ROYAL OBSERVATORY OF BELGIUM
Accurate Mars Express orbit determination to improve Martian moon ephemerides. Rosenblatt P., Lainey V., Le Maistre S., Marty J.C. Dehant V., Pätzold M., Häusler B., Van Hoolst T.
Presented at the first European workshop on solar system dynamics and ephemerides, ESOC (Darmstadt), June 21-22, 2007
Introduction ESOC’s MEX orbit Navigation purpose. It may lack of sufficient precision for reduction of MEX’ Super Resolution Camera (SRC) observations of Phobos. Accurate determination of MEX orbit To improve Phobos’ ephemerides at SRC observations. To improve Phobos’ mass estimate from close encounters Results and discussion.
Spacecraft data and ephemerides of Phobos (1) Phobos motion during flyby MEX motion during flyby MEX Orbit Phobos orbit
Phobos’ orbit
Spacecraft’s orbit
• Images of Phobos from
Mars
camera onboard spacecraft (s/c) to get Phobos‘ position on the plane-of-sky. • Reduction of these astrometric observations needs to know the position of the spacecraft.
Astrometric observations from camera onboard spacecrafts (Mariner 9,Viking, Phobos2, MGS and MEX)
Spacecraft data and ephemerides of Phobos (2) Post-fit residuals of Phobos positions from spacecraft observations
km
Viking 1-2 MEX
Mariner9
Phobos2
MGS
Using MEX position of ESOC’s navigation orbit.
From Lainey et al., 2006
Better MEX positioning may improve Phobos’ positioning from the observations of the Super Resolution Camera (SRC) onboard MEX.
Accurate orbit determination (1) •
We use the GINS1 software (validated on MGS tracking):
•
To model all the forces acting on the s/c and to numerically integrate its motion
•
To calculate the associated predicted tracking data
•
To perform an iterative least squares process on tracking data in order to adjust parameters related to these data and to dynamical model of MEX motion
•
Successive 7 days data-arcs to enhance the signal associated with the zonal gravity changes over the 2004-2006 period
1
Géodésie par Intégrations Numériques Simultanées, developed by CNES and applied by ROB for planetary geodesy applications
Accurate orbit determination (2) Forces acting on the spacecraft: Gravitational forces: Mars’ static gravity field (95x95, JGM95J from NASA JPL) JPL DE414 ephemeris for other Solar system bodies. Relativistic formulation.
Non-gravitational forces :
Atmospheric drag (atm. density, DTM model from CNES/GSFC). solar pressure radiation. albedo & IR radiations (F. Lemoine). Residual accelerations induced by each unbalanced wheel offloading (WoL) or desaturation event.
MEX vs MGS/ODY spacecraft orbits Steerable antenna. Continuous tracking from the Earth.
ODY 2001-now
From NASA
MGS
MEX
From NASA
1999-2006
2003-now
Circular orbit: 400x400 km
Fixed High Gain Antenna ! Non-continuous tracking from the Earth. Highly eccentric orbit: 250x10500 km From ESA
Non-gravitational accelerations Peri. at 250 km
Most perturbing forces on MEX: Solar pressure: 4. 10-08 m/s2 Drag at pericenter: up to 8. 10-08 m/s2 Wheel Off Loading (WoL) events near apocenter (~1 per day or per 4 orbits) (not on the graph). ~10-4 – 10-5 m/s2
Peri. at 400 km
Most perturbing forces on MGS: Solar pressure: up to 4. 10-08 m/s2 Angular Momentum Desaturation (AMD) events (~1 per day or per 12 orbits) (not on the graph): ~10-4 – 10-5 m/s2
Non-gravitational forces act any surface area of the s/c ‘Z’ axis
Bus Solar panel ‘Y’ axis
6 m2 ‘X’ axis
2.7 m2
“Macro-Model” :
It represents MEX as flat plates (6 for the bus & 4 for solar panels) with known area and optical properties (reflectivity and absorptivity). The orientation of this model follows the attitude mode of the bus as given by the quaternions (ESOC) and of the solar panels when associated quaternions are available. The shift between the MEX center of mass and the HGA center of phase and the s/c mass is fixed to a value given in SPICE kernels.
Example of quaternions of the bus of MEX
Inertial mode
Pointing mode
Attitude mode : Earth or Mars pointing or fixed inertial modes. We assume solar panels directed toward the Sun and a fixed value for high gain antenna center of phase/ MEX center of mass offset.
Pre-Processing Spacecraft
Radio-tracking data
Input from ESOC flight dynamics : Initial state vector : MEX ephemeris (ORMM files) Attitude mode as quaternions (ATNM files) but only available for the bus Epoch & strength of each wheel offloading (EVT files)
SPICE toolkit
Input from Köln university : DSN tracking as ODF files (JPL) NNO tracking as Level 2 IFMS data
Interfaces developed at ROB (NNO) & from CNES/NASA Goddard interfaces (ODF)
input for GINS:
MEX bus attitude MEX solar panels : Oriented toward the sun Epoch & initial strength of each WoL event
input for GINS:
Doppler + range tracking data
+ Coordinates of the center of phase of the HGA & MEX mass
Input for data-arcs :
Processing
Duration : 7 days + 21 hours (overlap) Initial state vector from MEX ephemeris (ESOC) Attitude mode as quaternions from ATNM files (ESOC) Epoch and delta velocity at each WOL events (ESOC) Tracking data : Doppler + Range from NNO + DSN
GINS software : Iterative Least Squares fit of MEX dynamical model
Output from data-arcs: New orbit (position & velocity) (+overlap differences) Post-fit Doppler and range residuals Drag & solar pressure scale factors Corrections on the WoL residual accelerations Estimate of bias on range data Normal matrix with information on geophysical parameters
Post-fit residuals of tracking data
Solar conjunction
Good residuals in Doppler and range. Effect of interplanetary plasma on signal at solar conjunction (Sept. 2004). However, this doesn’t mean a good orbit. Test of orbit quality: Orbit overlap (test of internal coherency).
Orbit overlap differences Overlap of 21 hours between each 8 days successive data-arcs. We obtain orbit ~2-3 times better than the navigation orbit of ESOC. However, it is 10 times larger than on MGS/ODY (JPL solution, Konopliv et al., 2006) Our residual errors express the mismodeling of our MEX dynamics: Non-gravitational forces.
Average (maximum) in meters: ROB/GINS ESOC (navigation)
Radial Tangential < 1 (5) ~17 (100) < 5 (10) ~50 (200)
Normal ~25 (100) ~50 (200)*
*T. Morley, Pers. Comm., 2007
Estimation of non-gravitational forces Period of moderate dust storms which are not taken into account in the atmospheric density model Solar conjunction
Artifact due to the default of true solar panel orientation?
Our drag and solar pressure scale factors show magnitudes comparable to MGS+ODY (ROB/CNES or JPL solutions). Our drag scale factors display signature of Mars’ atmospheric dynamics. However, limited resolution because of the lack of tracking data at most of the pericenter passes.
Adjustment of linear accelerations at desaturation events
Accelerations associated with WoL events not well resolved along the directions of the X and Y axes of the spacecraft frame. This degrades the determination of the orbit especially when WoL event is within a gap of tracking data.
Non-continuous tracking of MEX: A problem ! 7-days data-arc 7-days data-arc
Shorter data-arc
Depending on the data-arc, several orbits are not tracked at all. The best coverage only represents ~50-60% of the duration of the data-arc. Difficulty to correctly determine the effect of the desaturation (WoL) and of the drag around each pericenter pass (altitude of 250-400 km). A way to explore: shorter data-arc to avoid too large gaps of tracking data.
MEX range bias estimation
Solar conjunction
2004-2005.3: A bias of ~20 meters. About 10 times larger than with MGS/ODY. Error bias on our MEX orbit estimation OR Additional bias due to range group delay of MEX transponder (temperature fluctuations, electronic disturbances, …) ? > 2005.3: Confirmation of residual errors in the JPL-DE414 planetary ephemeris.
Improvement of Phobos’ ephemeris at MEX-SRC observations (1) Phobos motion during flyby MEX motion during flyby MEX Orbit Phobos orbit
MEX’ orbit
Phobos’ orbit
• Super Resolution Camera (SRC) on board MEX: Phobos‘ position in the planeof-sky used to calculate ephemerides of Phobos. • Use of SRC observations need to know the position of MEX.
SRC observations
Accurate determination of MEX orbit to improve Phobos’ positioning from SRC observations.
• We will use 34 SRC observations of Phobos preprocessed by K. Willner and J. Oberst (DLR).
Improvement of Phobos’ ephemeris at MEX-SRC observations (2) Using GINS/ROB MEX orbit
Using ESOC MEX orbit
Right Ascension: 0.008 +/- 0.417 (km) Declination: 0.071 +/- 0.265 (km)
Right Ascension: 0.026 +/- 0.411 (km) Declination: 0.081 +/- 0.291 (km)
Improvement of Phobos’ positions at SRC obs. External validation of our ROB/GINS MEX orbit.
Re-estimate of Phobos’ mass from MEX tracking data (1) Close encounters (flyby): Viking1 (1977) Phobos2 (1990) Doppler LOS variations GM of Phobos
M=?
LOS
Williams et al. 1988 0.9
Tolson et al. 1977
Model
3 2
GM [10 km /s ]
0.8
-3
Yuan et al. 2001
0.7
Kolyuka et al. 1990
0.6
Christensen et al. 1977 0.5
Smith et al. 1995
Difference of more than 40% Systematic errors!
MEX – Phobos flyby (March 23rd, 2006) distance : ~460 km
Fraction of day
ESOC orbit takes into account an initial value of Phobos’ mass. No clear signature on Doppler LOS profile.
Fraction of day
The Phobos’ mass has been omitted in the GINS orbit. A signature appears on the LOS Doppler profile around the flyby epoch.
Since the Phobos’ GM acts on MEX dynamics, we perform the GM estimate as a dynamical parameter in our MEX dynamics modeling despite a SNR value of 1
Preliminary estimates of Phobos’ mass with GINS Phobos’ mass (in 10^16 kg)
data used
ROB-GINS
1.27 +/- 0.03
MEX (March 23rd 2006)
Tolson et al., 1978
0.99 +/- 0.06
Viking
Duxbury et al., 1989
1.27 +/- 0.1
Viking
Kolyuka et al. 1990
1.08 +/- 0.007
Phobos2
Smith et al., 1995
0.88 +/- 0.05
Viking + Mariner 9
Konopliv et al. 2006
1.07 +/- 0.0007
Viking
Konopliv et al. 2006
1.07 +/- 0.013
MGS + Mars Odyssey
MEX’ estimation needs to be refined because of the low SNR value which enhances the effect of strong correlation between the parameters of MEX dynamics model and the Phobos’ GM. Another way to explore: Estimation of secular effect of Phobos’ mass on the MEX dynamics. Using all MEX orbit from 2004 to now (as done by Konopliv et al. 2006 for MGS & ODY).
CONCLUSION Our ROB/GINS MEX orbits show internal error comparable or better than the internal error of ESOC’s navigation orbits. A better orbit determination would require more continuous tracking of MEX ! At MEX-Phobos close encounter (< ~300 km), the Phobos’ mass determination could be improved. A better MEX orbit is required to improve other Mars’ geophysical parameters like the seasonal gravity field by merging both MEX and MGS/Mars Odyssey tracking data. A direct Mars to Earth radio-link: A new ‘fonction de mesure’ into GINS !
Many others projects …
A Martian Lander with radioscience experiment
LaRa: Lander Radio-science (PI V. Dehant) selected onboard ESA’s Exomars mission due to launch in 2013. Scientific goals: Better measurement of precession rate, to better constrain the moment of inertia of the core, thus its size. Better measurement of LOD variations over one Martian year to better constrain seasonal CO2 cycle. Work to be done: Need to develop the GINS software to make simulations and processing of future data (S. Le Maistre’s PhD, advisors: V. Dehant & P. Rosenblatt).
Gravity field variations and Mars’ CO2 seasonal mass budget
Seasonal gravity field to determine mass transfer budget, but insufficient precision to constrain the models of CO2 seasonal deposits (error less than 10-09 ) on J2 & J3 variations (i.e. less than 1016 kg in mass changes).
Mars’ atmosphere CO2 seasonal cycle
MEX + MGS can improve the solution of first zonal harmonics variations, given the orbits are well resolved. GINS simulations (Rosenblatt et al., AGU fall meeting 2005)
A possibility of geodesy experiment with a new ESA’s Mars’ orbiter: MEMO
MEMO orbit: 130x1000 km with an inclination of 77° more favorable for determination of zonal harmonics changes than polar orbits as suggested in Karatekin Ö, Duron J., Rosenblatt, P. et al., JGR, 2005.
First simulations from GINS software: A precision of less than 1 meter is required to improve Mars’ varying gravity field.
Possible scientific investigation in geodesy: Improvement of resolution of static gravity field and of gravity seasonal changes. Accelerometer to study thermosphere and Ka band to reduce noise on the data. Work to be done (preparation of the mission): Analytical & numerical (GINS) simulation taking into account all perturbations of the orbit: atmospheric drag, … (Rosenblatt et al., Europlanet meeting, 2007).
ESA’s Bepi-Colombo cornerstone mission. Launch in 2012 & arrival in 2017 (nominal).
Star tracking Tracking DSN
Terre Mesures photographiques Principle of librations measurements: Need accurate orbit of spacecraft !
V. Dehant is Co-I on MORE (radio-science) and Co-I on the BELA (Laser altimeter). T. Van Hoolst is Co-I on SYMBIO-SYS (Camera) Scientific goal: Interior structure and gravity field of Mercury. Work to be done: Development of GINS software to simulate the effect of orbit error on librations determination (G. Pfyffer’s PhD).
Estimation of thermosphere density (altitude > 100-200 km) from accurate spacecraft orbit determination Signature of seasonal variations of Mars’ atmosphere onto the drag scale factor.
Maximum CO2 deposit at south pole around solar longitude of ~180° Dust storm season at solar longitude > ~220°
(From ROB-GINS MEX orbit determination)
The experience acquired with MEX is being applied to the Venus Express (VEX) tracking data (V. Dehant is also Co-I on the radio-science experiment of VEX): Venus’ thermosphere density from VEX tracking data + accelerometer data (collaboration with our colleagues from CNES). Improvement of Venus’ local gravity anomalies to constrain the structure and evolution of the lithosphere structure M. Beuthe. Link with geological history.
Estimation of non-gravitational forces (2) Adjustment of one scale Factor of Drag (FD) per orbit
Test-period of 6 months. ‘Noisy’ drag scale factor series. Low improvement of orbit quality. Average (in meters): Radial Tangential Normal 3D 1 FD arc 1.3 17 40 27 1 FD revo 1.25 17.5 33.7 23.8 a priori uncertainty (0.04)
Mismodeling of drag effect due to lack of tracking data at pericenter passes. This prevents to get the in formation about time-variable gravity field. A way to explore: Shorter data-arcs in order to better take into account the non-continuous tracking.
Orbit overlap differences Edge-on
~ Face-on
Overlap of 21 hours between each 7 days successive data-arcs We obtain orbit ~5-10 times better than the navigation orbit of ESOC. However, it is 20 times larger than on MGS/ODY (JPL solution, Konopliv et al., 2006) Our residual errors express the mismodeling of our MEX dynamics: Non-gravitational forces. Need a tracking as continuous as possible, especially at pericenter pass. Average (in meters): ROB/GINS ESOC (navigation)
Radial Tangential Normal 2.9 41 39
3D 17.6 200
MGS+ODY (Konopliv et al. 2006)
Atmospheric drag scale factor. Orbit overlap differences
