct the S/C trajectory and realign it to the designed flyby conditions. For each flyby, a S/C onboard sequence of science observing activities including instrument pointing is based on the latest navigation reference trajectory at the time of its inception. These are programmed sev- eral months before the targeted encounter and remain somewhat inflexible to inevitable changes in the estimates of the S/C trajectory and satellite ephemeris. To overcome this, there are strategic opportunities for updating the instrument pointing vectors prior (5 days or more) to an encounter or occultation (ring or atmosphere). OD solutions with the latest data up to the 5 day requirement

3 10 10 SOI Ta Tb Tc T3 E1 T4T5 E2 SOI Ta Tb Tc T3 E1 T4T5 E2 34 m stations 34 m stations 70 m stations 70 m stations 1 1

0.1

Range Noise (m) 0.1 Doppler Noise (mm/s) 0.01

0.001 0.01 Jul Sep Nov Jan Mar May Jul Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2005 2005 2005 2005

(a) 2-Way Doppler (b) Range

Figure 1 Radio-metric data noise: Doppler in (a) and range in (b) are delivered to support these ‘live’ updates. The latest S/C to satellite (or Saturn) pointing vectors are compared to those from the reference trajectory and the latest dispersions are computed. These dispersions are tracked (comparing current ops solutions to covariance studies) in order to identify times when a pointing update is meaningful, that is, when the dispersion is generally less than the correction. Precise instrument pointing to targeted and non-targeted satellites levy requirements for OD predicted 1 − σ accuracies at better than 1.02 mrad for flyby altitudes between 20,000 – 30,000 km and 0.79 mrad for altitudes greater than 30,000 km.

Tracking Data

Cassini’s orbit determination is dependent on 2-way X-Band Doppler and range tracking data ac- quired via NASA’s Deep Space Network (DSN) and onboard optical navigation images (opnavs) of the major Saturn satellites against a background of known stars. Generally, one nine hour DSN tracking pass of radio-metric data is acquired per day while 3 to 6 opnav images are shuttered per day. The ranging signal is configured with adequate signal strength at Saturn’s distance to acquire data on 5 minute cycle times for range noise of 1 m or better. Because the science instruments are fixed-mounted to the S/C bus, radio-metric data are generally not acquired up to twelve hours before and after targeted encounters since the observing geometries preclude pointing the S/C’s High Gain Antenna to Earth for telecommunications. Due to the high declination of Saturn, Cassini is tracked exclusively by the northern DSN stations in Madrid, Spain and Goldstone, CA with the exception of an occasional Canberra, Australia pass.

The Doppler and range tracking data are weighted on a per-pass basis to the standard deviation of their residuals multiplied by a scale factor of 3.36. This scaling deweights the data to account for long-term solar plasma noise characteristics. Pass-to-pass data noise is generally better than 0.1 mm/s (for 60 sec count time) for 2-way Doppler data and 1 meter for the range data as shown in Figure 1. As such, the data weights account for these statistics from pass to pass. The better signal-to-noise capabilities of DSN’s 70 meter antennas than the smaller 34 meter dishes is evident in the better range noise as exhibited in Figure 1b. Once a year (July in 2004 and 2005), solar conjuction of Saturn as viewed from Earth occurs and the radio signal passing close to the is strongly affected by the solar plasma’s charged particles. During this time, the Doppler data is deweighted and the range data is subject to deletion especially for Sun-Earth-S/C angles of 5 deg or less. For of the current tour, the Doppler data has been compressed with 5 minute count times. Data acquired before and after maneuver executions are compressed to a more frequent count time of 60 sec. Because of the HGA mount, no tracking data are acquired during OTMs and occasional

4 presmrg.nio pwmrg.nio(show:cut thissession) N=35847 M=-4.18048e-05 RMS=0.00500935SD=0.00500917Min=-0.247877Max=0.121264 N=35848M=0.0018658 RMS=0.240593SD=0.240585 Min=-1.01303 Max=1.11213

Key Key 0.0500 1.200 Miscellaneous Miscellaneous DSS_14 DSS_14 DSS_15 DSS_15 0.0400 0.960 DSS_24 DSS_24 DSS_25 DSS_25 DSS_26 DSS_26 0.0300 0.720 DSS_34 DSS_34 DSS_43 DSS_43 DSS_45 DSS_45 0.0200 0.480 DSS_54 DSS_54 DSS_55 DSS_55 DSS_63 DSS_63 0.0100 0.240 DSS_65 DSS_65 C Canberra C Canberra G Goldstone G Goldstone -0.0000 0.000 M Madrid M Madrid Way Doppler Residuals

-0.0100 -0.240 2-Way Doppler Residuals (Hz)

-0.0200 Normalized 2- -0.480

-0.0300 -0.720

-0.0400 -0.960

-0.0500 -1.200

30-Jun-2004 11-Sep-2004 23-Nov-2004 04-Feb-2005 18-Apr-2005 30-Jun-2005 11-Sep-2005 30-Jun-2004 23-Aug-2004 17-Oct-2004 11-Dec-2004 04-Feb-2005 30-Mar-2005 24-May-2005 18-Jul-2005 11-Sep-2005 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 18:00:00.0 12:00:00.0 06:00:00.0 00:00:00.0 18:00:00.0 12:00:00.0 06:00:00.0 00:00:00.0

TIME (UTC) TIME (UTC)

(a) Actual (b) Normalized

presmrg.nio pwmrg.nio(show:cut thissession) N=26901 M=0.00802472 RMS=3.43985 SD=3.43984Min=-29.7063Max=46.8131 N=26901M=-0.000142063 RMS=0.284004 SD=0.284004 Min=-0.91144 Max=0.899674

Key Key 30.000 1.200 Miscellaneous Miscellaneous DSS_14 DSS_14 26.471 DSS_15 DSS_15 0.960 22.941 DSS_24 DSS_24 DSS_25 DSS_25

19.412 DSS_26 DSS_26 0.720 DSS_34 DSS_34 15.882 DSS_43 DSS_43 DSS_45 DSS_45 12.353 0.480 DSS_54 DSS_54

8.824 DSS_55 DSS_55 DSS_63 DSS_63 0.240 5.294 DSS_65 DSS_65 C Canberra C Canberra 1.765 G Goldstone G Goldstone 0.000 M Madrid M Madrid -1.765

-5.294 -0.240

-8.824 Normalized Range Residuals Range Residuals (R.U., 7 R.U. = 1 m) -12.353 -0.480

-15.882

-0.720 -19.412

-22.941 -0.960

-26.471

-30.000 -1.200

30-Jun-2004 11-Sep-2004 23-Nov-2004 04-Feb-2005 18-Apr-2005 30-Jun-2005 11-Sep-2005 30-Jun-2004 23-Aug-2004 17-Oct-2004 11-Dec-2004 04-Feb-2005 30-Mar-2005 24-May-2005 18-Jul-2005 11-Sep-2005 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 18:00:00.0 12:00:00.0 06:00:00.0 00:00:00.0 18:00:00.0 12:00:00.0 06:00:00.0 00:00:00.0

TIME (UTC) TIME (UTC)

(c) Actual (d) Normalized

Figure 2 2-way Doppler (a) & range (c) residuals from July 1, 2004 through July 22, 2005. Residuals normalized by their weights are shown in (b) and (d) respectively. small force ∆V events (as explained below).

The measured variability of the Earth’s ionosphere and troposphere is used to calibrate the radio data. Corrections to Earth’s motion and timing are also applied to the measurement models. Errors due to station locations (2-3 cm), troposphere (1 cm wet, 1 cm dry), ionosphere (5 cm day and 1 cm night), and Earth orientation (2 cm) are all considered in the OD filter. Per-station and per-pass ranging biases are estimated with a priori uncertainties of 1 meter and 3 meters, respectively.

The Doppler and range residuals are shown in Figures 2a, and 2c from July 1, 2004 through mid-July 2005. These residuals normalized by their weights are also displayed in Figures 2b, and 2d. The Doppler residual plots show how the noise characteristics increase during the solar conjunction periods (July 2004, 2005). The ranging biases estimated per pass are displayed in Figure 3. A few outliers during the solar conjunction of July 2004 have been removed in order to view the outstanding performance of the DSN’s ranging systems. These biases are well under 3 meters while the overall constant station biases are usually much less than 1 meter.

Three to six opnav images of any of the nine satellites are acquired daily by Cassini’s narrow angle

5 Range Bias Correction 120 SOI Ta Tb Tc T3 E1 T4T5 E2 DSS 14 Mimas 10 DSS 15 100 Enceladus DSS 24 Tethys DSS 25 Dione 5 DSS 26 80 Rhea DSS 34 Titan DSS 43 Hyperion DSS 45 60 Iapetus 0 DSS 54 DSS 55 DSS 63 40 Resolution (km/pix)

Correction (meters) -5 DSS 65 20 -10 0 May Jul Sep Nov Jan Mar May Jul Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2005 2005 2005 2005

Figure 3 Range biases per tracking pass. Figure 4 Resolution of opnav images. camera which has a 6 mrad field of view and a 2000 m focal length. The camera’s Charged-Couple Device contains 1025 x 1025 pixels giving the camera a resolution of approximately 6 µrad/pix. The centers of the known stars and the satellites’s diameters are measured in the pixel (x-axis) and line (y-axis) directions. Effectively, the opnavs are a two dimensional angular measurement of the apparent satellite’s position based on the locations of the stars in the camera’s focal plane. The optical residuals are a combined measure of both the S/C and satellite Saturn-barycentered orbit errors projected in the focal plane. Depending on Cassini-satellite geometry, some opnavs will show more sensitivity to the satellite’s down-track errors while other’s shuttered at their greatest elon- gations as viewed from Cassini are more sensitive to radial errors. Satellite and/or S/C trajectory parameter adjustments are influenced in the least-squares filter depending on the image resolution, optical weights and satellite and S/C state accuracies. The center-finding accuracy of the satellite centers is limited by the accuracy of the satellite’s shape model, variability in surface topography, and albedo. The fuzzy nature and variability of Titan’s atmosphere further degrades the center- finding accuracies for Titan opnav images. The unpredictable nature of Hyperion’s spin and its non-spherical shape complicates and degrades the accuracy of its opnavs. The drastic variation of Iapetus’ albedo also degrades these center-finding accuracies. Center-finding accuracies are on the order of 0.1 − 0.2% of the apparent image diameter for the icy satellites and between 0.2 − 0.4% for Titan. Corrections to the camera pointing (rotation angles about the pixel, line axes and camera boresight) based on the stars are estimated in the OD filter for each image with a priori of 1 degree for each axis using a white noise stochastic model. These corrections are usually much less than 1µrad in the angles about the pixel and line axes and less than 0.5 mrad for the twist angle about the boresight. Zeroth and first order phase biases are estimated for the Titan opnavs with an a priori sigma of 5%.

To properly account for the variable accuracy of the images taken at different ranges from the satellites, the opnavs are weighted using the following algorithm:

2 2 2 W = Wmin + (C · da)

Where W is the weight applied, Wmin is the minimum weight used (0.25 pixels for all satellites except Titan and Hyperion), C is an apparent diameter scale factor, and da is the apparent diameter of the satellite. The diameter scale factors are 0.02 for Mimas, Titan, and Iapetus, 0.04 for Hyperion, and 0.01 for the remaining satellites.

Each opnav also includes background stars to estimate the pointing and the stars are weighted at the larger of 0.1 pixels or their formal point-source sigma. The opnav weights of the inner (Mimas, Enceladus, Tethys, Dione and Rhea) and outer satellites (Titan, Hyperion, Iapetus and Phobe) for

6 Inner Satellite Weights Outer Satellite Weights 4 10 SOI Ta Tb Tc T3 E1 T4T5 E2 SOI Ta Tb Tc T3 E1 T4T5 E2 3.5 Mimas 9 Enceladus 8 3 Tethys Dione 7 2.5 Rhea 6 Titan 2 5 Hyperion Iapetus 1.5 4 Phoebe Weights (pixels) Weights (pixels) 3 1 2 0.5 1 0 0 Jul Sep Nov Jan Mar May Jul Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2005 2005 2005 2005

(a) Inner Satellites (b) Outer Satellites

Inner Satellite Weights Outer Satellite Weights 35 110 SOI Ta Tb Tc T3 E1 T4T5 E2 SOI Ta Tb Tc T3 E1 T4T5 E2 Mimas 100 30 Enceladus 90 Tethys Dione 80 25 Rhea 70 Titan 20 60 Hyperion Iapetus 50 Phoebe Weights (km) 15 Weights (km) 40 30 10 20 5 10 Jul Sep Nov Jan Mar May Jul Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2005 2005 2005 2005

(c) Inner Satellites (d) Outer Satellites

Figure 5 Optical weights for the inner satellites (a), outer satellites (b), inner satellites. These are normalized by resolution accuracy for the inner satellites(c) and outer satellites(d). this first year of the tour are displayed in Figures 5a and 5b, respectively. The resolutions of these images are shown in Figure 4. As shown in this plot, the resolutions of the opnav images after the start of 2005 vary between 5 km/pix during the S/C’s Saturn periapsis passage to 30 km/pix at apoapsis distances. Depending on the relative S/C-satellite distance, the weights normalized by their resolution accuracy are given in Figures 5c and 5d. After the Ta encounter, these weights vary from 8 – 11 km for Mimas, 5 – 10 km for Enceladus, 10 – 13 km for Tethys, 11 – 14 km for Dione, 15 – 17 km for Rhea, 13 – 24 km for Hyperion, 29 – 32 km for Iapetus, 23 – 28 km for Phoebe and finally 100 – 102 km for Titan. The optical pixel and line residuals for the inner and the outer satellites are shown in Figures 6a and 7a from July 1, 2004 through mid-July 2005. These residuals normalized by their weights are also displayed Figures 6b and 7b.

Spacecraft Modeling

While in orbit around the Saturn-system , ignoring the dominant Saturn’s point source gravity, the major perturbations affecting the S/C motion in order of significance include thrusting events from OTMs or small forces from the Reaction Control System (RCS), gravity due to the satellites, sun’s gravity, oblateness of Saturn, forces due to the S/C thermally-emitted radiation, solar pressure, relativity, satellite oblateness and drag forces during close Titan flybys. The many turns for instrument observations and the counteraction of drag torques during low Titan altitude (1025 - 1200 km) encounters require the S/C attitude to be controlled by the RCS system. The

7 Key

Satellite

presmrg.nio SAT1LN pwmrg.nio(show:cut thissession) Key N=730 M=0.056702 RMS=1.37938SD=1.37821 Min=-8.11541 Max=9.86896 N=730M=-0.00779599RMS=0.639086SD=0.639039Min=-3.24777 Max=2.41402 SAT1PX Satellite SAT2LN 10.000 3.0 SAT1LN SAT2PX SAT1PX SAT3LN SAT2LN SAT3PX 2.5 8.000 SAT2PX SAT4LN SAT3LN SAT4PX 2.0 SAT3PX SAT5LN 6.000 SAT4LN SAT5PX 1.5 SAT4PX SAT6LN SAT5LN SAT6PX 4.000 SAT5PX SAT7LN 1.0 SAT6LN SAT7PX SAT6PX SAT8LN 0.5 2.000 SAT7LN SAT8PX SAT7PX SAT9LN 0.0 SAT8LN SAT9PX 0.000 SAT8PX 1 SAT1LN SAT9LN 1 SAT1PX -0.5 SAT9PX 2 SAT2LN Post-fit Residuals 1 -2.000 SAT1LN 2 SAT2PX -1.0 1 SAT1PX 3 SAT3LN 2 SAT2LN 3 SAT3PX 2 -4.000 -1.5 SAT2PX 4 SAT4LN

Outer Satellite Optical Residuals (pixel, line) 3 SAT3LN 4 SAT4PX 3 SAT3PX -2.0 5 SAT5LN 4 -6.000 SAT4LN 5 SAT5PX 4 SAT4PX 6 SAT6LN -2.5 5 SAT5LN 6 SAT6PX 5 -8.000 SAT5PX 7 SAT7LN -3.0 6 SAT6LN 7 SAT7PX 6 SAT6PX 8 SAT8LN 7 -10.000 -3.5 SAT7LN 8 SAT8PX 7 SAT7PX 9 SAT9LN 30-Jun-2004 11-Sep-2004 23-Nov-2004 04-Feb-2005 18-Apr-2005 30-Jun-2005 11-Sep-2005 30-Jun-2004 23-Aug-2004 17-Oct-2004 11-Dec-2004 04-Feb-2005 30-Mar-2005 24-May-2005 18-Jul-20058 SAT8LN11-Sep-2005 9 SAT9PX 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 18:00:00.0 12:00:00.0 06:00:00.0 00:00:00.0 18:00:00.0 12:00:00.0 06:00:00.0 8 SAT8PX00:00:00.0 TIME (UTC) TIME (UTC) 9 SAT9LN 9 SAT9PX

(a) Actual (b) Normalized

Figure 6 Outer Satellite Optical Residuals (July 1, 2004 – July 22, 2005). Residuals normalized by their weights are shown in (b). Symbols: 6 = Titan, 7 = Hyperion, 8 = Iapetus, 9 = Phoebe. satellite harmonic gravity field effects cannot be determined or separated from these other perturba- tions without the close-in radio tracking data so these parameters are not included in the OD filter. Although a set of predicted ∆V ’s is given, the estimation of these events are complicated by the fact that data is not acquired for several hours before to after the flyby. The filter is sometimes unable to discern between the errors in the RCS predicts and the Titan ephemeris and is furthermore hindered by the contribution of drag forces.7 ,12 After these encounters the OD Team is under pressure to quickly determine the error from the flyby predictions, the satellite orbit correction and the effects of the RCS thrusting and the drag forces during the flyby. The OD Team only has the equivalent of two passes of post-flyby tracking data to determine these parameters and to predict ahead to the next orbit before an OD delivery is made to the Maneuver Team to design the +3 day clean-up maneuver which sets the S/C on course for the next encounter. The small force ∆V telemetry is used to update the nominal models, if time permits. In the past, this telemetry data resolution was set at 2 mm/s which made it is difficult to calibrate the RCS system. A recent flight software upload in May 2005 had lowered this resolution down to 0.02 mm/s and, based on recent RCS Earth-line ∆V events, this change shows promise in achieving a good calibration of the RCS system.

The finite burn ‘rocket equation’ is used to model the OTM maneuvers. The maneuver ∆V magnitude, right ascension, and declination of the burn vector are estimated in the filter using an a priori uncertainty based on the Gates error model which accounts for fixed and proportional errors.9 Data cut offs (DCO) for OTM designs are generally set at 2 days or less from their execution. The S/C thermal radiation acceleration is modeled as an exponential decay model with an estimated scale parameter in each of the spacecraft axes. The force due to solar pressure is modeled with a cylindrical bus and parabolical antenna using nominal reflectivity values but no parameters are estimated. At 9.5 A.U. from the sun, magnitude of the thermal radiation acceleration (∼ 5.0 nm/) is approximately one order of magnitude larger than the solar pressure acceleration (∼ 0.5 nm/s2). Thrusting due to the RCS events (discussed below) are generally modeled as impulsive maneuvers and only the ∆V magnitude is estimated. Unmodeled small forces (such as solar pressure mis- modeling) acting on the spacecraft are accounted for with the use of a set of stochastic accelerations with scale parameters estimated in spacecraft-fixed axes. These are modeled as white noise with spherical a priori uncertainty of 0.5 − 1.5 nm/s2 and batches every 8 hours. High resolution S/C attitude predicts from the S/C sequences are used in the S/C trajectory integration.

The S/C attitude is three-axis stabilized by the Reaction Wheel Assembly (RWA). Periodic

8 presmrg.nio Key pwmrg.nio(show:cut thissession) Key N=1512 M=-0.0875306 RMS=0.54155 SD=0.534429Min=-3.83189 Max=2.52772 N=1512M=-0.157456 RMS=0.739034SD=0.722066 Min=-3.58088 Max=2.93445 Satellite Satellite

4.000 SAT1LN 3.5 SAT1LN SAT1PX SAT1PX

SAT2LN 3.0 SAT2LN 3.200 SAT2PX SAT2PX SAT3LN 2.5 SAT3LN SAT3PX SAT3PX

2.400 SAT4LN 2.0 SAT4LN SAT4PX SAT4PX

SAT5LN 1.5 SAT5LN 1.600 SAT5PX SAT5PX SAT6LN 1.0 SAT6LN SAT6PX SAT6PX

0.800 SAT7LN 0.5 SAT7LN SAT7PX SAT7PX

SAT8LN 0.0 SAT8LN 0.000 SAT8PX SAT8PX SAT9LN -0.5 SAT9LN SAT9PX SAT9PX 1 1 -0.800 SAT1LN -1.0 SAT1LN 1 SAT1PX 1 SAT1PX 2 2 SAT2LN -1.5 SAT2LN 2 2 -1.600 SAT2PX SAT2PX

Inner Satellite Optical Residuals (pixel, line) 3 3 SAT3LN -2.0 SAT3LN 3 SAT3PX 3 SAT3PX

4 Normalized Inner Satellite Optical Residuals (pixel, line) 4 -2.400 SAT4LN -2.5 SAT4LN 4 SAT4PX 4 SAT4PX 5 5 SAT5LN -3.0 SAT5LN 5 5 -3.200 SAT5PX SAT5PX 6 6 SAT6LN -3.5 SAT6LN 6 SAT6PX 6 SAT6PX 7 7 -4.000 SAT7LN -4.0 SAT7LN 7 SAT7PX 7 SAT7PX 30-Jun-2004 11-Sep-2004 23-Nov-2004 04-Feb-2005 18-Apr-2005 30-Jun-2005 8 11-Sep-2005SAT8LN 30-Jun-2004 23-Aug-2004 17-Oct-2004 11-Dec-2004 04-Feb-2005 30-Mar-2005 24-May-2005 18-Jul-20058 SAT8LN11-Sep-2005 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 00:00:00.0 8 SAT8PX00:00:00.0 00:00:00.0 18:00:00.0 12:00:00.0 06:00:00.0 00:00:00.0 18:00:00.0 12:00:00.0 06:00:00.0 8 SAT8PX00:00:00.0 TIME (UTC) 9 SAT9LN TIME (UTC) 9 SAT9LN 9 SAT9PX 9 SAT9PX

(a) Actual (b) Normalized

Figure 7 Inner Satellite Optical Residuals (July 1, 2004 – July 22, 2005). Residuals normalized by their weights are shown in (b). Symbols: 1 = Mimas, 2 = Enceladus, 3 = Tethys, 4 = Dione, 5 = Rhea.

RWA wheel momentum dumps or biases are performed one or more times per orbit. These events are performed while the S/C is on Earth point and are thus covered by 2-way tracking data for direct determination of their ∆V contribution. The Attitude and Articulation Control Subsystem Team (AACS) is responsible for sending the OD Team predictions of these RCS ∆V events as they are placed in future sequences. Every six months to one year an RWA friction test is performed to study the health of the wheels. Occasionally, flight software uploads are performed; significant ∆V events occur while the new onboard software is checked-out. Such a significant event occurred less than one month before the Ta flyby as discussed in ref[6]. The OD Team relies on accurate predicts of these events for mapping the S/C orbit to encounters for maneuver designs or satellite pointing predictions so the errors of their predictions are tracked. Doppler data acquired during these events measure the ∆V while the ranging data measures the timing offsets from their predictions.

Generally, 15 – 30 minutes of tracking outage occurs during a ME burn: the S/C spins down the reaction control wheels and transitions the attitude control to the RCS. Under RCS control, the S/C yaws then rolls to burn attitude. After the burn, the S/C rolls then yaws to Earth point, and finally the reaction control wheels are spun up to transition the S/C back to RWA control. During the first yaw turn, the S/C loses contact with the DSN and is subsequently reacquired afterwards. Higher frequency Doppler data is needed to discern between the ∆V events: RWA spin-down, burn (yaw, roll turns included), and RWA spin-up. For smaller burns (< 0.4 m/s), the RCS system is used,9 the S/C turns to burn attitude on RWA. During these burns, a somewhat looser attitude tolerance is used, this tolerance is tightened after the burn to resume nominal operations, resulting in an additional ∆V in the burn direction. This bias, which could be a significant fraction of the total burn ∆V , is somewhat predictable, therefore the designed burn includes its effects.

Data Arc Strategy

For OD purposes, a new orbital data arc is established at each Saturn apoapsis. This data arc is responsible for OD solutions pertaining to the targeted satellite or Saturn periapsis activities used for clean-up maneuvers 1/2 revolutions later. After initiation, the solutions of this short arc become available as important comparisons to the longer arc which is prime for the upcoming encounter.

9 OD solutions routinely include estimates of 90 – 150 constant bias parameters, and 10 – 20 stochastic terms. Tracking the satellite parameter estimates and how the dynamics of the Saturnian system is affected is a major challenge of the OD Team. Cassini OD involves fitting the S/C tra- jectory, Saturn and the satellite ephemeris to the tracking data (both radio and optical) in a least squares sense using the JPL pseudo- state estimation filter. These linear corrections are then used to update the S/C dynamical models and measurement biases as well as the Saturn ephemeris (state, Saturn pole, J2, J4, and system ) and the estimated satellite parameters (satellite states, masses). Then the S/C trajectory is numerically integrated following that of all nine satellite orbits. Due to the highly non-linear nature of this complicated system, these orbits are then refit to the data and this process is iterated until the linearized corrections become small enough that the post-fit residuals closely match that of the pre-fit. Parameter estimates are routinely compared to prior solutions, those from other data arcs and various filter strategies. Parameter corrections on the order of formal 1-σ or more usually require further investigation as well as 1 or more sigma corrections in the stochastic parameters from their zero nominals.

To establish a new data arc at a new apoapsis epoch: The current prime long arc is fit up to this epoch, the Saturn ephemeris is corrected, the satellite parameters are corrected and then their orbits are numerically integrated before the S/C trajectory is integrated and the OD is converged, a new S/C initial state is interpolated from this new integrated trajectory. The S/C state uncertainties from the long arc are mapped to this new epoch and this correlated state covariance is generally scaled by 5, the estimated satellite parameters (satellite states, masses, Saturn, pole, J2,J4, and system mass) from the long arc fit are used to establish an updated satellite model, the post-fit correlated covariance of these satellite-Saturn parameters are then used as the new arc’s a priori satellite covariance, the thermal radiation acceleration terms are updated based on S/C mass decre- ments (from probe release or propellant expended during burns).

Due to the integration and partial derivative errors and increases of the information matrix conditioning during multiple satellite flybys, data arcs rarely extend more than a few days beyond the second encounter. Arcs that cover two flybys and Saturn periapses are difficult to fully converge, i.e. repetitive iterations cannot resolve fully the non-linearities in the system.

Filter Strategy

The baseline filter strategy utilizes the radio-metric and optical data. Baseline filter parameters include the satellite parameters as mentioned above and their unscaled covariance (formal statistics), burn parameters according to the error execution model in ref[9], small force impulsive ∆V s with 5 mm/s a priori each, thermal radiation acceleration with uncertainty of 10% on the S/C z−axis (aligned with S/C’s HGA) and 50% on the x and y axes, stochastic accelerations on the order of 0.5 nm/s2. The baseline OD filtering strategy is routinely compared to a large set of 50 – 60 filtering strategies that singly bound the filter parameter errors or data noise using loose or tight a priori covariances or data weights and data type combination sets. The capability to consistently and efficiently compute these large filtering strategy sets on a daily basis so that their progress can be tracked and compared was provided through the use of the filter loop program that was originally developed for the Exploration Rover mission interplanetary navigation.13 The overall results of these filter cases show how the individual data types or filter parameters move the solution and give insight into how the baseline case may need to be tuned. Interesting cases include the scaling of the satellite covariance and the removal of inner or outer satellite opnavs.

COVARIANCE ANALYSIS

The predicted tour covariance analysis as specified in the Nav Plan1 forms the basis of navigation performance and capability. This study, which was completed before tracking schedules and detailed

10 Semi-major Axis SOI Ta Tb Tc T3 E1 T4 T5 E2 1e+06 100000 OTM-2 3 4 5 6 8 9 10 11 12 1314 151617 18 19 20212223 24 25 10000 1000 100 10 Uncertainty (km) 1 0.1 Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul 2004 2004 2004 2004 2004 2004 2005 2005 2005 2005 2005 2005 2005

Semi-minor Axis 10000SOI Ta Tb Tc T3 E1 T4 T5 E2 1000 OTM-2 3 4 5 6 8 9 10 11 12 13 14 1516 17 18 19 20 212223 24 25

100 10

Uncertainty (km) 1 0.1 Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul 2004 2004 2004 2004 2004 2004 2005 2005 2005 2005 2005 2005 2005

Time of Closest Approach 100000SOI Ta Tb Tc T3 E1 T4 T5 E2 10000 OTM-2 3 4 5 6 8 9 10 11 12 1314 151617 18 19 20212223 24 25 1000 100 10 1

Uncertainty (sec) 0.1 Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul 2004 2004 2004 2004 2004 2004 2005 2005 2005 2005 2005 2005 2005

Nav Plan T-A Nav Plan T-3 Nav Plan T-5 HiFi T-B HiFi E-1 HiFi E-2 Nav Plan T-B Nav Plan E-1 Nav Plan E-2 HiFi T-C HiFi T-4 Nav Plan T-C Nav Plan T-4 HiFi T-A HiFi T-3 HiFi T-5

Figure 8 Tracking the OD convergence by comparing the achieved OD statistics (X symbols) during operations compared to the Nav Plan (thin lines) and HiFi covariance studies (thick lines). The locations of the OTMs are indicated by their numbers. dynamic events were known, made somewhat conservative assumptions on the OD filter models, radio-metric and opnav tracking schedules and data quality. Before a segment or data arc begins, a high-fidelity (HiFi) covariance study is performed using the latest tracking schedules, updated dynamic models, and latest OD filter assumptions. As this new data arc becomes operational, these covariance analyses (as shown in Figure 8) help track the OD convergence of orbit errors and provide a map to track operational OD performance as a function of time leading up to each targeted flyby. The main product of these covariance analyses is the mapping of the S/C dispersions to the encounter B-plane as a function of DCO. The B-plane semi-major and semi-minor axis dispersions are computed as well as the uncertainty in the time of closest approach (TCA). To show how the tracking data is converging or reducing the S/C mapped uncertainties, all thrusting events and filter parameters are included in the filter at each DCO; down-stream events except OTMs are included as considered errors since the mapped OTM dispersions to the encounter B-plane are typically much larger than the OD errors and thus would mask the OD convergence. Instead these OTM events are included into the filter at their execution times. Their contributions to the OD errors are shown in Figure 8 by the relatively large spikes in these plots. It is also shown how these dispersions are reduced as the post-burn data is fed into the filter. These rev-by-rev high-fidelity covariance analyses are generally performed one and one half orbit revolutions before each encounter. During the progression or evolution of the data arc for a particular targeted encounter, the current OD statistics are routinely plotted in Figure 8(designated by the X symbols) against the HiFi and Nav Plan covariance studies to ensure that the OD is converging (errors are declining) as expected from these studies. As shown in Figure 8, the HiFi analyses typically show better statistics than the

11 Nav Plan. This is expected and is directly attributed to the conservatism in the Nav Plan study which assumed that the S/C would be under RCS control for each encounter with ∆V uncertainty of 160 mm/s applied in the filter. The Nav Plan also assumed the stochastic accelerations to be 9 times larger than that of the HiFi value. Departures in actual operation solution statistics shown in Figure 8 can be attributed to the following: the late addition or removal of RCS ∆V events, optical or radio data outages, and changes in satellite covariance scaling.

RESULTS OF TARGETED ENCOUNTERS

Orbital Trim Maneuvers (OTMs) target for satellite encounters using the satellite-centered orthog- onal B-plane coordinate frame where the S axis lies parallel to the S/C’s approach asymptote, the R and T axes form the impact B-plane, and T lies in the Earth-Mean-Orbit of J2000. The B-vector points within the B-plane from the center of the coordinate system to where the S/C approach asymptote pierces this plane.

Figure 9 shows the B-plane results for each of the nine targeted satellite encounters. These results are presented using the formal 1-sigma statistics. These statistics don’t represent the full uncertainty of the OD solutions due to the complexity of the satellite system, but they do provide a means to gauge the OD performance. The final reconstructed solution which incorporates the post-flyby radio-metric data is plotted against the final approach maneuver target and dispersion. These reconstructions usually determine the satellite-relative flyby position to better than a few 100 m. Occasionally, the final approach (-3 day) maneuver was canceled, and in these cases the reconstructed solution is compared against both the final pre-encounter OD solution and the last targeting maneuver (at apoapsis). In some cases, this final pre-flyby OD solution was used for up- dating the sequence instrument pointing vectors.

Results of the encounter conditions for these nine targeted satellite encounters are listed in Table 2. Target miss parameters are given as a difference in the position from the target in the B-plane and in the time of closest approach. The table indicates whether the post-flyby reconstruction is compared to the last navigation control point, which includes an OTM that targeted the trajectory to the desired aim point and the associated maneuver execution errors in the dispersion, or to the last pre-encounter OD solution, which was used to cancel the final approach maneuver or was used for the last science-instrument pointing update. Generally, for instances where the final approach maneuver had been canceled, the last nav control point would have occurred at the apoapsis maneuver (Apo); these maneuver error contributions would normally dominate the target dispersions so that the miss in terms of the standard deviation is relatively small. Also given in Table 2 are 3-dimensional position errors for each encounter which are expressed in terms of the formal predicted dispersions by the following equation: √ T −1 σ3−D = ∆B Λ ∆B where ∆B is the target miss vector (reconstruction – prediction) in the encounter B-plane:

 ∆B · R  ∆B =  ∆B · T  ∆TCA and the final nav or OD control B-plane covariance is

 2  σB·T σB·T,B·R σB·T,T CA 2 Λ =  σB·R,B·T σB·R σB·R,T CA  2 σT CA,B·T σT CA,B·R σTCA

12 Table 2 Encounter Summary (Error given in terms of formal (unscaled) statistics)

Target Last Last Maneuver Nav or Position 3-D Delivery Reason for Miss Control Maneuver Error OD Error B-plane Accuracy Point Design Error? (km) error Probability (1σ)

Ph -15 day TCM-20 < 1σ Nav 73.6 0.5 3% -5 day Phoebe N.A. OD 13.8 1.3 36% Pointing Update

T-A -3 day OTM-4 1σ Nav 40.3 −− −− Titan eph error (∼35 km, ∼ 2σ), OTM-4 ∼ 1σ execution error

T-B Apo OTM-6 < 1σ Nav 22.5 0.3 0.7% -5 day OTM-7 Canceled OD 5.5 3.0 97% Titan eph error (∼4 km, ∼ 2σ)

T-C -10 day OTM-10a ∼ 1σ Nav 37.3 1.8 64% OTM-10a ∼ 1σ execution error, & Unobserved OTM-10 error

T-3 -3 day OTM-13 < 1σ Nav 4.6 1.5 48% Unobserved OTM-12 error

E-1 Apo OTM-15 < 1σ Nav 10.4 0.6 5% -5 day OTM-16 Canceled OD 3.1 2.4 88% Enceladus eph error &(∼4 km, ∼ 2σ)

T-4 Apo OTM-18 < 1σ Nav 8.3 1.3 36% -5 day OTM-19 Canceled OD 9.1 −− −− Titan eph error &(∼10 km out-of- plane error, ∼ 4σ)

T-5 -3 day OTM-22 < 1σ Nav 0.5 0.3 0.7%

E-2 -6 day OTM-25 < 1σ Nav 6.2 0.8 11%

Phoebe

Details of the Phoebe flyby are reported in ref[5]. On May 27, 2004, during the final approach to Saturn, TCM-20 targeted a 2000 km flyby of Phoebe on June 11, 2005. The maneuver execution error, reported in ref [5], was below 1σ. At five days before the encounter, an OD solution was delivered in order to update the instrument pointing vectors in the onboard sequence. The Phoebe B-plane in Figure 9a shows the TCM-20 target and dispersion, the last delivered OD for the ‘live’ update before the encounter and the achieved (reconstructed) flyby results. As shown in Table 2, the altitude difference from the TCM-20 target was approximately 71 km higher. Figures 19 and 25 show the improvements made to the Phoebe mass and ephemeris estimates. Phoebe’s were later improved from post-SOI data, opnavs taken in early 2005 and the recent set of orbits between T5 and E2 because of the improved Saturn-system mass determination (discussed below).

Titan-A

The challenges of the Ta OD and the final results are discussed in ref [6] . Due to its extended atmosphere, the center-finding algorithm had difficulties with the Titan opnavs on approach to the Oct 26, 2004 Ta encounter. It was this algorithm that created the optical observables for determining Titan’s ephemeris prior to this first Titan encounter. The optical data was unable to determine the relatively large 40 km miss at the Ta flyby. This was about 4.9 σ relative to the formal statistics which we believed did not give the true error due to the difficulty of the center-finding of Titan

13 opnavs. Most of this error was due to Titan’s ephemeris estimate which shifted approximately 40 km (2 − σ) in its down-track position and 5 km in the out-of-plane direction. This determination of the Titan ephemeris after the Ta encounter was made difficult because the S/C was on RCS control, and it experienced atmospheric drag with no radio-metric data during the flyby. The targeted 1200 km altitude was missed by 26 km, so that the S/C flew a bit lower (1174 km). The last targeting maneuver for Ta, OTM-4, was found to have over performed by a little more than 1σ yet this was not the reason for the miss. Figure 9b compares the reconstruction against the OTM-4 and OTM-3 dispersions in the Ta B-plane.

Titan-B

The OD leading up to the Dec 13, 2004 Tb encounter was just as challenging as Ta. Although the Titan ephemeris had been improved at Ta, it was found that different assumptions for the RCS ∆V events and the atmospheric drag during the Ta encounter produced different changes in Titan’s ephemeris, mostly in its . This concern was lessened by the fact the Tb encounter would take place at Titan’s same orbital longitude as the Ta event. The nominal execution of the apoapsis burn, OTM-6, placed Cassini on course for the Tb flyby. The solutions produced for the final approach maneuver, OTM-7, showed that there was no reason to perform OTM-7 since the solutions were close to the target (∼ 20 km). Even though OTM-7 was canceled, the OD delivery for its final design was used for an update of the onboard pointing parameters. As shown in the Tb B-plane (Figure 9c), and in Table 2, the control error for OTM-6 was approximately 23 km, well under 1σ, especially since it had a relatively large dispersion. The OD delivery for OTM-7 was found to be only 6 km off from the reconstructed value as seen in Table 2. Since the formal statistics of this OD were very small, the reconstruction was shown to be approximately 3σ off this prediction. The OD filter strategy that removes the inner satellite opnavs from the filter did show better predictions (as compared to the reconstruction) at the time of the OTM-7 DCO. The Titan ephemeris was estimated to be in error by approximately 4 km which was 2 σ relative to its a priori. The S/C flew 7.7 km lower than the targeted altitude of 1200 km. From Figure 23, the eccentricity of Titan became better determined from this flyby. More details of this encounter and the modeling of events surrounding the close flybys of Ta and Tb will be discussed in ref[7].

Titan-C

As mentioned, the Jan 14, 2005 Tc results are discussed in ref [8]. The error in the Tc flyby as shown in Figure 9d and Table 2 was 37 km off the target, this represented a nearly 2σ error from the control dispersion of OTM-10a (the Orbit Deflection Clean-up Maneuver, ODMCU). Part of the reason for this error was the last targeting maneuver, OTM-10a, over performed by nearly 1σ. Also, it was found after the Tc flyby that the determination of the OTM-10 (Orbit Deflection Maneuver) in solutions leading up to the OTM-10a design were in error. The post-Tc reconstruction showed the OTM-10 burn to be closer to nominal than the operational solutions indicated, they were over estimating the ∆V magnitude by nearly 10 mm/s (1σ). There was no significant change in Titan’s ephemeris.

Titan-3

The T3 OD solutions leading up to the final T3 -3 day targeting maneuver, OTM-13, suffered the same problem as the OTM-10a solutions. Here, the execution errors of the large apoapsis maneuver, OTM-12 (18.7 m/s), were unresolved until after the Feb 15, 2005 T3 flyby (see Figure 9e). The OTM-13 burn performed nominally (< 1σ). Table 2 shows that the S/C flew 4.6 km (or 1.5σ) from the target. The post-T3 data showed that the pre-T3 determination of the OTM-12 ∆V magnitude estimate was low by only 3 mm/s. However, this was enough error to account for the flyby offset. Again, there was no appreciable change in Titan’s ephemeris.

14 Enceladus-1

Two days after the T3 flyby on Feb 17, 2005, Cassini flew by Enceladus at approximately 1263 km (designated as the E0 flyby). This flyby was non-targeted meaning that no maneuver was designed to achieve a certain flyby target. The radio-metric data before and after this flyby enabled an accurate determination of Enceladus’ mass as shown in Figures 12a & b. The uncertainties drop nearly 2 orders of magnitude after the flyby. This mass was verified during the 502 km E1 flyby on March 9, 2005. The OD solutions leading up to the final E1 -3 day targeting maneuver (OTM-16) were very consistent. The final OD for OTM-16 as shown in Figure 9f was only approximately 5 km from the target. It was useless to perform the OTM-16 maneuver as the statistical likelihood of achieving the target was not any better than that of the OD solution since the OD statistics nearly encompassed the target. Therefore, OTM-16 was cancelled. Table 2 shows that with respect to the apoapsis burn (OTM-15), the S/C flew within 10.4 km from its target which was mainly a down-track error (+1.5 sec). Comparing the reconstruction to the OD solution for OTM-16 design in Table 2 reveals that its prediction was only 3.1 km in error. This represents a nearly 2.4σ shift given the formal statistics. The miss was mainly due to a down-track Enceladus ephemeris error of ∼ 4 km (which was a 2σ change from its a priori ephemeris).

Titan-4

T4 was the first outbound Titan encounter. Even though Titan’s ephemeris had already been determined through four flybys, these determinations occurred at the same orbital longitude. It takes at least two flybys at different longitudes to fully determine the six components of the satellite’s orbital elements. After the nominal execution of the apoapsis targeting maneuver, OTM-18, the OD solutions leading up to the design of the clean-up maneuver showed very little variation in the solutions as viewed in the T4 B-plane. This was true for various filtering strategies. As a result the final targeting maneuver, OTM-19, was canceled. The apoapsis OTM-18 maneuver dispersion and target are shown in the T4 B-plane in Figure 9g. The final OD delivery for the OTM-19 design is compared against the reconstructed solution. The miss from the OTM-18 target was ∼ 8 km while it was 9 km from the final pre-T4 OD. This small error was actually 4.2σ relative to the formal statistics which we didn’t believe because the optical data was not providing enough information on Titan’s ephemeris. After the encounter, it was found that again the Titan ephemeris was in error, this time there was a large 10 km error in Titan’s out-of-plane position which was nearly 4 times its formal statistics. The Figure 23b shows that the T4 flyby significantly corrected Titan’s longitude of the ascending node and .

Titan-5

The orbit from T4 to T5 was the first 16 day orbit of the satellite tour. There will be many more of these to come. Since Titan has a 16 day period, the T5 encounter takes place at the same orbital longitude as the T4 encounter. The T4 encounter data helped to significantly improve the Titan ephemeris knowledge. Figure 9h compares the flyby results for the April 16, 2005 T5 encounter. As indicated in this figure, the actual target for the last targeting maneuver OTM-22 was updated because of an error in the prediction for the RCS ∆V events surrounding the burn. With the nominal execution of OTM-22, the T5 reconstructed results showed remarkable agreement to the final OTM-22 target. As shown in Table 2, this was less than 0.5 km from the corrected T5 target which is only 0.3σ error from the formal statistics. Again, Titan showed no significant changes.

Enceladus-2

The E2 encounter occurred five orbits (89 days) after the T5 flyby. Six days before the encounter, the final targeting maneuver OTM-25 corrected the S/C’s trajectory for the low 175 km E2 flyby. As

15 discussed in the next section, these ‘empty’ revs allowed a better determination of the Saturn-system mass. Furthermore, the inner satellite residuals, especially Enceladus (Figure 7) showed a negative bias, indicating that either the opnavs had a systematic bias or the filter strategy was incorrect. These two facts led us to believe that our current satellite covariance could be over constraining the system so it was decided to scale the covariance up by a factor of three. This scaling the satellite covariance effectively puts more weight on the opnavs. With the nominal execution of OTM-25, the post-flyby reconstruction, as shown in Figure 9i, was only 6 km (0.8σ) from the target. Furthermore, the Enceladus ephemeris changed very little (< 1 km). Reconstruction analysis of the flyby showed that the pre-encounter OD solutions which had more weight on the opnavs moved further from the truth than solutions which placed more weight on the satellite covariance. This flyby showed that the opnavs do appear to have a systematic bias.

SATELLITE EPHEMERIS DEVELOPMENT

The estimation and integration of the satellite ephemeris are a major ingredient in the OD processes and present one of the major challenges to accurate OD. Prior to the final Saturn approach Jacobson [14] supported satellite ephemeris development for the Cassini mission based on the flyby’s of the Voyager and Pioneer 11 S/C radio and optical tracking data, US Naval Observatory, Hubble, and Table Mountain astrometric observations as well as numerous historical observations dating back to the 1960’s. The large data set used to estimate the satellite ephemeris is important to determine the long period dynamical interactions. To properly compute the satellite orbits, the dynamical environment of the Saturnian system needs to be modeled and estimated. In addition to the Sat- urn ephemeris, this environment includes the satellites’ initial Cartesian state at epoch (January 2, 2004), the Saturn pole position at epoch, the masses (GM) of the satellites, Saturn, the oblateness (J2) and zonal harmonic J4 of Saturn. Through the large data set, meaningful or significant cor- relations between these parameters are formed in the covariance and provide the mechanisms that allow some parameters to be improved based on the observability of another or how the covariance becomes over constrained. For instance, there exists a ∼72 yr period longitude libration of Mimas and Tethys due to their 2:1 commensurability.14

The OD Team frequently interacts during weekly Satellite Working Group and OD meetings to discuss current satellite results, issues, problems and to provide direction for filter strategies and modeling. Jacobson[14] provides the OD Team with periodic ephemeris updates. These include a priori satellite-Saturn covariances. It is the belief of the team that this global fit of the satellite ephemeris based on the large data set is superior to the localized fit of the OD Team performed during operations on a rev-by-rev basis. It is known that the operational OD satellite ephemeris estimates tend to run-off from those provided from the global fit of the data as the long period terms such as the Mimas-Tethys libration may become lost.

Solutions for the determination of the satellite classical orbital elements are shown in Figure 21 for Mimas & Enceladus, Figure 22 for Dione & Tethys, Figure 23 for Rhea & Titan, Figure 24 for Hyperion & Iapetus and Figure 25 for Phoebe. These formal 1-sigma statistics don’t represent the full uncertainty of these orbits nor the mass estimates stated in the next section. It would not be as meaningful to show these estimates with their believed statistics as this would mask the truly complicated nature of this system. These figures show how the data is improving the satellite uncertainties. The change in the Saturn position from JPL’s DE-410 ephemeris is approximately 284 km. Table 3 shows that this was a predominately down-track change.

The improvements of these ephemeride uncertainties at each data epoch are compared against the Nav Plan covariance study. These errors are mapped 30, 90 and 180 days from these epochs to show if there are any secular growth in these errors. As shown in Figure 10, the satellite statistics from the operational OD solutions are as good or better than the Nav Plan for most of the year except for

16 (a) Ph (b) Ta (c) Tb 17

(d) Tc

(e) T3 (f) E1

(g) T4 (h) T5 (i) E2

Figure 9 Encounter B-plane results (T axis lies in the Earth-Mean-Orbit plane) for the nine satellite flybys. Times are in spacecraft event time, ET (UTC + 64.2 sec) Mimas : RSS Uncertainty of Mapped Satellite Ephemeris Enceladus: RSS Uncertainty of Mapped Satellite Ephemeris Tethys : RSS Uncertainty of Mapped Satellite Ephemeris Dione : RSS Uncertainty of Mapped Satellite Ephemeris Nav Plan Vs Operations Nav Plan Vs Operations Nav Plan Vs Operations Nav Plan Vs Operations 45 45 25 20 30 days Nav Plan 30 days Nav Plan 30 days Nav Plan 30 days Nav Plan 40 90 days 40 90 days 90 days 18 90 days 180 days 180 days 180 days 180 days 30 days Ops 30 days Ops 20 30 days Ops 16 30 days Ops 35 90 days 35 90 days 90 days 90 days 180 days 180 days 180 days 180 days 14 30 30 15 12 25 25 10 20 20 10 8 15 15 6

10 10 5 4 1−Sigma RSS Prediction Uncertainty (km) 1−Sigma RSS Prediction Uncertainty (km) 1−Sigma RSS Prediction Uncertainty (km) 1−Sigma RSS Prediction Uncertainty (km)

5 5 2

0 0 0 0 SOI Ta Tb Tc T3 E1 T4 T5 S07 S08 S09 S10 E2 SOI Ta Tb Tc T3 E1 T4 T5 S07 S08 S09 S10 E2 SOI Ta Tb Tc T3 E1 T4 T5 S07 S08 S09 S10 E2 SOI Ta Tb Tc T3 E1 T4 T5 S07 S08 S09 S10 E2 Tour Leg Number Tour Leg Number Tour Leg Number Tour Leg Number (a) Mimas (b) Enceladus (c) Tethys (d) Dione

Rhea : RSS Uncertainty of Mapped Satellite Ephemeris Titan : RSS Uncertainty of Mapped Satellite Ephemeris Hyperion : RSS Uncertainty of Mapped Satellite Ephemeris Iapetus : RSS Uncertainty of Mapped Satellite Ephemeris Nav Plan Vs Operations Nav Plan Vs Operations Nav Plan Vs Operations Nav Plan Vs Operations 18 45 60 25 30 days Nav Plan 30 days Nav Plan 30 days Nav Plan 30 days Nav Plan 16 90 days 40 90 days 90 days 90 days 180 days 180 days 180 days 180 days 50 30 days Ops 30 days Ops 30 days Ops 20 30 days Ops 14 90 days 35 90 days 90 days 90 days 180 days 180 days 180 days 180 days 12 30 40 15 10 25 30 8 20 10 6 15 20

4 10 5 1−Sigma RSS Prediction Uncertainty (km) 1−Sigma RSS Prediction Uncertainty (km) 1−Sigma RSS Prediction Uncertainty (km) 10 1−Sigma RSS Prediction Uncertainty (km) 2 5

0 0 0 0 SOI Ta Tb Tc T3 E1 T4 T5 S07 S08 S09 S10 E2 SOI Ta Tb Tc T3 E1 T4 T5 S07 S08 S09 S10 E2 SOI Ta Tb Tc T3 E1 T4 T5 S07 S08 S09 S10 E2 SOI Ta Tb Tc T3 E1 T4 T5 S07 S08 S09 S10 E2 Tour Leg Number Tour Leg Number Tour Leg Number Tour Leg Number (e) Rhea (f) Titan (g) Hyperion (h) Iapetus

Figure 10 Comparing the operational satellite uncertainties against Nav Plan as satellite tour progresses.

Hyperion and Iapetus. This was expected since the opnavs for these satellites have been deweighted as compared to the Nav Plan assumptions due to their center-finding difficulties. Enceladus and especially Titan show significant improvements over the Nav Plan. This can be attributed to the conservative models used in the Nav Plan. The uncertainties in the last two data arcs at the S10+ and E2+ apo epochs show significant increases for most of the moons. This is due to scaling up the satellite covariance by three prior to the E2 encounter. During this time, the scaling was applied to alleviate the concern that the satellite covariance was over constraining the OD estimates, especially for Enceladus which was the current targeted body. This was further exacerbated by the fact the optical residuals of the inner satellites, particularly Mimas and Enceladus, showed a clear negative bias (see Figure 7). As it turns out for the E2 flyby, the satellite covariance was correctly predicting the Enceladus orbit as there were little corrections to its ephemeris as a result of the flyby. This flyby helped to show that the optical data do have systematic errors. This discovery is recent and ways to mitigate these biases are being investigated.

ESTIMATION OF THE SATURNIAN MASSES

Significant improvements to the mass (GM) estimates of Enceladus, Iapetus, Phoebe, Titan and Saturn have been made through close flybys to these moons and Saturn periapsis passages. Figures 11 – 19 exhibit the improvements in the satellite mass estimates in the operational and reconstruction OD solutions as a function of time. The weighted mean value of these estimates are shown with the solid red line in these Figures. The level of improvement is indicated by the uncertainty plot in (b) of these Figures. Occasionally, the satellite covariance which at each data arc epoch represents a current fit of the data is scaled by a factor of 3 or more to reduce its constraints in the OD filter and give the more recent optical and/or radio-metric data more influence or weight on determining

Table 3 Saturn ephemeris corrections from JPL ephemeris DE410 Date of Radial Transverse Normal Comparison (km) (km) (km) July 18, 2005 -29.5 ±0.006 280.6 ±0.3 -28.4 ±6.9

18 2.58 0.1 SOI Ta Tb Tc T3E1T4T5 E2 SOI Ta Tb Tc T3E1T4T5 E2 2.57

2.56 ODR.Ta ODR.Tc ODR.Tb

) 2.55 ) ODR.T3 ODR.T5 ODR.E1 ODR.T4 2 2 ODR.007Sa ODR.008Sa ODR.009Sa /s /s ODR.010Sa 3 3 2.54 ODR.010Sa 0.01 2.53 ODR.Sa ODR.Ta ODR.Tb ODR.Tc ODR.Sa ODR.T3 ODR.E1 ODR.T4 Mass (km Mass (km ODR.T5 ODR.007Sa ODR.008Sa 2.52 ODR.009Sa

2.51

2.5 601GM 601GM 2.49 0.001 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005

(a) Estimates (b) Uncertainties

Figure 11 Mimas mass (GM) estimates from operational, reconstructed (labeled) OD solutions versus time. the satellite parameters. This is desired especially when multi-sigma corrections are estimated for a significant subset of the satellite parameters.

9.5 10 SOI Ta Tb Tc T3E1T4T5 E2 SOI Ta Tb Tc T3E1T4T5 E2 9

8.5 1 ODR.Ta ODR.Sa ) ) 2 2 ODR.Tb ODR.Tc ODR.Ta 8 ODR.Tb ODR.Tc ODR.Sa /s /s 3 3 7.5 0.1 ODR.010Sa ODR.T3 ODR.009Sa ODR.E1 ODR.008Sa ODR.007Sa ODR.T4 ODR.T5

Mass (km 7 Mass (km

6.5 0.01 ODR.010Sa ODR.T3 ODR.E1 ODR.T4 ODR.T5 ODR.007Sa ODR.008Sa 6 ODR.009Sa 602GM 602GM 5.5 0.001 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005

(a) Estimates (b) Uncertainties

Figure 12 Enceladus mass (GM) estimates from operational, reconstructed (labeled) OD solutions versus time.

Iapetus Mass Determination

After Titan and Rhea, Iapetus is the third largest of the nine major satellites in the Saturnian system. Iapetus orbits Saturn approximately every 79 days at a mean distance of 3.56 Mkm from the Saturn system barycenter and its orbit is inclined 15.1 deg to the Saturn equator. Because of its mass and distance from Saturn, Iapetus plays a significant role in the shift of the Saturnian system barycenter from the center of Saturn. Shortly before the Huygens Probe Mission Navigation Review, it was determined that our current (post-SOI) mass estimate of Iapetus varied by more than three times its formal uncertainty. The accuracy of the Huygens probe delivery to Titan on January 14, 2005 (Tc) was dependent on the knowledge of the Iapetus mass prior to probe release on December 25, 2004 because of a close flyby of Iapetus at a distance of approximately 64,000 km subsequent to release on December 31, 2004. The flyby distance was later increased to 126,000 km to lessen the dependence on our knowledge of the Iapetus mass.8

19 41.23 ODR.Sa 0.1 SOI Ta Tb Tc T3E1T4T5 E2 SOI Ta Tb Tc T3E1T4T5 E2 41.225 41.22 ODR.Ta ODR.Tc ODR.010Sa ODR.Sa 41.215 ODR.T3 ODR.Tb ODR.E1 ) ) ODR.T4 ODR.009Sa 2 ODR.T5 2 ODR.008Sa ODR.007Sa

/s 41.21 /s 3 3 41.205 0.01 ODR.010Sa 41.2 Mass (km Mass (km

41.195 ODR.Ta ODR.Tb ODR.Tc ODR.T3 ODR.E1 ODR.T4 ODR.T5 ODR.007Sa ODR.009Sa 41.19 ODR.008Sa 41.185 603GM 603GM 41.18 0.001 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005

(a) Estimates (b) Uncertainties

Figure 13 Tethys mass (GM) estimates from operational, reconstructed (labeled) OD solutions versus time.

73.135 0.1 SOI Ta Tb Tc T3E1T4T5 E2 SOI Ta Tb Tc T3E1T4T5 E2 73.13

73.125 ODR.Sa

) ) 0.01 2 2 ODR.Sa /s /s

3 73.12 3 ODR.010Sa ODR.010Sa ODR.Ta 73.115 ODR.Tb ODR.Tc ODR.009Sa ODR.008Sa ODR.007Sa ODR.T3 ODR.T5 ODR.T4 ODR.T3 ODR.E1 ODR.Tc ODR.E1 ODR.T4 Mass (km Mass (km ODR.Tb ODR.Ta 0.001 ODR.T5 ODR.007Sa ODR.008Sa ODR.009Sa 73.11

73.105 604GM 604GM 73.1 1e-04 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005

(a) Estimates (b) Uncertainties

Figure 14 Dione mass (GM) estimates from operational, reconstructed (labeled) OD solutions versus time.

OD covariance studies showed that the Iapetus mass estimate could be improved through either direct measurements using radio-metric data before and after a close flyby of Iapetus or indirect measurements inferred through improvements in the Saturn barycenter position determination us- ing radio-metric data before and after the first and second Titan flybys & Saturn periapses (Ta, Oct 26 and Tb, Dec 13). Prior to Cassini’s arrival at Saturn, knowledge of Iapetus mass (GM) has been primarily determined using the radio-metric data through the Pioneer, Voyager 1 & 2 flybys. Prior to Cassini’s Saturn insertion, the Iapetus GM value was 132 km3/s2 as shown in Figure 18. The formal uncertainty of this value was approximately ±4 km3/s2, but lack of confidence in this number led to raising it to ±16 km3/s2. Shortly after Saturn orbit insertion (SOI) on July 1st, 2004, we saw the Iapetus GM increase to ∼134 km3/s2 and then drop down to ∼118 km3/s2. The post-SOI radio-metric data was found to improve the knowledge of Iapetus by nearly 15% through better barycenter position determination. Cassini’s first direct measure of Iapetus mass came after a distant 2.5 Mkm flyby on July 13th, 2004. This flyby improved the mass of Iapetus by nearly 50% relative to its formal a priori uncertainty. Although these determinations indicated that we had im- proved our knowledge of Iapetus’ mass, these two events occurred during Cassini’s solar conjuction period where the radio-metric data is greatly affected by the charged particles in the solar plasma. We found that a closer flyby of 1.1 Mkm would occur on Oct 18, 2004 prior to Ta. A covariance study showed that this flyby would help determine its mass significantly (below 1 km3/s2) especially after the radio-metric data measured its barycentric position after the Ta flyby. In addition, the

20 162 10 SOI Ta Tb Tc T3E1T4T5 E2 SOI Ta Tb Tc T3E1T4T5 E2 160 ODR.Sa ODR.Ta

158 ODR.Sa

) ) 1 2 156 2 /s /s 3 3 ODR.Tb ODR.Tc ODR.010Sa ODR.007Sa ODR.T5 ODR.009Sa ODR.008Sa ODR.T3 ODR.T4 ODR.E1 ODR.Tc ODR.Tb 154 ODR.Ta ODR.T3 ODR.E1

Mass (km 152 Mass (km ODR.T4 0.1 ODR.010Sa ODR.T5 ODR.007Sa ODR.008Sa 150 ODR.009Sa

148 605GM 605GM 146 0.01 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005

(a) Estimates (b) Uncertainties

Figure 15 Rhea mass (GM) estimates from operational, reconstructed (labeled) OD solutions versus time.

8979 10 SOI Ta Tb Tc T3E1T4T5 E2 SOI Ta Tb Tc T3E1T4T5 E2

8978.5 ODR.Tb ODR.010Sa ODR.Tc ODR.Sa ODR.009Sa ODR.008Sa ODR.007Sa ODR.T5 ODR.T4 ODR.E1 ODR.T3 ODR.Ta

) ) 1 2 2

/s 8978 /s 3 3 ODR.Sa

8977.5 Mass (km Mass (km 0.1 ODR.Ta ODR.010Sa ODR.Tc

8977 ODR.Tb ODR.T3 ODR.T5 ODR.T4 ODR.E1 ODR.008Sa ODR.009Sa 606GM 606GM ODR.007Sa 8976.5 0.01 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005

(a) Estimates (b) Uncertainties

Figure 16 Titan mass (GM) estimates from operational, reconstructed (labeled) OD solutions versus time. covariance studies indicated that the Iapetus mass uncertainty would be further reduced after the Tb flyby, a result of another radio-metric measurement of Saturn’s barycentric position. This time because of Iapetus’ 79 day orbit it was now opposite of its position during the Ta flyby time.

To further confirm the estimates from the Oct 2004 flyby, we acquired several interferometric measurements using the National Radio Observatory’s (NRAO) Very Long Baseline Ar- ray data of Cassini. The VLBA measurement involved the differencing of several interferometric (plane-of-sky) measurements of Cassini with a galactic radio source using many baseline combina- tions of the NRAO radio telescopes. The measurement is similar to the ∆DOR measurement used by several recent deep space missions.13 This VLBA technique was experimental for deep space navigation, but had already been shown with the Mars Exploration Rovers’ approach to Mars to be exceptionally accurate (geometric delays < 0.10 ns). Covariance studies showed that the data acquired during the Iapetus flyby would significantly improve the Saturn barycenter in the Earth plane-of-sky frame from ±40 km down to ±2 km. Indeed the data did improve Saturn’s barycenter to this level, however at the time of processing the data in Nov 2004, it was inconclusive in deter- mining Iapetus’ GM. Figure 18 shows that the value had settled to approximately 120.5 km3/s2 prior to the Huygens probe release on Dec 25, 2005. The close flyby on Dec 31, 2004 confirmed our results as we saw little change in this value.

21 0.65 0.1 SOI Ta Tb Tc T3E1T4T5 E2 SOI Ta Tb Tc T3E1T4T5 E2 0.6

0.55 ) ) 2 2 /s /s

3 0.5 3 0.01 0.45 ODR.010Sa ODR.Tc ODR.Tb Mass (km Mass (km ODR.T3

0.4 ODR.E1 ODR.T4 ODR.010Sa ODR.Tb ODR.T3 ODR.E1 ODR.008Sa ODR.Ta ODR.T5 ODR.007Sa ODR.009Sa ODR.Tc ODR.T4 ODR.Ta ODR.T5 ODR.007Sa ODR.008Sa ODR.009Sa 0.35 607GM 607GM 0.3 0.001 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005

(a) Estimates (b) Uncertainties

Figure 17 Hyperion mass (GM) estimates from operational, reconstructed (labeled) OD solutions versus time.

Tethys and Dione masses are well known from observations of the librations of the Lagrangian satellites, Helene, Telesto and Calypso.15 Post-E0, E1 and E2 flyby data have determined Enceladus mass. These estimates are statistically consistent with earlier values determined solely from Ence- ladus resonance with the minor satellites Dione and Helene.15 During the Ta approach it has been found that Hyperion’s ephemeris has a significant effect on the determination of Titan’s orbit (3:4 resonance) even though its mass is small. The mass estimates for operation solutions showed improvements even though no close flyby of Hyperion has yet occurred and these values were much lower than scientists originally believed based on theories of its formation. Forcing Hyperion’s mass to the higher assumed theoretical mass estimate had detrimental effect on OD solutions. With the latest data, all satellite masses except Hyperion have been determined to better than 1%. Given the current volumes, the densities for all satellites except Hyperion are known to better than 3%. Hyperion and Rhea are the last satellites masses to be significantly improved through flyby data. These will be improved during encounters in September for Hyperion (∼500km) and November for Rhea (500km).16

140 10 SOI Ta Tb Tc T3E1T4T5 E2 SOI Ta Tb Tc T3E1T4T5 E2

135 ODR.Sa

) ) 1 ODR.Ta 2 2

/s 130 /s 3 3 ODR.Tb

125 ODR.Sa Mass (km Mass (km 0.1 ODR.Ta ODR.Tb ODR.Tc ODR.E1 ODR.T4 ODR.010Sa ODR.T3 ODR.T5 ODR.007Sa ODR.008Sa ODR.009Sa 120 ODR.010Sa ODR.Tc ODR.T3 ODR.E1 ODR.T4 ODR.T5

608GM 608GM ODR.008Sa ODR.007Sa 115 0.01 ODR.009Sa May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005

(a) Estimates (b) Uncertainties

Figure 18 Iapetus mass (GM) estimates from operational, reconstructed (labeled) OD solutions versus time.

Saturn-System Mass Estimation

The evolution of the Saturn-System mass (GM6) estimates in Figure 20 show several formal sigma shifts during the course of the tour. We believe that the cause of these excursions can be attributed

22 1.6 1 SOI Ta Tb Tc T3E1T4T5 E2 SOI Ta Tb Tc T3E1T4T5 E2 1.4 1.2 0.1 1 ) ) 2 2

/s 0.8 /s 3 3 ODR.010Sa ODR.Sa ODR.T5 ODR.007Sa ODR.008Sa ODR.009Sa 0.6 ODR.T3 ODR.T4 0.01 0.4 Mass (km Mass (km 0.2 0.001 0 ODR.010Sa ODR.Sa ODR.T5 ODR.007Sa ODR.008Sa ODR.009Sa ODR.T4

-0.2 ODR.T3 609GM 609GM -0.4 1e-04 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005

(a) Estimates (b) Uncertainties

Figure 19 Phoebe mass (GM) estimates from operational, reconstructed (labeled) OD solutions versus time. to the filter’s occasional inability to distinguish maneuver and flyby induced S/C orbit changes from Saturn’s gravity. Typically, the targeting maneuvers at apoapsis are fairly large but their ∆V components are not completely observable during the final approach to a flyby. Later the targeted satellite and S/C parameters, including the apoapsis maneuver, are significantly improved by the ad- dition of the post-flyby radio-metric data in the OD filter. However, it is thought that the unknown autonomous RCS thrusting activities during the Titan flybys (Ta, Tb, Tc, etc) and atmospheric drag forces12 could be corrupting these maneuver estimates. Between April 28 and July 8 this year during a set of 5 empty revs (including 4 periapse passages) the S/C experienced no close satellite flybys and minimal thrusting events. This allowed the tracking and opnav data to provide an esti- mate of GM6 at a previously unavailable accuracy.

750 100 SOI Ta Tb Tc T3E1T4T5 E2 SOI Ta Tb Tc T3E1T4T5 E2 )) 2 700 /s 3 ODR.Ta ODR.Sa ODR.Tb ODR.Sa ODR.Tc ODR.E1 ODR.T4 ODR.T3

650 ODR.T5

) 10 ODR.Ta 2 ODR.007Sa /s 3 ODR.Tb 600 ODR.008Sa ODR.010Sa ODR.008Sa ODR.009Sa ODR.009Sa ODR.007Sa 550 ODR.010Sa ODR.Tc Mass (km ODR.E1

ODR.T3 1 ODR.T4 500 ODR.T5

Mass (Value - 37940000.0 (km 450 ∆ GM6 GM6 400 0.1 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005

(a) Estimates (b) Uncertainties

Figure 20 Saturn System mass (GM) estimates from operational, reconstructed (labeled) OD solutions versus time.

Figure 20 shows the progression of estimates of GM6 from the end of April 2004 – July 2005. From this Figure, one can see that the GM6 estimates more or less steadily declined from the pre- SOI values by several formal sigma until about Dec 2004. A relatively large drop in this value took place in March 2005 when a new planetary ephemeris (JPL satellite & ephemeris SAT199) was introduced based on the powerful Very Long Baseline Array (VLBA) measurements taken of Cassini in September and October of 2004 to support the Iapetus mass determination. The VLBA data provided a direct measurement of the plane-of-sky position of the S/C which in turn contained strong information about the Saturn barycentric location normal to its orbit plane. An a priori

23 correlation between this Saturn position information and GM6 caused the GM6 drop at this time. Over the course of the next few months up to the T5 flyby in mid-April 2005, a further smaller downward drift in GM6 had been observed. After T5, during the 5 empty arcs in April – July, GM6 was determined independently and its estimate increased and settled to 37, 940, 585.0 ± 1.0 km3/s2. We have confidence in this value but the formal uncertainty may be too constraining and should be scaled by 3.

An illustration of how the incorrect value of GM6 can affect the orbit determination was presented at the beginning of the empty rev sequence. Shortly after OTM-24 the filter estimated a large over- performance of 70 mm/s in the maneuver magnitude, this estimate did not match what was seen in telemetry. This 1.5σ variation in the maneuver parameters could fit the available data and was cheaper in terms of its effect on the estimator cost function than would be a change in GM6 by several sigma. The correlation between GM6 and the burn parameters was high shortly after the maneuver due to the dependence of the inner satellite opnavs. The inclusion of more data eventually broke down this correlation and a shift toward a maneuver estimate more in line with telemetry was seen alongside the increase in GM6.

CONCLUSIONS

The complex interaction of Saturn and the satellites and how these dynamics influence the motion of Cassini have been observed improving our knowledge of this system during the first year of the satellite tour. Significant ephemeris improvements have been made to all the major satellites, especially Titan and Enceladus due to the close flybys. All major satellite masses except Hyperion have been determined to better than 1%. These improvements have enabled better predictions of the mapped encounter conditions, especially for the T5 and E2 encounters. Careful consideration in altering filter parameter a priori’s and data weighting must be taken so that the important information contained in the satellite ephemeris and covariance, obtained through the close flybys, is not lost.

ACKNOWLEDGEMENTS

This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Reference to any specific commercial product, process, or service by trade name, trademark, manufacturer or otherwise, does not constitute or imply its endorsement by the United States Government or the Jet Propulsion Laboratory, California Institute of Technology.

REFERENCES

1. Cassini Navigation Plan. Technical Report 699-101 Update, D-11621, JPL, August 2003. 2. D.C. Roth, M.D. Guman, R. Ionasescu, and A.H. Taylor. Cassini Orbit Determination form Launch to the First Venus Flyby. AAS Paper 98-4563, AAS/AIAA Astrodynamics Specialist Conference, Boston, MA, August 10-12 1998. 3. M.D. Guman, D.C. Roth, R. Ionasescu, T.D. Goodson, A.H. Taylor, and J.B. Jones. Cassini Orbit Determination form First Venus Flyby to Earth Flyby. AAS Paper 00-168, AAS/AIAA Space Flight Mechanics Meeting, Clearwater, FL, January 23-26 2000. 4. D.C. Roth, M.D. Guman, and R Ionasescu. Cassini Orbit Reconstruction from Earth to Jupiter. AAS Paper 02-156, AAS/AIAA Space Flight Mechanics Meeting, San Antonio, TX, January 27-30 2002. 5. D. C. Roth, P. G. Antreasian, J. J. Bordi, K. E. Criddle, R. Ionasescu, R. A. Jacobson, J. B. Jones, M. C. Meek, I. M. Roundhill, and J. R. Stauch. Cassini orbit reconstruction from Jupiter to Saturn. AAS Paper 05-311, AAS/AIAA Astrodynamics Specialist Conference, Lake Tahoe, Ca., August 7-11 2005.

24 6. I.M. Roundhill, P.G. Antreasian, K.E. Criddle, R. Ionasescu, M.C. Meek, and J.R. Stauch. Orbit Determination Results for the Cassini Titan-A Flyby. AAS Spaceflight Mechanics Meeting, Copper Mtn, CO, Paper AAS 05-113, Jan 2005. 7. J. Stauch, P. Antreasian, J. Bordi, K. Criddle, R. Ionasescu, R. Jacobson, J. Jones, M. Meek, D. Roth, and I. Roundhill. Preparing for the Huygens Probe Mission, Cassini Orbit Determination Results for the First and Second Targeted Titan Encounters. 6th International ESA Conference on Guidance, Navigation and Control Systems, Greece, October 2005. 8. J. Bordi, P. Antreasian, J. Jones, C. Meek, R. Ionasescu, I. Roundhill, and D. Roth. Orbit Determination Results and Trajectory Reconstruction for the Cassini/Huygens Mission. International Planetary Probe Workshop, IPPW-3, Anavyssos, Attica, Greece, June 27 2005. 9. S.V. Wagner, B.B. Buffington, T.D. Goodson, Y. Hahn, N.J. Strange, and M.C. Wong. Cassini-Huygens Maneuver Experience: First Year of Saturn Tour. AAS Paper 05-287, AAS/AIAA Astrodynamics Specialist Conference, Lake Tahoe, Ca., August 7-11 2005. 10. B.B. Buffington, N.J. Strange, and R. Ionasescu. Addition of a Low Altitude Tethys Flyby to the Nominal Cassini Tour. AAS Paper 05-270, AAS/AIAA Astrodynamics Specialist Conference, Lake Tahoe, Ca., August 7-11 2005. 11. R. Ionasescu. 6-Month Covariance Study for the Cassini Tour T2005-050505 Using the S10-S17 OPNAV Schedule. JPL IOM-343J-05-027, June 2005. 12. F.J. Pelletier. Modeling of Drag for Orbit Determination During Cassini’s Titan-5 Encounter. JPL IOM 343J-05-025, July 2005. 13. T. McElrath, M. Watkins, B. Portock, E. Graat, D. Baird, G. Wawrzyniak, J. Guinn, P. Antreasian, A. Attiyah, R. Baalke, and W. Taber. Mars Exploration Rover Orbit Determination Filter Strategy. AIAA/AAS Astrodynamics Specialists Meeting, Providence, RI, August 16-19 2004. 14. R. A. Jacobson. The orbits of the major Saturnian satellites and the gravity field of the Saturn from spacecraft and earth-based observations. AJ, 128:492–501, 2004. 15. R. A. Jacobson, P. G. Antreasian, J. J. Bordi, R. Ionasescu, J. B. Jones, K. E. Criddle, M. C. Meek, W. M. Owen Jr., D. C. Roth, I. M. Roundhill, and J. R. Stauch. The orbits of the major Saturnian satellites and the gravity field of the Saturnian system. BAAS, 36(4):1097, 2004. 36th Meeting of the American Astronomical Society Division for Planetary Sciences, Louisville, Kentucky. 16. R. A. Jacobson, P. G. Antreasian, J. J. Bordi, K. E. Criddle, R. Ionasescu, J. B. Jones, R. A. Mackenzie, M. C. Meek, F.J. Pelletier, D. C. Roth, I. M. Roundhill, and J. R. Stauch. The orbits of the major Saturnian satellites and the gravity field of the Saturnian system. BAAS, 37(2):524, 2005. presented at the 36th Annual Meeting of the American Astronomical Society Division on Dynamical Astronomy, Santa Barbara, CA.

25 ∆a = Value - 186000 km Mimas, Semimajor Axis Mimas, Time from Periapsis 527.5 -13340 Operations Operations 527 Reconstruction -13360 Reconstruction 526.5 -13380 -13400 526 -13420 525.5 -13440 ODR.010Sa

525 ODR.Sa ODR.Sa

ODR.Ta -13460 ODR.009Sa ODR.007Sa ODR.Tb ODR.008Sa ODR.010Sa ODR.008Sa ODR.007Sa ODR.009Sa ODR.Ta ODR.Tc ODR.E1 ODR.T4 ODR.T5 ODR.T3 a, Semimajor Axis (km) ODR.T5 ODR.T4 524.5 ODR.E1 ∆ ODR.Tc ODR.Tb

-13480 ODR.T3 Time from Periapsis (sec) SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 524 -13500 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC) Mimas, Eccentricity Mimas, Longitude of Ascending Node 0.022 -46.2 Operations Operations -46.3 0.02195 Reconstruction Reconstruction ODR.T5 ODR.T3 ODR.T4 ODR.E1 ODR.008Sa ODR.007Sa ODR.Tc

ODR.009Sa -46.4 ODR.Tb ODR.Ta ODR.Sa ODR.Sa

0.0219 ODR.010Sa ODR.Ta ODR.Tc ODR.E1 ODR.007Sa ODR.008Sa ODR.T5 ODR.T4

-46.5 ODR.T3 ODR.010Sa ODR.Tb ODR.009Sa 0.02185 -46.6 -46.7

Eccentricity 0.0218 -46.8 0.02175 -46.9 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 0.0217 -47

May Jul Sep Nov Jan Mar May Jul Longitude of Ascending Node (deg) May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

Mimas, Inclination Mimas, Argument of Periapsis 1.566 7.3 ODR.Tb

Operations ODR.T3 Operations 1.565 7.2 ODR.Tc ODR.T4 ODR.E1 ODR.T5 ODR.Ta ODR.009Sa

Reconstruction Reconstruction ODR.008Sa 1.564 ODR.007Sa 7.1 ODR.010Sa ODR.Sa 1.563 ODR.010Sa ODR.009Sa ODR.T3 7 ODR.007Sa ODR.T5 ODR.008Sa ODR.Tb ODR.Tc ODR.E1 ODR.T4 1.562 ODR.Sa 6.9

1.561 ODR.Ta 6.8 1.56 6.7 1.559 6.6

Inclination (deg) 1.558 1.557 6.5 1.556 6.4 SOI Ta Tb Tc T3 E1 T4 T5 E2 Argument of Periapsis (deg) SOI Ta Tb Tc T3 E1 T4 T5 E2 1.555 6.3 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

(a) Mimas

∆a = Value - 238000 km Enceladus, Semimajor Axis Enceladus, Time from Periapsis 964 22690 963.5 Operations Operations Reconstruction 22680 Reconstruction 963 22670

962.5 ODR.Sa 22660 962 ODR.Ta ODR.Tc ODR.Tb ODR.T3 ODR.010Sa ODR.009Sa ODR.008Sa 961.5 ODR.007Sa 22650 ODR.T5 ODR.T4 ODR.E1 961 ODR.Sa 22640

960.5 ODR.Ta ODR.Tb ODR.010Sa ODR.008Sa ODR.007Sa ODR.009Sa a, Semimajor Axis (km) ODR.Tc ODR.E1 ODR.T4 ODR.T3 ODR.T5 22630 ∆

960 Time from Periapsis (sec) SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 959.5 22620 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC) Enceladus, Eccentricity Enceladus, Longitude of Ascending Node 0.00529 -80 Operations -100 Operations

0.005285 Reconstruction ODR.010Sa Reconstruction ODR.T3 ODR.Tc

ODR.T4 -120 ODR.007Sa ODR.009Sa ODR.008Sa ODR.E1 ODR.Tb ODR.Ta ODR.007Sa ODR.008Sa ODR.T5 ODR.010Sa ODR.009Sa ODR.T5 ODR.Tc 0.00528 ODR.T4 ODR.T3 ODR.E1 ODR.Sa ODR.Ta -140 ODR.Tb 0.005275 -160 0.00527 -180 ODR.Sa

Eccentricity -200 0.005265 -220 0.00526 -240 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 0.005255 -260

May Jul Sep Nov Jan Mar May Jul Longitude of Ascending Node (deg) May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

Enceladus, Inclination Enceladus, Argument of Periapsis 0.012 20 Operations Operations 0 0.01 Reconstruction Reconstruction -20 ODR.Tb

0.008 ODR.010Sa -40 ODR.008Sa ODR.007Sa ODR.009Sa ODR.T5 ODR.Sa ODR.T4 ODR.Ta ODR.E1 ODR.T3 0.006 ODR.Tc -60 ODR.Ta ODR.Tb ODR.Sa ODR.T3 ODR.Tc ODR.E1 ODR.T4 ODR.010Sa ODR.T5 ODR.009Sa ODR.008Sa

-80 ODR.007Sa 0.004

Inclination (deg) -100 0.002 -120

SOI Ta Tb Tc T3 E1 T4 T5 E2 Argument of Periapsis (deg) SOI Ta Tb Tc T3 E1 T4 T5 E2 0 -140 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

(b) Enceladus

Figure 21 Classical orbital elements of Mimas (a) and Enceladus (b) at Epoch January 2, 2004 ( wrt Saturn Equator of J2000). Reconstructed values are indicated.

26 ∆a = Value - 294000 km Tethys, Semimajor Axis Tethys, Time from Periapsis 243.5 72000 243 Operations 71000 Operations ODR.Ta Reconstruction Reconstruction ODR.Tb ODR.010Sa ODR.008Sa ODR.007Sa ODR.009Sa

ODR.Tc 70000 ODR.E1 ODR.T3 ODR.T4 ODR.T5

242.5 ODR.Sa 242 69000 68000 241.5 67000 241 66000 240.5

65000 ODR.Ta ODR.Sa 240 ODR.010Sa ODR.E1 ODR.T3 ODR.Tc ODR.T4

64000 ODR.T5 ODR.007Sa ODR.008Sa ODR.009Sa a, Semimajor Axis (km) ODR.Tb ∆ 239.5 Time from Periapsis (sec) 63000 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 239 62000 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC) Tethys, Eccentricity Tethys, Longitude of Ascending Node 0.00044 132.5 Operations Operations 0.00042 Reconstruction 132.4 Reconstruction 0.0004 132.3 0.00038 132.2 ODR.Ta ODR.010Sa ODR.Tb ODR.T3 ODR.E1 ODR.Tc ODR.007Sa ODR.T4 ODR.008Sa ODR.009Sa ODR.T5

0.00036 132.1 ODR.010Sa ODR.Sa ODR.Ta ODR.Tb ODR.008Sa ODR.007Sa ODR.009Sa ODR.T5 ODR.Sa ODR.T4 ODR.E1 ODR.T3 0.00034 132 ODR.Tc Eccentricity 0.00032 131.9 0.0003 131.8 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 0.00028 131.7

May Jul Sep Nov Jan Mar May Jul Longitude of Ascending Node (deg) May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

Tethys, Inclination Tethys, Argument of Periapsis

1.095 145 ODR.Tb ODR.010Sa ODR.009Sa ODR.007Sa ODR.008Sa ODR.Tc ODR.T3 ODR.T5 ODR.T4 ODR.E1

Operations ODR.Sa Operations 1.094 Reconstruction ODR.Ta Reconstruction

ODR.Sa 140 1.093 ODR.Ta ODR.010Sa ODR.Tb ODR.Tc ODR.T4 ODR.E1 ODR.T3 ODR.T5 ODR.009Sa 1.092 ODR.008Sa ODR.007Sa 135 1.091 1.09 130

Inclination (deg) 1.089 125 1.088

SOI Ta Tb Tc T3 E1 T4 T5 E2 Argument of Periapsis (deg) SOI Ta Tb Tc T3 E1 T4 T5 E2 1.087 120 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

(a) Tethys

∆a = Value - 377000 km Dione, Semimajor Axis Dione, Time from Periapsis 315.6 -96400

315.4 ODR.Ta Operations -96600 Operations Reconstruction Reconstruction ODR.010Sa 315.2 ODR.Tb -96800 ODR.008Sa ODR.007Sa ODR.009Sa ODR.Tb ODR.010Sa ODR.Tc ODR.T5 ODR.008Sa ODR.007Sa ODR.Sa ODR.T3 ODR.009Sa ODR.Ta ODR.E1 ODR.T4 315 ODR.Tc -97000 ODR.E1 ODR.T3 ODR.T4 ODR.Sa 314.8 ODR.T5 -97200 314.6 -97400 314.4 -97600 314.2 -97800 314 -98000 a, Semimajor Axis (km) ∆ 313.8 Time from Periapsis (sec) -98200 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 313.6 -98400 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC) Dione, Eccentricity Dione, Longitude of Ascending Node 0.00254 -10 Operations Operations 0.00252 Reconstruction -12 Reconstruction 0.0025 -14 ODR.010Sa

0.00248 -16 ODR.Ta ODR.Sa ODR.T3 ODR.Tb ODR.E1 ODR.T4 ODR.Tc ODR.T5 ODR.009Sa ODR.007Sa ODR.008Sa 0.00246 -18

Eccentricity 0.00244 -20 ODR.Sa

0.00242 ODR.Ta -22 ODR.010Sa ODR.T5 ODR.008Sa ODR.Tc ODR.007Sa ODR.009Sa ODR.E1 ODR.T4 ODR.Tb SOI Ta Tb Tc T3 ODR.T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 0.0024 -24

May Jul Sep Nov Jan Mar May Jul Longitude of Ascending Node (deg) May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

Dione, Inclination Dione, Argument of Periapsis 0.034 150 Operations Operations 0.033 Reconstruction 148 Reconstruction 0.032 ODR.Ta 146 ODR.E1 ODR.Tc ODR.T3 ODR.010Sa ODR.007Sa ODR.T4 ODR.T5 ODR.008Sa ODR.009Sa 0.031 ODR.Tb

ODR.Sa 144

0.03 ODR.Tc ODR.Sa ODR.008Sa ODR.T5 ODR.007Sa ODR.009Sa ODR.Tb ODR.E1 ODR.T4 ODR.Ta ODR.T3 142 ODR.010Sa 0.029 140 Inclination (deg) 0.028 0.027 138

SOI Ta Tb Tc T3 E1 T4 T5 E2 Argument of Periapsis (deg) SOI Ta Tb Tc T3 E1 T4 T5 E2 0.026 136 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

(b) Dione

Figure 22 Classical orbital elements of Tethys (a) and Dione (b) at Epoch January 2, 2004 ( wrt Saturn Equator of J2000). Reconstructed values are indicated.

27 ∆a = Value - 526000 km Rhea, Semimajor Axis Rhea, Time from Periapsis 389 66000

388.5 ODR.Ta Operations Operations ODR.Tb 64000 ODR.010Sa ODR.008Sa Reconstruction Reconstruction ODR.007Sa ODR.009Sa ODR.Sa ODR.Tc ODR.E1 ODR.T3 ODR.T4 388 ODR.T5

62000 ODR.Sa

387.5 ODR.Ta ODR.Tb ODR.Tc ODR.E1 ODR.T4 ODR.T5 ODR.T3 ODR.009Sa ODR.007Sa ODR.008Sa 387 60000 ODR.010Sa 386.5 58000 386 56000 385.5

a, Semimajor Axis (km) 54000 ∆

385 Time from Periapsis (sec) SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 384.5 52000 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC) Rhea, Eccentricity Rhea, Longitude of Ascending Node 0.00048 107.7 ODR.Tb ODR.010Sa ODR.Tc

ODR.T3 Operations Operations ODR.E1 ODR.T4 ODR.009Sa ODR.T5

ODR.007Sa 107.6 ODR.008Sa 0.00047 ODR.Ta Reconstruction Reconstruction 107.5

0.00046 ODR.Sa ODR.Sa

107.4 ODR.Ta

0.00045 ODR.Tb

107.3 ODR.010Sa ODR.Tc ODR.007Sa ODR.008Sa ODR.009Sa ODR.T5 ODR.T4 ODR.T3 ODR.E1 0.00044 107.2

Eccentricity 107.1 0.00043 107 0.00042 106.9 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 0.00041 106.8

May Jul Sep Nov Jan Mar May Jul Longitude of Ascending Node (deg) May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

Rhea, Inclination Rhea, Argument of Periapsis 0.3475 -114 0.347 Operations Operations Reconstruction -116 Reconstruction 0.3465 -118

0.346 ODR.010Sa ODR.E1 ODR.T3 ODR.Tb ODR.007Sa ODR.Tc ODR.T4 ODR.008Sa ODR.T5 ODR.009Sa

0.3455 ODR.010Sa ODR.Sa -120 ODR.008Sa ODR.007Sa ODR.009Sa 0.345 ODR.T3 ODR.T5 ODR.Tc ODR.E1 ODR.T4 ODR.Ta ODR.Tb 0.3445 -122 ODR.Ta ODR.Sa 0.344 -124 Inclination (deg) 0.3435 -126 0.343 SOI Ta Tb Tc T3 E1 T4 T5 E2 Argument of Periapsis (deg) SOI Ta Tb Tc T3 E1 T4 T5 E2 0.3425 -128 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

(a) Rhea

∆a = Value - 1220000 km Titan, Semimajor Axis Titan, Time from Periapsis 712 148250 Operations Operations 711 Reconstruction 148200 Reconstruction ODR.Ta ODR.Tb ODR.Sa ODR.Ta ODR.T3 ODR.E1 ODR.010Sa ODR.Tc ODR.T4 ODR.T5 ODR.008Sa ODR.010Sa ODR.007Sa ODR.008Sa ODR.009Sa ODR.007Sa

148150 ODR.Tb 710 ODR.009Sa ODR.Tc ODR.E1 ODR.T3 ODR.T4 ODR.Sa 709 ODR.T5 148100 708 148050 707 148000

a, Semimajor Axis (km) 706 147950 ∆ Time from Periapsis (sec) SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 705 147900 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC) Titan, Eccentricity Titan, Longitude of Ascending Node 0.028165 47.68 Operations 47.66 Operations 0.02816 Reconstruction Reconstruction

ODR.Sa 47.64

ODR.Ta 47.62

0.028155 ODR.Tc ODR.E1 ODR.T4 ODR.T5 ODR.T3 ODR.E1 ODR.010Sa ODR.Tc ODR.T3 ODR.007Sa ODR.008Sa ODR.009Sa ODR.Ta ODR.Tb 47.6 ODR.Sa 0.02815 47.58

47.56 ODR.Tb Eccentricity 0.028145 47.54 ODR.T5 ODR.T4 ODR.010Sa ODR.007Sa ODR.008Sa 0.02814 47.52 ODR.009Sa 47.5 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 0.028135 47.48

May Jul Sep Nov Jan Mar May Jul Longitude of Ascending Node (deg) May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

Titan, Inclination Titan, Argument of Periapsis 0.383 -41 Operations Operations

0.3825 Reconstruction Reconstruction ODR.010Sa ODR.008Sa ODR.009Sa ODR.007Sa

-41.05 ODR.T4 ODR.T5 ODR.Tb 0.382 ODR.Sa -41.1 ODR.Ta ODR.T3 ODR.E1 ODR.Tc ODR.T3 ODR.Ta ODR.E1 ODR.Tc ODR.Sa ODR.T5 ODR.T4 ODR.Tb ODR.007Sa ODR.008Sa ODR.009Sa 0.3815 ODR.010Sa -41.15 0.381 Inclination (deg) 0.3805 -41.2

SOI Ta Tb Tc T3 E1 T4 T5 E2 Argument of Periapsis (deg) SOI Ta Tb Tc T3 E1 T4 T5 E2 0.38 -41.25 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

(b) Titan

Figure 23 Classical orbital elements of Rhea and Titan at Epoch January 2, 2004 ( wrt Saturn Equator of J2000). Reconstructed values are indicated.

28 ∆a = Value - 1486000 km Hyperion, Semimajor Axis Hyperion, Time from Periapsis 174 39520

ODR.Ta Operations Operations ODR.010Sa ODR.Tc ODR.Tb ODR.T3 ODR.T5 ODR.007Sa ODR.008Sa ODR.009Sa ODR.E1 39500 ODR.T4 ODR.Ta 173 ODR.Tb Reconstruction Reconstruction ODR.Sa

ODR.010Sa 39480 ODR.008Sa ODR.007Sa ODR.009Sa ODR.Sa ODR.Tc

172 ODR.E1 ODR.T4 ODR.T3 ODR.T5 39460 171 39440 170 39420 39400 169 39380

a, Semimajor Axis (km) 168 ∆

Time from Periapsis (sec) 39360 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 167 39340 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC) Hyperion, Eccentricity Hyperion, Longitude of Ascending Node 0.123975 50 Operations Operations 0.12397 Reconstruction 49.95 Reconstruction ODR.010Sa ODR.Tc ODR.T3 ODR.009Sa ODR.008Sa ODR.Tb ODR.007Sa ODR.T5 ODR.E1 ODR.Sa ODR.Ta 0.123965 ODR.T4 49.9

0.12396 ODR.Ta ODR.Sa ODR.010Sa ODR.Tb ODR.T4 ODR.T5 ODR.E1 ODR.009Sa ODR.Tc ODR.008Sa ODR.007Sa

ODR.T3 49.85 0.123955

Eccentricity 49.8 0.12395 0.123945 49.75 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 0.12394 49.7

May Jul Sep Nov Jan Mar May Jul Longitude of Ascending Node (deg) May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

Hyperion, Inclination Hyperion, Argument of Periapsis 1.094 -81.6 ODR.T4 ODR.010Sa ODR.Tc Operations Operations ODR.T5 ODR.T3 ODR.009Sa ODR.008Sa ODR.007Sa ODR.E1

1.0935 ODR.Tb Reconstruction -81.65 Reconstruction ODR.Sa 1.093 ODR.Ta -81.7 1.0925 1.092 -81.75 ODR.Ta

1.0915 ODR.T4 -81.8 ODR.Sa ODR.E1 ODR.Tb ODR.T5 ODR.Tc ODR.007Sa ODR.T3 ODR.008Sa ODR.009Sa ODR.010Sa Inclination (deg) 1.091 -81.85 1.0905

SOI Ta Tb Tc T3 E1 T4 T5 E2 Argument of Periapsis (deg) SOI Ta Tb Tc T3 E1 T4 T5 E2 1.09 -81.9 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

(a) Hyperion

∆a = Value - 3560000 km Iapetus, Semimajor Axis Iapetus, Time from Periapsis 440 13100 Operations 13000 Operations 438 Reconstruction Reconstruction ODR.Sa ODR.Ta 12900 ODR.Tb 436 12800 ODR.Sa ODR.010Sa ODR.Tb ODR.010Sa ODR.008Sa ODR.007Sa ODR.T3 ODR.E1 ODR.009Sa ODR.Tc ODR.T4 ODR.007Sa ODR.008Sa ODR.009Sa ODR.T5 ODR.Ta ODR.Tc 12700 ODR.E1

434 ODR.T3 ODR.T4 ODR.T5 12600 432 12500 12400

a, Semimajor Axis (km) 430 ∆

Time from Periapsis (sec) 12300 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 428 12200 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC) Iapetus, Eccentricity Iapetus, Longitude of Ascending Node

0.027805 55.132 ODR.Ta ODR.010Sa ODR.Tb ODR.T3 ODR.T5 ODR.Tc ODR.T4 ODR.E1 ODR.009Sa ODR.007Sa Operations 55.1315 Operations ODR.008Sa Reconstruction Reconstruction 0.0278 55.131 ODR.Sa 0.027795 55.1305 ODR.Sa 55.13 0.02779 55.1295 ODR.E1 ODR.Tc ODR.008Sa ODR.T4 ODR.007Sa ODR.T3 ODR.010Sa ODR.T5 ODR.009Sa 55.129 ODR.Tb ODR.Ta Eccentricity 0.027785 55.1285 0.02778 55.128 55.1275 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 0.027775 55.127

May Jul Sep Nov Jan Mar May Jul Longitude of Ascending Node (deg) May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

Iapetus, Inclination Iapetus, Argument of Periapsis 15.5615 -12.225 Operations -12.23 Operations Reconstruction Reconstruction 15.561 -12.235 15.5605 -12.24 -12.245 ODR.010Sa ODR.T5 ODR.Ta ODR.008Sa ODR.Tc ODR.009Sa ODR.007Sa ODR.T4 ODR.E1 ODR.T3 ODR.Tb

15.56 -12.25 ODR.Sa -12.255 ODR.Sa 15.5595 -12.26 ODR.Ta Inclination (deg) ODR.010Sa ODR.Tc ODR.T3 ODR.Tb ODR.E1 ODR.T4 ODR.007Sa ODR.008Sa ODR.009Sa 15.559 ODR.T5 -12.265 -12.27 SOI Ta Tb Tc T3 E1 T4 T5 E2 Argument of Periapsis (deg) SOI Ta Tb Tc T3 E1 T4 T5 E2 15.5585 -12.275 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

(b) Iapetus

Figure 24 Classical orbital elements of Hypeion and Iapetus at Epoch January 2, 2004 ( wrt Saturn Equator of J2000). Reconstructed values are indicated.

29 ∆a = Value - 12880000 km Phoebe, Semimajor Axis Phoebe, Time from Periapsis 1340 -1.0133e+07 Operations -1.01331e+07 Operations Reconstruction Reconstruction 1330 -1.01332e+07 1320 -1.01333e+07 ODR.Sa -1.01334e+07 1310 -1.01335e+07 ODR.010Sa ODR.T3 ODR.008Sa ODR.007Sa ODR.009Sa -1.01336e+07 ODR.E1 ODR.T4 1300 ODR.T5 -1.01337e+07 ODR.Sa ODR.010Sa ODR.008Sa ODR.009Sa

-1.01338e+07 ODR.007Sa ODR.T5 a, Semimajor Axis (km) ODR.E1 1290 ODR.T4 ODR.T3 ∆ Time from Periapsis (sec) -1.01339e+07 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 1280 -1.0134e+07 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC) Phoebe, Eccentricity Phoebe, Longitude of Ascending Node 0.154508 -144.273 Operations Operations ODR.T3 ODR.010Sa ODR.E1 ODR.T4 ODR.Sa ODR.T5 -144.274 0.154506 ODR.007Sa ODR.009Sa Reconstruction ODR.008Sa Reconstruction 0.154504 -144.274 0.154502 -144.274 ODR.010Sa ODR.Sa

0.1545 -144.274 ODR.E1 ODR.T4 ODR.008Sa ODR.T3 ODR.007Sa ODR.009Sa ODR.T5 Eccentricity 0.154498 -144.274 0.154496 -144.275 SOI Ta Tb Tc T3 E1 T4 T5 E2 SOI Ta Tb Tc T3 E1 T4 T5 E2 0.154494 -144.275

May Jul Sep Nov Jan Mar May Jul Longitude of Ascending Node (deg) May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

Phoebe, Inclination Phoebe, Argument of Periapsis 151.658 -75.416 ODR.T3 ODR.E1 ODR.T4

Operations Operations ODR.T5 ODR.010Sa ODR.007Sa ODR.008Sa 151.658 -75.417 ODR.009Sa

Reconstruction ODR.Sa Reconstruction -75.418 151.658 -75.419 151.658

ODR.010Sa -75.42 ODR.T3 ODR.T5 ODR.T4 ODR.E1 ODR.007Sa ODR.009Sa ODR.008Sa -75.421 151.658 ODR.Sa -75.422 151.658 Inclination (deg) -75.423 151.658 -75.424 SOI Ta Tb Tc T3 E1 T4 T5 E2 Argument of Periapsis (deg) SOI Ta Tb Tc T3 E1 T4 T5 E2 151.657 -75.425 May Jul Sep Nov Jan Mar May Jul May Jul Sep Nov Jan Mar May Jul 2004 2004 2004 2004 2005 2005 2005 2005 2004 2004 2004 2004 2005 2005 2005 2005 Data Cut Off (UTC) Data Cut Off (UTC)

Figure 25 Classical orbital elements of Phoebe at Epoch January 2, 2004 ( wrt Saturn Equator of J2000). Reconstructed values are indicated.

30