- Email: [email protected]
Huygens probe entry and descent trajectory analysis and reconstruction techniques
ARTICLE IN PRESS
Planetary and Space Science 53 (2005) 586–593 www.elsevier.com/locate/pss
Huygens probe entry and descent trajectory analysis and reconstruction techniques D.H. Atkinsona,, B. Kazeminejadb, V. Gaboritc, F. Ferrid, J.-P. Lebretone a
Department of Electrical and Computer Engineering, University of Idaho, Moscow, ID 83844-1023, USA Department of Extraterrestrial Physics, Space Research Institute (IWF), Austrian Academy of Sciences, 8042 Graz, Austria c Observatoire de Paris-Meudon (LESIA), 5 Place Jules Janssen, 92195 Meudon, France d CISAS ‘‘G. Colombo’’ Universita` di Padova, via Venezia 1, 35131 Padova, Italy e ESA Research and Scientific Support Department, ESTEC/SCI-SB, 2200 AG Noordwijk, The Netherlands
b
Received 5 August 2003; received in revised form 20 November 2003; accepted 20 November 2004 Available online 2 March 2005
Abstract Cassini/Huygens is a joint National Aeronautics and Space Administration (NASA)/European Space Agency (ESA)/Agenzia Spaziale Italiana (ASI) mission on its way to explore the Saturnian system. The ESA Huygens Probe is scheduled to be released from the Orbiter on 25 December 2004 and enter the atmosphere of Titan on 14 January 2005. Probe delivery to Titan, arbitrarily defined to occur at a reference altitude of 1270 km above the surface of Titan, is the responsibility of the NASA Jet Propulsion Laboratory (JPL). ESA is then responsible for safely delivering the probe from the reference altitude to the surface. The task of reconstructing the probe trajectory and attitude from the entry point to the surface has been assigned to the Huygens Descent Trajectory Working Group (DTWG), a subgroup of the Huygens Science Working Team. The DTWG will use data provided by the Huygens Probe engineering subsystems and selected data sets acquired by the scientific payload. To correctly interpret and correlate results from the probe science experiments and to provide a reference set of data for possible ‘‘ground-truthing’’ Orbiter remote sensing measurements, it is essential that the trajectory reconstruction be performed as early as possible in the post-flight data analysis phase. The reconstruction of the Huygens entry and descent trajectory will be based primarily on the probe entry state vector provided by the Cassini Navigation Team, and measurements of acceleration, pressure, and temperature made by the Huygens Atmospheric Structure Instrument (HASI). Other data sets contributing to the entry and descent trajectory reconstruction include the mean molecular weight of the atmosphere measured by the probe Gas Chromatograph/Mass Spectrometer (GCMS) in the upper atmosphere and the Surface Science Package (SSP) speed of sound measurement in the lower atmosphere, accelerations measured by the Central and Radial Accelerometer Sensor Units (CASU/ RASU), and the probe altitude by the two probe radar altimeters during the latter stages of the descent. In the last several hundred meters, the altitude determination will be constrained by measurements from the SSP acoustic sounder. Other instruments contributing data to the entry and descent trajectory and attitude determination include measurements of the zonal wind drift by the Doppler Wind Experiment (DWE), and probe zonal and meridional drift and probe attitude by the Descent Imager and Spectral Radiometer (DISR). In this paper, the need for and the methods by which the Huygens Probe entry and descent trajectory will be reconstructed are reviewed. r 2005 Elsevier Ltd. All rights reserved. Keywords: Huygens Probe; Entry and descent trajectory
Abbreviations: ASI, Agenzia Spaziale Italiana (Italian Space Agency); ASI/MET, Atmospheric Structure Instrument/Meterology Package; CASU, Central Acceleration Sensor Unit; DISR, Descent Imager and Spectral Radiometer; DTWG, Descent Trajectory Working Group; DWE, Doppler Wind Experiment; EDL, Entry Descent and Landing; ESA, European Space Agency; ESTEC, European Space Research and Technology Centre; GCMS, Gas Chromatograph/Mass Spectrometer; HASI, Huygens Atmospheric Structure Instrument; HGA, High Gain Antenna; HK, Housekeeping; HSWT, Huygens Science Working Team; JPL, Jet Propulsion Laboratory; MPF, Mars Pathfinder; NAIF, Navigation and Ancillary Information Facility (at JPL); NASA, National Aeronautics and Space Administration; POSW, Probe Onboard Software; PSE, Probe Support Equipment; RASU, Radial Accelerometer Sensor Unit; RAU, Radar Altimeter Unit; SSP, Surface Science Package. Corresponding author. E-mail addresses: [email protected] (D.H. Atkinson), [email protected] (B. Kazeminejad). 0032-0633/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2004.11.005
ARTICLE IN PRESS D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
1. Introduction
calibration opportunities for synergistic studies with orbiter remote sensing instruments, an accurate reconstruction of the probe entry and descent trajectory is needed. If a common and consistent descent profile is not available, each probe experiment team would need to independently develop a profile, thereby causing not only a significant duplication of effort and expenditure of resources, but also making correlation and comparison of results from different experiments somewhat suspect and therefore less meaningful. Furthermore, direct (in situ) atmospheric sampling by the probe will provide groundtruth verification of orbiter observations of the atmosphere and surface of Titan. The value of the groundtruth support for orbiter science at Titan will be significantly compromised if the altitude, location, and velocity of the Huygens Probe are not precisely known as a function of time throughout the descent mission. The responsibility of developing analysis techniques by which the Huygens Probe entry and descent trajectory will be reconstructed from the official NASA/ESA handoff point at the interface altitude of 1270 km to the surface is given to the Huygens DTWG, chartered in 1996 as a subgroup of the Huygens Science Working Team (HSWT) (Atkinson, 2003). The membership of the DTWG includes the Huygens and Cassini project scientists, The Huygens Operations Scientist, and representatives from each of the probe science instrument teams and contributing orbiter teams (see Table 1). The primary goals of the Huygens DTWG are to
The Huygens Probe is the European Space Agency (ESA)-provided element of the joint National Aeronautics and Space Administration (NASA)/ESA/Agenzia Spaziale Italiana (ASI) Cassini/Huygens mission to Saturn and Titan (Lebreton and Matson, 2002). Launched on 15 October, 1997, Cassini/Huygens will arrive at Saturn on 1 July, 2004. After two orbits of Saturn, the Huygens Probe will be released on December 25, 2004 and will enter the atmosphere of Titan on at 9:00 UTC on January 14, 2005. The probe system comprises two principal elements: the Huygens atmospheric entry probe, and the probe support equipment (PSE). The PSE remains attached to the Cassini Orbiter as part of the probe-to-orbiter communication link system used during the probe mission (Clausen et al., 2002). During both the entry and descent phase the probe will perform scientific measurements to determine the physical and chemical properties of Titan’s atmosphere, measure winds and global temperatures, and investigate energy sources important for the planet’s chemistry. It is also expected that the probe will survive impact for an investigation of the physical and chemical properties of Titan’s surface. Huygens will transmit all its entry and descent science and engineering data to the Cassini Orbiter, targeted to flyby Titan at a periapse distance of 60,000 km. The probe data will be received on the orbiter through the Cassini High Gain Antenna (HGA) which will be continuously pointed towards the probe’s predicted landing site on Titan.
2. The Huygens Descent Trajectory Working Group (DTWG)
To correctly interpret and correlate the results from all of the probe science experiments and to provide
587
develop a framework between experiment teams and the Huygens Mission Team for sharing and exchanging data relevant to the descent trajectory analysis and modeling; develop methodologies by which the probe descent trajectory and attitude can be accurately reconstructed from the probe and orbiter science and engineering data; and
Table 1 Membership of Huygens Descent Trajectory Working Group Name
Affiliation
Position
Dr. David H. Atkinson Dr. Bobby Kazeminejad Dr. Jean-Pierre Lebreton Dr. Olivier Witasse Dr. Dennis Matson Dr. David Coscia Dr. Francesca Ferri Mr. Chuck See Dr. Hasso Niemann Dr. Jonathan Lunine Mr. Brijen Hathi Dr. Daniel Gautier Dr. Francois Raulin Dr. Ralph Lorenz
Univ. Idaho Austrian Acad. Sci. ESTEC ESTEC NASA JPL Univ. Paris CISAS/Univ. Padova LPL/Univ. Arizona NASA GSFC LPL/Univ. Arizona The Open University Obs. de Paris-Meudon Lisa Univ. Paris LPL/Univ. of Arizona
DTWG Chair, DWE DTWG Co-Chair Huygens Proj. Scientist Huygens Op. Scientist Cassini Proj. Scientist ACP HASI DISR GCMS IDS SSP IDS IDS RADAR
ARTICLE IN PRESS 588
D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
provide a single, common descent profile that is consistent with all the available probe and orbiter engineering and science data, and that can be utilized by each instrument team for analysis of experiment measurements, and correlation of results between experiments.
It is planned that an initial determination of the probe entry and descent trajectory will be made available by the DTWG within 2 days after the initial download and validation of the Huygens engineering and science data. The DTWG must therefore have the necessary algorithms developed, tested, and validated by the time of the probe mission in January 2005.
3. Probe mission phases
Fig. 2. Simulated Huygens Probe descent altitude profiles for the maximum, recommended, and minimum Titan Yelle atmosphere. Nominal probe impact is 139:5 min past interface epoch (Kazeminejad et al., 2004).
The Huygens entry and descent mission can be subdivided into the following phases: (1) Entry: The entry phase commences at the interface altitude of 1270 km above the surface of Titan and ends at the start of the parachute sequence, designated as time t ¼ T 0 : At the interface altitude, the Cassini Navigation team at Jet Propulsion Laboratory (JPL) will provide to the DTWG the full state vector (i.e., position and velocity) of the Huygens Probe in a Titan-centered EME2000 coordinate system together with associated uncertainties in the form of a covariance matrix. During the entry phase the probe will decelerate from an initial velocity of Mach 22.5–1.5 (corresponding to an inertial velocity of 6 and 0:35 km=s; respectively) in less than 5 min : This implies a peak deceleration of approximately 12 g (Kazeminejad
et al., 2004). The force causing this deceleration is atmospheric drag, which depends both on the entry velocity and the atmospheric density. Throughout the entry phase the probe will be protected by a 2.75 m heat-shield. (2) Descent: About 4.6 min after the interface epoch the parachute deployment sequence commences (T 0 ; Fig. 1), comprising a 2.59 m pilot chute deployed at Mach 1.5, an 8.30 m main chute, and a 3.03 m stabilizing drogue parachute for the final portion of the descent (Clausen et al., 2002). The descent phase lasts about 140 min from T 0 to surface impact for the nominal Yelle model of the atmosphere (Yelle et al., 1997) (see Fig. 2). (3) Surface: If the probe survives impact, then it is instrumented to provide a direct characterization of the surface at the landing site. The probe batteries nominally can provide power for at least 30 min on the surface for an extended surface phase. In the current mission scenario, the Cassini Orbiter will listen to the probe for a full 4.5 h until the orbiter disappears beyond the probe horizon.
4. Instrument and data description
Fig. 1. The simulated Huygens Probe deceleration for the nominal and maximum Yelle atmosphere model; T A ¼ triggering of the parachute sequence arming timer, S0 ¼ probe onboard software (POSW) descent timer start, and T 0 ¼ parachute sequence deployment (Kazeminejad et al., 2004).
The Huygens scientific payload comprises six instruments (Lebreton and Matson, 2002)—the Gas Chromatograph and Mass Spectrometer (GCMS) (Niemann et al., 2002), the Descent Imager/Spectral Radiometer (DISR) (Tomasko et al., 2002), the Huygens Atmospheric Structure Instrument (HASI) (Fulchignoni et al., 2002a), the Doppler Wind Experiment (DWE) (Bird et al., 2002), the Surface Science Package (SSP) (Zarnecki et al., 2002), and the Aerosol Collector and
ARTICLE IN PRESS D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
Pyrolyser (ACP) (Israel et al., 2002). It is expected that the first five of these instruments will provide data essential to the entry and descent trajectory reconstruction. Additionally, data from engineering subsystems provided in the probe housekeeping (HK), and the probe entry state vector as provided by the Cassini Navigation team will also be used in the reconstruction effort. During the entry phase from the interface altitude of 1270 km to the start of the parachute sequence at T 0 the only data set available for the trajectory reconstruction will be the measured aerodynamic accelerations. The probe possesses three sets of accelerometers—the Central Acceleration Sensor Unit (CASU), the Radial Acceleration Sensor Unit (RASU), and the HASI science 3-axis accelerometers. During the descent phase, all the probe science instruments will be operating. Especially important for the trajectory reconstruction will be the HASI measurements of pressure and temperature. From the assumption of hydrostatic equilibrium and real gas behavior, and from the knowledge of the atmospheric mean molecular weight as determined by the probe GCMS experiment and the speed of sound measurements by SSP, the probe altitude and descent speed can be determined. Beneath 25 km the probe Radar Altimeter Unit (RAU) will provide a completely independent measurement of the probe altitude and descent speed, and should also provide topographical data along the probe groundtrack. The Radar Altimeter is likely to loose lock in the final several hundred meters, and the only direct measurement of altitude and descent speed will be from the SSP acoustic sounder and possibly indirectly by the DISR.
5. Reconstruction procedure During atmospheric entry, aerodynamic forces and gravity will cause the Huygens Probe’s trajectory to deviate from the gravity-only case, calculated from a pre-existing gravity model. A set of three mutually orthogonal accelerometers mounted inside the probe can accurately measure these aerodynamic accelerations. However, it is important to note that the gravitational force acting on the spacecraft’s center of mass cannot be detected by measurements made in a frame fixed with respect to the spacecraft since the spacecraft and the accelerometer instrument are both experiencing the same gravitational acceleration. To reconstruct a probe’s entry and descent trajectory from accelerometer measurements and the subsequent numerical integration of the equations of motion, additional inputs are required, including the state vector at an initial epoch ti ¼ tentry ; a model of the gravity field of the planet, and a table of probe aerodynamic coefficients.
589
To reconstruct a probe’s entry and descent trajectory, the equations of motion are traditionally formulated and integrated in a rotating, planet-fixed coordinate frame. By introducing ‘‘intermediate frames’’ wherein the coordinate axes are defined to be instantaneously coincident with a rotating planet-fixed frame at each time step, the Coriolis and centrifugal force terms are removed from the equations of motion in the rotating frame (Withers et al., 2003). For the Huygens reconstruction, the added complexity of including the Coriolis and centrifugal forces has been eliminated by integrating the equations of motion in a planet-centered inertial frame. For the Huygens trajectory the initial conditions, including probe state vector at the interface (entry) epoch, uncertainties in the form of a covariance matrix, and Titan’s gravitational parameter GM will be provided by the Cassini Navigation team in the form of a NAIF SPICE kernel (NASA Navigation and Ancillary Information Facility (NAIF) at JPL, http:// naif.jpl.nasa.gov/naif/), a special data file that can be easily read and used in computer algorithms. Additionally, the gravitational effects of the planet’s flattening (currently assumed to be zero for Titan) as well as perturbations from the Saturnian and the Solar gravitational effects are included in the model. The accelerometers onboard the Huygens Probe will measure the linear accelerations of the spacecraft center of mass in the three orthogonal directions as1 ; as2 ; as3 aligned with the spacecraft s1 -, s2 -, and s3 -axes, respectively. The correct transformation of the accelerations measured in the spacecraft frame ðs1 ; s2 ; s3 Þ to the inertial frame requires the knowledge of the orientation of the spacecraft attitude with respect to the direction of the flow velocity (given in the inertial frame of integration). In case of axisymmetry this orientation can be expressed by the angle of attack aðtÞ which can be estimated using the ratio of normal to axial accelerations aN C N ¼ ¼ f ða; MaÞ, aA C A
(1)
where aN and aA are the normal and axial accelerations qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi given by aN ¼ a2s2 þ a2s3 and aA ¼ as1 ; respectively, and C N and C A are the corresponding aerodynamic coefficients. An existing pre-flight aerodynamic database of the Huygens Probe (Schipper, 2002) provides C N and C A as a function of a and the Mach number Ma: From the normal and axial accelerations aN and aA ; the angle of attack a can be found by interpolating the aerodynamic database. The drag and lift accelerations aD and aL can then be found from aD ¼ aA cos a þ aN sin a, aL ¼ aN cos a aA sin a,
ð2Þ
ARTICLE IN PRESS D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
590
where, again, aN ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2s2 þ a2s3 and aA ¼ as1 (Kazemi-
nejad, 2005). Due to probe spin, the lift and side force vectors will rotate with the probe and average to zero (assuming that they are essentially constant over a spin period) and can therefore be neglected. The drag force vector aAd is always pointing in the opposite direction of the relative flow velocity vector vrel of the spacecraft with respect to the fluid (i.e., the atmosphere) in the inertial frame of integration and can be found from aAd ¼ aD
vrel jvrel j
(3)
and vrel can be calculated using the relation vrel ¼ v op r vw ,
(4)
where r and v are the probe position and velocity vectors in the inertial frame, op the angular velocity vector of the planet, and vw the velocity vector of the atmospheric wind. It is important to note that the calculation of the Mach number requires the knowledge of the atmospheric temperature T and molecular weight m; neither of which are directly measured during the entry phase. The relative abundance of methane and argon (if present) will vary with altitude in the upper atmosphere because of diffusive separation but should be constant at altitudes below 600 km (Yelle et al., 1997). In the upper atmosphere m can be modelled using analytic expressions for the methane and argon mole fractions as a function of altitude (Strobel et al., 1992; Steiner and Bauer, 1990). During the descent phase (160 km to the surface) m will be measured by the GCMS experiment, and indirectly by the SSP speed of sound experiment. In the upper atmosphere the physical properties of the atmosphere (density r; pressure P and temperature T) can be derived from the measured aerodynamic accelerations (Magalha˜es et al., 1999; Kazeminejad and Atkinson, 2004). Therefore, an iterative process will be necessary whereby the measured accelerations are used to derive the atmospheric properties, and the atmospheric properties are used to refine the trajectory calculation. This iterative approach converges rather quickly. The numerical integration of the measured spacecraft accelerations and the modelled gravitational accelerations provide an initial reference trajectory to the surface. The reference trajectory will then be refined using additional independent data sets, including measurements of probe altitude and descent speed z and z_ as determined from the RAU, DISR, and HASI. The probe altitude and descent speed can be found from HASI pressure P and temperature T measure-
ments. The altitude zi at an epoch ti is given by X Dzi1 , zi ¼ z0
(5)
i
where z0 is the initial altitude (i.e., the altitude at which the first pressure measurement was taken) and Dzi is the distance the probe has travelled in the time interval Dti which is calculated by Gaborit (2004) RT i12 z Pi Dzi ¼ ln . (6) Pi1 mg The subscript i is relative to a value obtained at the mission time ti and the temperature T is assumed to be constant between times ti1 and ti having the value T 1 ¼ 12ðT i1 þ T i Þ: R again is the universal gas i2
constant, m the molecular weight of the gas mixture, g the vertical component of the effective gravitational field, and z the compressibility factor that takes into account the non perfect gas behavior (Dymond and Smith, 1992). Note that the compressibility factor is a function of the temperature, the density and the chemical composition of the gas. Using several imaging sensors, the Descent Imager will provide data supporting the reconstruction of the probe altitude and descent speed, as well as probe attitude [Private Communication with Bashar Rizk, University of Arizona LPL (2002)].
6. Error treatment In the trajectory estimation process, various error sources with the potential to degrade the accuracy of the reconstructed probe entry and descent trajectory must be considered: (1) The accelerometers are not directly positioned at the center of mass of the probe. (2) The aerodynamic acceleration measurements will be affected by the intrinsic accuracy of the instrument. The best way to assess the impact of this error source is to utilize a Monte Carlo technique whereby a large number (e.g., 10,000) of entry and descent trajectory reconstructions are simulated, each including randomly applied 0–3s errors in the accelerometer data. (3) The probe initial state vector at the interface altitude will be provided to the DTWG by the Cassini Navigation team together with an uncertainty estimation in form of a covariance matrix. (4) The measurement uncertainties of each instrument are directly included in the trajectory estimation process by specifying a weighting matrix W that contains the standard deviation of each measurement.
ARTICLE IN PRESS D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
(5) The aerodynamic coefficients are provided to the DTWG in the form of a pre-flight aerodynamic database. Uncertainties in the various coefficients translate into uncertainties in the angle of attack determination which will affect the conversion of the aerodynamic accelerations from the spacecraft to the inertial frame (see Section 5). Uncertainties in the aerodynamic database are not directly taken into account by the algorithm, but can be assessed by an additional reconstruction process with a modified database with increased (or decreased) coefficients, or by additional Monte Carlo techniques.
7. Data sets for the testing of the algorithm As the Huygens data will be available in January 2005, it is important that a test program be developed that can utilize both synthetic data sets and existing data sets from past atmospheric probe missions. The following missions will be considered:
The entry, descent and landing (EDL) of the Mars Pathfinder (MPF) spacecraft on July 4, 1997 provides a unique test case since the Atmospheric Structure Instrument and Meteorology Package (ASI/MET) on MPF was equipped with three orthogonal engineering and three orthogonal science accelerometers as well as pressure, temperature and wind sensors (Duxbury and Schofield, 1998). It is important to note however, that the pressure, temperature and wind sensors are located behind the heatshield throughout much of the EDL and therefore did not provide reliable data. After heatshield separation, the sensor properties were influenced both by the atmosphere and the lander environment. Although the descent temperature sensor was exposed for EDL, the exposure was not good enough to prevent serious contamination from the lander environment so that its result could not readily be converted to atmospheric temperature during the parachute descent, terminal or landing phases of EDL (Duxbury and Schofield, 1998). MPF was also equipped with a radar altimeter that acquired altitude information and vertical motion between 1.36 km and 388 m. The MPF entry and descent trajectory as well as the physical properties of the Martian atmosphere were reconstructed by Magalha˜es et al. (1999) using the science accelerometer data and an existing aerodynamic pre-flight database (Moss et al., 1998; Gnoffo et al., 1996). An independent reconstruction effort was done by Spencer et al. (1999) based on accelerometer, altimeter, and ground-based measurements of received frequency using sequential filtering (i.e., a linearized Kalman filter) and smoothing techniques. A reconstruction of the MPF trajectory
591
using both science accelerometer data and altimeter data is therefore a very important test case for the Huygens reconstruction algorithm. The Galileo probe separated from the orbiter on July 13, 1995 and followed a ballistic trajectory to its Jupiter entry point (6:54 north latitude, 4:46 west longitude). The Galileo probe ASI was equipped with 2 axial and normal accelerometer sensors as well as pressure and temperature sensors which were exposed to the ambient atmosphere once the heat shield was jettisoned (Seiff and Knight, 1992). A mass spectrometer and helium abundance sensor provided the molecular weight of the atmosphere (Mahaffy et al., 2000). Although no solid surface exists on Jupiter to provide a convenient absolute altitude reference, the Galileo probe accelerations, temperature, pressure and molecular weight measurements will provide a useful test case for the Huygens reconstruction algorithm. To test the HASI hardware and software in the terrestrial atmosphere, the HASI team has developed a series of balloon drop experiments. The first balloon campaign (COMAS SOLA experiment) was conducted in Leo´n, Spain, in December 1995 (Lo´pezMoreno et al., 2002), followed by balloon flights in June 2001, May 2002, and June 2003 from the Italian Space Agency Base ‘‘Luigi Broglio’’ in Sicily (Fulchignoni et al., 2002b). Subsystems from the HASI instrument that were flown include the pressure profile instrument, the accelerometer package, and the temperature profile package with their corresponding sensors. These instrument packages and sensors were accommodated on a full scale Huygens Probe mockup and launched by a stratospheric balloon that reached a maximum altitude of approximately 30 km. The Huygens mission at Titan was simulated by separating the probe from the balloon, and descending to the surface under parachute. Atmospheric reconstruction activities were conducted during both balloon ascent and parachute descent. Since GPS receivers were included as part of the instrument payload and the trajectory is therefore very well known, the HASI balloon flight data will provide another important test of the Huygens reconstruction algorithm. A very important test will be the reconstruction of the Huygens entry and descent trajectory utilizing a properly timed and formatted synthetic data set. An extensive effort is devoted to the preparation of this data set that will be representative of all the measurement parameters of the various Huygens instruments contributing to the DTWG reconstruction effort (Pe´rez-Ayu´car et al., 2004). This data set will serve as the main test bed for the final implementation of the full reconstruction algorithm.
ARTICLE IN PRESS 592
D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
By comparing the trajectory reconstructed from the synthetic data with the known input atmosphere and trajectory, the effect of errors, data dropouts, and instrument failures will be tested.
8. Reconstruction of probe attitude Similar to MPF, the Huygens Probe is not equipped with onboard gyroscopes which therefore precludes a direct reconstruction of the probe attitude during entry. However, the spin of the probe about its symmetry axis will be directly measured by the RASU. From the ratio of the measured normal and axial aerodynamic accelerations (measured by the HASI and CASU accelerometers), the Huygens Probe’s angle of attack during entry can be reconstructed using the aerodynamic database (see Section 5). A probable slight misalignment between the vehicle’s body axes (defined by the probe/aeroshell axis of symmetry) and the principal axes (defined by the probe/aeroshell mass distribution) will cause a coning of the vehicle about its principal axis. This coning motion was observed in the MPF normal acceleration measurements even prior to atmospheric entry (Spencer et al., 1999) and will likely be visible in slight oscillations of the Huygens Probe normal acceleration measurements. During the descent phase the probe attitude will be reconstructed from DISR images. A dedicated algorithm is currently under development by the instrument Principal Investigator at the Lunar and Planetary Laboratory of the University of Arizona, USA (Rizk, 2002). Furthermore, the DWE and the SSP will also provide data to support the reconstruction of the probe descent attitude (Atkinson, 2003). 9. Summary The ESA Huygens Probe with a suite of six instruments will enter the atmosphere of Titan in January, 2005. For the correct scientific interpretation and correlation of the different measurements a single and common entry and descent profile is needed that is consistent with all available probe science and engineering data. The Huygens DTWG is developing trajectory and attitude reconstruction methodologies, including a dedicated reconstruction algorithm. Standard techniques of entry probe accelerometry will provide an entry and descent trajectory that is maximally consistent with all the experiment data. The algorithm will be tested on existing data sets from past planetary probe missions and synthetic data sets that are representative of the format and data sampling rates of the various Huygens instruments.
Acknowledgements The authors would like to acknowledge support from ESA under a Huygens Science Operations Contract, and DHA also acknowledges support provided by NASA JPL as a Co-Investigator on the Huygens Doppler Wind Experiment. Additionally, the authors thank Bill Clabough, Erica Lively, and Ben Pollard at the University of Idaho for many useful discussions. References Atkinson, D., 2003. Report of the Huygens Descent Trajectory Working Group. Technical Report Review 3, University of Idaho. Bird, M.K., Dutta-Roy, R., Heyl, M., Allison, M., Asmar, S.W., Folkner, W.M., Preston, R.A., Atkinson, D.H., Edenhofer, P., Plettemeier, D., Wohlmuth, R., Iess, L., Tyler, G.L., 2002. The Huygens doppler wind experiment—Titan Winds derived from probe radio frequency measurements. Space Sci. Rev. 104, 611–638. Clausen, K.C., Hassan, H., Verdant, M., Couzin, P., Huttin, G., Brisson, M., Sollazzo, C., Lebreton, J.-P., 2002. The Huygens probe system design. Space Sci. Rev. 104, 155–189. Duxbury, E.D., Schofield, J.T., 1998. MPFL-M-ASIMET-2/3-EDR/ RDR- EDL-V1.0, Data set information. Technical Report, NASAPDS File: edlerds.cat. Dymond, J.H., Smith, E.B., 1992. The Virial Coefficients of Pure Gases and Mixtures, a Critical Compilation. Oxford University Press, Oxford. Fulchignoni, M., Ferri, F., Angrilli, F., Bar-Nun, A., Barucci, M.A., Bianchini, G., Borucki, W., Coradini, M., Coustenis, A., Falkner, P., Flamini, E., Grard, R., Hamelin, M., Harri, A.M., Leppelmeier, G.W., Lopez-Moreno, J.J., McDonnell, J.A.M., McKay, C.P., Neubauer, F.H., Pedersen, A., Picardi, G., Pirronello, V., Rodrigo, R., Schwingenschuh, K., Seiff, A., Svedhem, H., Vanzani, V., Zarnecki, J., 2002a. The characterisation of Titan’s atmospheric physical properties by the Huygens Atmospheric Structure Instrument (HASI). Space Sci. Rev. 104, 397–434. Fulchignoni, M., Gaborit, V., Aboudam, A., Angrilli, F., Antonello, M., Bastianello, S., Bettanini, C., Bianchini, G., Colombatti, G., Ferri, F., Lion Stoppato, P., 2002b. Huygens Atmospheric Structure Instrument (HASI) test by a stratospheric balloon experiment. AAS/Division for Planetary Sciences Meeting 34. Gaborit, V., 2004. Procedure development for the trajectory reconstruction of a probe descending in a planetary atmosphere: application to Galileo and HASI balloon tests. In: ESA SP-544: Planetary Probe Atmospheric Entry and Descent Trajectory Analysis and Science. Gnoffo, P.A., Weilmuenster, K.J., Braun, R.D., Cruz, C.I., 1996. Influence of sonic-line location on Mars Pathfinder probe aerothermodynamics. J. Spacecraft Rockets 33 (2), 167–177. Israel, G., Cabane, M., Brun, J.-F., Niemann, H., Way, S., Riedler, W., Steller, M., Raulin, F., Coscia, D., 2002. Huygens probe aerosol collector pyrolyser experiment. Space Sci. Rev. 104, 433–468. Kazeminejad, B., 2005. Methodology development for the reconstruction of the ESA Huygens probe entry and descent trajectory. Ph.D. Thesis, Karl-Franzens University Graz. Kazeminejad, B., Atkinson, D.H., 2004. The ESA Huygens probe entry and descent trajectory reconstruction. In: ESA SP-544: Planetary Probe Atmospheric Entry and Descent Trajectory Analysis and Science, pp. 137–149. Kazeminejad, B., Pe´rez-Ayu´car, M., Lebreton, J.-P., Sanchez-Nogales, M., Bello´-Mora, M., Strange, N., Roth, D., Popken, L., Clausen,
ARTICLE IN PRESS D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593 K., Couzin, P., 2004. Simulation and analysis of the revised Huygens probe entry and descent trajectory and radio link modelling. Planet. Space Sci. 52, 799–814. Lebreton, J.-P., Matson, D.L., 2002. The Huygens probe: science, payload and mission overview. Space Sci. Rev. 104, 59–100. Lo´pez-Moreno, J.J., Molina-Cuberos, G.J., Hamelin, M., Brown, V.J.G., Ferri, F., Grard, R., Jernej, I., Jero´nimo, J.M., Leppelmeier, G.W., Ma¨kinen, T., Rodrigo, R., Sabau, L., Schwingenschuh, K., Svedhem, H., Zarnecki, J., Fulchignoni, M., 2002. The Comas sola mission to test the HUYGENS/HASI instrument on board a stratospheric balloon. Adv. Space Res. 30, 1359–1364. Magalha˜es, J.A., Schofield, J.T., Seiff, A., 1999. Results of the Mars Pathfinder atmospheric structure investigation. J. Geophys. Res. 104, 8943–8956. Mahaffy, P.R., Niemann, H.B., Alpert, A., Atreya, S.K., Demick, J., Donahue, T.M., Harpold, D.N., Owen, T.C., 2000. Noble gas abundance and isotope ratios in the atmosphere of Jupiter from the Galileo probe Mass Spectrometer. J. Geophys. Res. 105, 15061–15072. Moss, J., Blanchard, R.C., Wilmoth, R.G., Braun, R.D., 1998. Mars Pathfinder Rarefied Aerodynamics: Computations and Measurements. AIAA 98-0298. Niemann, H.B., Atreya, S.K., Bauer, S.J., Biemann, K., Block, B., Carignan, G.R., Donahue, T.M., Frost, R.L., Gautier, D., Haberman, J.A., Harpold, D., Hunten, D.M., Israel, G., Lunine, J.I., Mauersberger, K., Owen, T.C., Raulin, F., Richards, J.E., Way, S.H., 2002. The gas chromatograph mass spectrometer for the Huygens probe. Space Sci. Rev. 104, 551–590. Pe´rez-Ayu´car, M., Witasse, O., Lebreton, J.-P., Kazeminejad, B., Atkinson, D.H., 2004. A simulated dataset of the Huygens mission.
593
In: ESA SP-544: Planetary Probe Atmospheric Entry and Descent Trajectory Analysis and Science, pp. 343–349. Rizk, B., 2002. Using DISR SLI strip data to reconstruct the Huygens probe attitude—progress. Technical Report DTWG5: Power Point Presentation, LPL, University of Arizona. Schipper, A., 2002. Private Communication. Seiff, A., Knight, T.C.D., 1992. The Galileo probe atmosphere structure instrument. Space Sci. Rev. 60, 203–232. Spencer, D.A., Blanchard, R.C., Braun, R.D., Kallemeyn, P.H., Thurmann, S.W., 1999. Mars Pathfinder entry, descent, and landing reconstruction. J. Spacecraft Rockets 36 (3), 357–366. Steiner, G., Bauer, S.J., 1990. Molecular and eddy diffusion in the atmosphere of Titan. Ann. Geophys. 8, 473–476. Strobel, D.F., Summers, M.E., Zhu, X., 1992. Titan’s upper atmosphere—structure and ultraviolet emissions. Icarus 100, 512–526. Tomasko, M.G., Buchhauser, D., Bushroe, M., Dafoe, L.E., Doose, L.R., Eibl, A., Fellows, C., Farlane, E.M., Prout, G.M., Pringle, M.J., Rizk, B., Sec, C., Smith, P.H., Tsetsenekos, K., 2002. The descent imager/spectral radiometer (DISR) experiment on the Huygens entry probe of Titan. Space Sci. Rev. 104, 467–549. Withers, P., Towner, M.C., Hathi, B., Zarnecki, J.C., 2003. Analysis of entry accelerometer data: a case study of Mars Pathfinder. Planet. Space Sci. 51, 541–561. Yelle, R.V., Strobell, D.F., Lellouch, E., Gautier, D., 1997. The Yelle Titan atmosphere engineering models. In: Wilson, A. (Ed.), Huygens: Science, Payload and Mission, ESA SP-1177, pp. 243–256. Zarnecki, J.C., Leese, M.R., Garry, J.R.C., Ghafoor, N., Hathi, B., 2002. Huygens’ surface science package. Space Sci. Rev. 104, 591–609.
Planetary and Space Science 53 (2005) 586–593 www.elsevier.com/locate/pss
Huygens probe entry and descent trajectory analysis and reconstruction techniques D.H. Atkinsona,, B. Kazeminejadb, V. Gaboritc, F. Ferrid, J.-P. Lebretone a
Department of Electrical and Computer Engineering, University of Idaho, Moscow, ID 83844-1023, USA Department of Extraterrestrial Physics, Space Research Institute (IWF), Austrian Academy of Sciences, 8042 Graz, Austria c Observatoire de Paris-Meudon (LESIA), 5 Place Jules Janssen, 92195 Meudon, France d CISAS ‘‘G. Colombo’’ Universita` di Padova, via Venezia 1, 35131 Padova, Italy e ESA Research and Scientific Support Department, ESTEC/SCI-SB, 2200 AG Noordwijk, The Netherlands
b
Received 5 August 2003; received in revised form 20 November 2003; accepted 20 November 2004 Available online 2 March 2005
Abstract Cassini/Huygens is a joint National Aeronautics and Space Administration (NASA)/European Space Agency (ESA)/Agenzia Spaziale Italiana (ASI) mission on its way to explore the Saturnian system. The ESA Huygens Probe is scheduled to be released from the Orbiter on 25 December 2004 and enter the atmosphere of Titan on 14 January 2005. Probe delivery to Titan, arbitrarily defined to occur at a reference altitude of 1270 km above the surface of Titan, is the responsibility of the NASA Jet Propulsion Laboratory (JPL). ESA is then responsible for safely delivering the probe from the reference altitude to the surface. The task of reconstructing the probe trajectory and attitude from the entry point to the surface has been assigned to the Huygens Descent Trajectory Working Group (DTWG), a subgroup of the Huygens Science Working Team. The DTWG will use data provided by the Huygens Probe engineering subsystems and selected data sets acquired by the scientific payload. To correctly interpret and correlate results from the probe science experiments and to provide a reference set of data for possible ‘‘ground-truthing’’ Orbiter remote sensing measurements, it is essential that the trajectory reconstruction be performed as early as possible in the post-flight data analysis phase. The reconstruction of the Huygens entry and descent trajectory will be based primarily on the probe entry state vector provided by the Cassini Navigation Team, and measurements of acceleration, pressure, and temperature made by the Huygens Atmospheric Structure Instrument (HASI). Other data sets contributing to the entry and descent trajectory reconstruction include the mean molecular weight of the atmosphere measured by the probe Gas Chromatograph/Mass Spectrometer (GCMS) in the upper atmosphere and the Surface Science Package (SSP) speed of sound measurement in the lower atmosphere, accelerations measured by the Central and Radial Accelerometer Sensor Units (CASU/ RASU), and the probe altitude by the two probe radar altimeters during the latter stages of the descent. In the last several hundred meters, the altitude determination will be constrained by measurements from the SSP acoustic sounder. Other instruments contributing data to the entry and descent trajectory and attitude determination include measurements of the zonal wind drift by the Doppler Wind Experiment (DWE), and probe zonal and meridional drift and probe attitude by the Descent Imager and Spectral Radiometer (DISR). In this paper, the need for and the methods by which the Huygens Probe entry and descent trajectory will be reconstructed are reviewed. r 2005 Elsevier Ltd. All rights reserved. Keywords: Huygens Probe; Entry and descent trajectory
Abbreviations: ASI, Agenzia Spaziale Italiana (Italian Space Agency); ASI/MET, Atmospheric Structure Instrument/Meterology Package; CASU, Central Acceleration Sensor Unit; DISR, Descent Imager and Spectral Radiometer; DTWG, Descent Trajectory Working Group; DWE, Doppler Wind Experiment; EDL, Entry Descent and Landing; ESA, European Space Agency; ESTEC, European Space Research and Technology Centre; GCMS, Gas Chromatograph/Mass Spectrometer; HASI, Huygens Atmospheric Structure Instrument; HGA, High Gain Antenna; HK, Housekeeping; HSWT, Huygens Science Working Team; JPL, Jet Propulsion Laboratory; MPF, Mars Pathfinder; NAIF, Navigation and Ancillary Information Facility (at JPL); NASA, National Aeronautics and Space Administration; POSW, Probe Onboard Software; PSE, Probe Support Equipment; RASU, Radial Accelerometer Sensor Unit; RAU, Radar Altimeter Unit; SSP, Surface Science Package. Corresponding author. E-mail addresses: [email protected] (D.H. Atkinson), [email protected] (B. Kazeminejad). 0032-0633/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2004.11.005
ARTICLE IN PRESS D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
1. Introduction
calibration opportunities for synergistic studies with orbiter remote sensing instruments, an accurate reconstruction of the probe entry and descent trajectory is needed. If a common and consistent descent profile is not available, each probe experiment team would need to independently develop a profile, thereby causing not only a significant duplication of effort and expenditure of resources, but also making correlation and comparison of results from different experiments somewhat suspect and therefore less meaningful. Furthermore, direct (in situ) atmospheric sampling by the probe will provide groundtruth verification of orbiter observations of the atmosphere and surface of Titan. The value of the groundtruth support for orbiter science at Titan will be significantly compromised if the altitude, location, and velocity of the Huygens Probe are not precisely known as a function of time throughout the descent mission. The responsibility of developing analysis techniques by which the Huygens Probe entry and descent trajectory will be reconstructed from the official NASA/ESA handoff point at the interface altitude of 1270 km to the surface is given to the Huygens DTWG, chartered in 1996 as a subgroup of the Huygens Science Working Team (HSWT) (Atkinson, 2003). The membership of the DTWG includes the Huygens and Cassini project scientists, The Huygens Operations Scientist, and representatives from each of the probe science instrument teams and contributing orbiter teams (see Table 1). The primary goals of the Huygens DTWG are to
The Huygens Probe is the European Space Agency (ESA)-provided element of the joint National Aeronautics and Space Administration (NASA)/ESA/Agenzia Spaziale Italiana (ASI) Cassini/Huygens mission to Saturn and Titan (Lebreton and Matson, 2002). Launched on 15 October, 1997, Cassini/Huygens will arrive at Saturn on 1 July, 2004. After two orbits of Saturn, the Huygens Probe will be released on December 25, 2004 and will enter the atmosphere of Titan on at 9:00 UTC on January 14, 2005. The probe system comprises two principal elements: the Huygens atmospheric entry probe, and the probe support equipment (PSE). The PSE remains attached to the Cassini Orbiter as part of the probe-to-orbiter communication link system used during the probe mission (Clausen et al., 2002). During both the entry and descent phase the probe will perform scientific measurements to determine the physical and chemical properties of Titan’s atmosphere, measure winds and global temperatures, and investigate energy sources important for the planet’s chemistry. It is also expected that the probe will survive impact for an investigation of the physical and chemical properties of Titan’s surface. Huygens will transmit all its entry and descent science and engineering data to the Cassini Orbiter, targeted to flyby Titan at a periapse distance of 60,000 km. The probe data will be received on the orbiter through the Cassini High Gain Antenna (HGA) which will be continuously pointed towards the probe’s predicted landing site on Titan.
2. The Huygens Descent Trajectory Working Group (DTWG)
To correctly interpret and correlate the results from all of the probe science experiments and to provide
587
develop a framework between experiment teams and the Huygens Mission Team for sharing and exchanging data relevant to the descent trajectory analysis and modeling; develop methodologies by which the probe descent trajectory and attitude can be accurately reconstructed from the probe and orbiter science and engineering data; and
Table 1 Membership of Huygens Descent Trajectory Working Group Name
Affiliation
Position
Dr. David H. Atkinson Dr. Bobby Kazeminejad Dr. Jean-Pierre Lebreton Dr. Olivier Witasse Dr. Dennis Matson Dr. David Coscia Dr. Francesca Ferri Mr. Chuck See Dr. Hasso Niemann Dr. Jonathan Lunine Mr. Brijen Hathi Dr. Daniel Gautier Dr. Francois Raulin Dr. Ralph Lorenz
Univ. Idaho Austrian Acad. Sci. ESTEC ESTEC NASA JPL Univ. Paris CISAS/Univ. Padova LPL/Univ. Arizona NASA GSFC LPL/Univ. Arizona The Open University Obs. de Paris-Meudon Lisa Univ. Paris LPL/Univ. of Arizona
DTWG Chair, DWE DTWG Co-Chair Huygens Proj. Scientist Huygens Op. Scientist Cassini Proj. Scientist ACP HASI DISR GCMS IDS SSP IDS IDS RADAR
ARTICLE IN PRESS 588
D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
provide a single, common descent profile that is consistent with all the available probe and orbiter engineering and science data, and that can be utilized by each instrument team for analysis of experiment measurements, and correlation of results between experiments.
It is planned that an initial determination of the probe entry and descent trajectory will be made available by the DTWG within 2 days after the initial download and validation of the Huygens engineering and science data. The DTWG must therefore have the necessary algorithms developed, tested, and validated by the time of the probe mission in January 2005.
3. Probe mission phases
Fig. 2. Simulated Huygens Probe descent altitude profiles for the maximum, recommended, and minimum Titan Yelle atmosphere. Nominal probe impact is 139:5 min past interface epoch (Kazeminejad et al., 2004).
The Huygens entry and descent mission can be subdivided into the following phases: (1) Entry: The entry phase commences at the interface altitude of 1270 km above the surface of Titan and ends at the start of the parachute sequence, designated as time t ¼ T 0 : At the interface altitude, the Cassini Navigation team at Jet Propulsion Laboratory (JPL) will provide to the DTWG the full state vector (i.e., position and velocity) of the Huygens Probe in a Titan-centered EME2000 coordinate system together with associated uncertainties in the form of a covariance matrix. During the entry phase the probe will decelerate from an initial velocity of Mach 22.5–1.5 (corresponding to an inertial velocity of 6 and 0:35 km=s; respectively) in less than 5 min : This implies a peak deceleration of approximately 12 g (Kazeminejad
et al., 2004). The force causing this deceleration is atmospheric drag, which depends both on the entry velocity and the atmospheric density. Throughout the entry phase the probe will be protected by a 2.75 m heat-shield. (2) Descent: About 4.6 min after the interface epoch the parachute deployment sequence commences (T 0 ; Fig. 1), comprising a 2.59 m pilot chute deployed at Mach 1.5, an 8.30 m main chute, and a 3.03 m stabilizing drogue parachute for the final portion of the descent (Clausen et al., 2002). The descent phase lasts about 140 min from T 0 to surface impact for the nominal Yelle model of the atmosphere (Yelle et al., 1997) (see Fig. 2). (3) Surface: If the probe survives impact, then it is instrumented to provide a direct characterization of the surface at the landing site. The probe batteries nominally can provide power for at least 30 min on the surface for an extended surface phase. In the current mission scenario, the Cassini Orbiter will listen to the probe for a full 4.5 h until the orbiter disappears beyond the probe horizon.
4. Instrument and data description
Fig. 1. The simulated Huygens Probe deceleration for the nominal and maximum Yelle atmosphere model; T A ¼ triggering of the parachute sequence arming timer, S0 ¼ probe onboard software (POSW) descent timer start, and T 0 ¼ parachute sequence deployment (Kazeminejad et al., 2004).
The Huygens scientific payload comprises six instruments (Lebreton and Matson, 2002)—the Gas Chromatograph and Mass Spectrometer (GCMS) (Niemann et al., 2002), the Descent Imager/Spectral Radiometer (DISR) (Tomasko et al., 2002), the Huygens Atmospheric Structure Instrument (HASI) (Fulchignoni et al., 2002a), the Doppler Wind Experiment (DWE) (Bird et al., 2002), the Surface Science Package (SSP) (Zarnecki et al., 2002), and the Aerosol Collector and
ARTICLE IN PRESS D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
Pyrolyser (ACP) (Israel et al., 2002). It is expected that the first five of these instruments will provide data essential to the entry and descent trajectory reconstruction. Additionally, data from engineering subsystems provided in the probe housekeeping (HK), and the probe entry state vector as provided by the Cassini Navigation team will also be used in the reconstruction effort. During the entry phase from the interface altitude of 1270 km to the start of the parachute sequence at T 0 the only data set available for the trajectory reconstruction will be the measured aerodynamic accelerations. The probe possesses three sets of accelerometers—the Central Acceleration Sensor Unit (CASU), the Radial Acceleration Sensor Unit (RASU), and the HASI science 3-axis accelerometers. During the descent phase, all the probe science instruments will be operating. Especially important for the trajectory reconstruction will be the HASI measurements of pressure and temperature. From the assumption of hydrostatic equilibrium and real gas behavior, and from the knowledge of the atmospheric mean molecular weight as determined by the probe GCMS experiment and the speed of sound measurements by SSP, the probe altitude and descent speed can be determined. Beneath 25 km the probe Radar Altimeter Unit (RAU) will provide a completely independent measurement of the probe altitude and descent speed, and should also provide topographical data along the probe groundtrack. The Radar Altimeter is likely to loose lock in the final several hundred meters, and the only direct measurement of altitude and descent speed will be from the SSP acoustic sounder and possibly indirectly by the DISR.
5. Reconstruction procedure During atmospheric entry, aerodynamic forces and gravity will cause the Huygens Probe’s trajectory to deviate from the gravity-only case, calculated from a pre-existing gravity model. A set of three mutually orthogonal accelerometers mounted inside the probe can accurately measure these aerodynamic accelerations. However, it is important to note that the gravitational force acting on the spacecraft’s center of mass cannot be detected by measurements made in a frame fixed with respect to the spacecraft since the spacecraft and the accelerometer instrument are both experiencing the same gravitational acceleration. To reconstruct a probe’s entry and descent trajectory from accelerometer measurements and the subsequent numerical integration of the equations of motion, additional inputs are required, including the state vector at an initial epoch ti ¼ tentry ; a model of the gravity field of the planet, and a table of probe aerodynamic coefficients.
589
To reconstruct a probe’s entry and descent trajectory, the equations of motion are traditionally formulated and integrated in a rotating, planet-fixed coordinate frame. By introducing ‘‘intermediate frames’’ wherein the coordinate axes are defined to be instantaneously coincident with a rotating planet-fixed frame at each time step, the Coriolis and centrifugal force terms are removed from the equations of motion in the rotating frame (Withers et al., 2003). For the Huygens reconstruction, the added complexity of including the Coriolis and centrifugal forces has been eliminated by integrating the equations of motion in a planet-centered inertial frame. For the Huygens trajectory the initial conditions, including probe state vector at the interface (entry) epoch, uncertainties in the form of a covariance matrix, and Titan’s gravitational parameter GM will be provided by the Cassini Navigation team in the form of a NAIF SPICE kernel (NASA Navigation and Ancillary Information Facility (NAIF) at JPL, http:// naif.jpl.nasa.gov/naif/), a special data file that can be easily read and used in computer algorithms. Additionally, the gravitational effects of the planet’s flattening (currently assumed to be zero for Titan) as well as perturbations from the Saturnian and the Solar gravitational effects are included in the model. The accelerometers onboard the Huygens Probe will measure the linear accelerations of the spacecraft center of mass in the three orthogonal directions as1 ; as2 ; as3 aligned with the spacecraft s1 -, s2 -, and s3 -axes, respectively. The correct transformation of the accelerations measured in the spacecraft frame ðs1 ; s2 ; s3 Þ to the inertial frame requires the knowledge of the orientation of the spacecraft attitude with respect to the direction of the flow velocity (given in the inertial frame of integration). In case of axisymmetry this orientation can be expressed by the angle of attack aðtÞ which can be estimated using the ratio of normal to axial accelerations aN C N ¼ ¼ f ða; MaÞ, aA C A
(1)
where aN and aA are the normal and axial accelerations qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi given by aN ¼ a2s2 þ a2s3 and aA ¼ as1 ; respectively, and C N and C A are the corresponding aerodynamic coefficients. An existing pre-flight aerodynamic database of the Huygens Probe (Schipper, 2002) provides C N and C A as a function of a and the Mach number Ma: From the normal and axial accelerations aN and aA ; the angle of attack a can be found by interpolating the aerodynamic database. The drag and lift accelerations aD and aL can then be found from aD ¼ aA cos a þ aN sin a, aL ¼ aN cos a aA sin a,
ð2Þ
ARTICLE IN PRESS D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
590
where, again, aN ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2s2 þ a2s3 and aA ¼ as1 (Kazemi-
nejad, 2005). Due to probe spin, the lift and side force vectors will rotate with the probe and average to zero (assuming that they are essentially constant over a spin period) and can therefore be neglected. The drag force vector aAd is always pointing in the opposite direction of the relative flow velocity vector vrel of the spacecraft with respect to the fluid (i.e., the atmosphere) in the inertial frame of integration and can be found from aAd ¼ aD
vrel jvrel j
(3)
and vrel can be calculated using the relation vrel ¼ v op r vw ,
(4)
where r and v are the probe position and velocity vectors in the inertial frame, op the angular velocity vector of the planet, and vw the velocity vector of the atmospheric wind. It is important to note that the calculation of the Mach number requires the knowledge of the atmospheric temperature T and molecular weight m; neither of which are directly measured during the entry phase. The relative abundance of methane and argon (if present) will vary with altitude in the upper atmosphere because of diffusive separation but should be constant at altitudes below 600 km (Yelle et al., 1997). In the upper atmosphere m can be modelled using analytic expressions for the methane and argon mole fractions as a function of altitude (Strobel et al., 1992; Steiner and Bauer, 1990). During the descent phase (160 km to the surface) m will be measured by the GCMS experiment, and indirectly by the SSP speed of sound experiment. In the upper atmosphere the physical properties of the atmosphere (density r; pressure P and temperature T) can be derived from the measured aerodynamic accelerations (Magalha˜es et al., 1999; Kazeminejad and Atkinson, 2004). Therefore, an iterative process will be necessary whereby the measured accelerations are used to derive the atmospheric properties, and the atmospheric properties are used to refine the trajectory calculation. This iterative approach converges rather quickly. The numerical integration of the measured spacecraft accelerations and the modelled gravitational accelerations provide an initial reference trajectory to the surface. The reference trajectory will then be refined using additional independent data sets, including measurements of probe altitude and descent speed z and z_ as determined from the RAU, DISR, and HASI. The probe altitude and descent speed can be found from HASI pressure P and temperature T measure-
ments. The altitude zi at an epoch ti is given by X Dzi1 , zi ¼ z0
(5)
i
where z0 is the initial altitude (i.e., the altitude at which the first pressure measurement was taken) and Dzi is the distance the probe has travelled in the time interval Dti which is calculated by Gaborit (2004) RT i12 z Pi Dzi ¼ ln . (6) Pi1 mg The subscript i is relative to a value obtained at the mission time ti and the temperature T is assumed to be constant between times ti1 and ti having the value T 1 ¼ 12ðT i1 þ T i Þ: R again is the universal gas i2
constant, m the molecular weight of the gas mixture, g the vertical component of the effective gravitational field, and z the compressibility factor that takes into account the non perfect gas behavior (Dymond and Smith, 1992). Note that the compressibility factor is a function of the temperature, the density and the chemical composition of the gas. Using several imaging sensors, the Descent Imager will provide data supporting the reconstruction of the probe altitude and descent speed, as well as probe attitude [Private Communication with Bashar Rizk, University of Arizona LPL (2002)].
6. Error treatment In the trajectory estimation process, various error sources with the potential to degrade the accuracy of the reconstructed probe entry and descent trajectory must be considered: (1) The accelerometers are not directly positioned at the center of mass of the probe. (2) The aerodynamic acceleration measurements will be affected by the intrinsic accuracy of the instrument. The best way to assess the impact of this error source is to utilize a Monte Carlo technique whereby a large number (e.g., 10,000) of entry and descent trajectory reconstructions are simulated, each including randomly applied 0–3s errors in the accelerometer data. (3) The probe initial state vector at the interface altitude will be provided to the DTWG by the Cassini Navigation team together with an uncertainty estimation in form of a covariance matrix. (4) The measurement uncertainties of each instrument are directly included in the trajectory estimation process by specifying a weighting matrix W that contains the standard deviation of each measurement.
ARTICLE IN PRESS D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
(5) The aerodynamic coefficients are provided to the DTWG in the form of a pre-flight aerodynamic database. Uncertainties in the various coefficients translate into uncertainties in the angle of attack determination which will affect the conversion of the aerodynamic accelerations from the spacecraft to the inertial frame (see Section 5). Uncertainties in the aerodynamic database are not directly taken into account by the algorithm, but can be assessed by an additional reconstruction process with a modified database with increased (or decreased) coefficients, or by additional Monte Carlo techniques.
7. Data sets for the testing of the algorithm As the Huygens data will be available in January 2005, it is important that a test program be developed that can utilize both synthetic data sets and existing data sets from past atmospheric probe missions. The following missions will be considered:
The entry, descent and landing (EDL) of the Mars Pathfinder (MPF) spacecraft on July 4, 1997 provides a unique test case since the Atmospheric Structure Instrument and Meteorology Package (ASI/MET) on MPF was equipped with three orthogonal engineering and three orthogonal science accelerometers as well as pressure, temperature and wind sensors (Duxbury and Schofield, 1998). It is important to note however, that the pressure, temperature and wind sensors are located behind the heatshield throughout much of the EDL and therefore did not provide reliable data. After heatshield separation, the sensor properties were influenced both by the atmosphere and the lander environment. Although the descent temperature sensor was exposed for EDL, the exposure was not good enough to prevent serious contamination from the lander environment so that its result could not readily be converted to atmospheric temperature during the parachute descent, terminal or landing phases of EDL (Duxbury and Schofield, 1998). MPF was also equipped with a radar altimeter that acquired altitude information and vertical motion between 1.36 km and 388 m. The MPF entry and descent trajectory as well as the physical properties of the Martian atmosphere were reconstructed by Magalha˜es et al. (1999) using the science accelerometer data and an existing aerodynamic pre-flight database (Moss et al., 1998; Gnoffo et al., 1996). An independent reconstruction effort was done by Spencer et al. (1999) based on accelerometer, altimeter, and ground-based measurements of received frequency using sequential filtering (i.e., a linearized Kalman filter) and smoothing techniques. A reconstruction of the MPF trajectory
591
using both science accelerometer data and altimeter data is therefore a very important test case for the Huygens reconstruction algorithm. The Galileo probe separated from the orbiter on July 13, 1995 and followed a ballistic trajectory to its Jupiter entry point (6:54 north latitude, 4:46 west longitude). The Galileo probe ASI was equipped with 2 axial and normal accelerometer sensors as well as pressure and temperature sensors which were exposed to the ambient atmosphere once the heat shield was jettisoned (Seiff and Knight, 1992). A mass spectrometer and helium abundance sensor provided the molecular weight of the atmosphere (Mahaffy et al., 2000). Although no solid surface exists on Jupiter to provide a convenient absolute altitude reference, the Galileo probe accelerations, temperature, pressure and molecular weight measurements will provide a useful test case for the Huygens reconstruction algorithm. To test the HASI hardware and software in the terrestrial atmosphere, the HASI team has developed a series of balloon drop experiments. The first balloon campaign (COMAS SOLA experiment) was conducted in Leo´n, Spain, in December 1995 (Lo´pezMoreno et al., 2002), followed by balloon flights in June 2001, May 2002, and June 2003 from the Italian Space Agency Base ‘‘Luigi Broglio’’ in Sicily (Fulchignoni et al., 2002b). Subsystems from the HASI instrument that were flown include the pressure profile instrument, the accelerometer package, and the temperature profile package with their corresponding sensors. These instrument packages and sensors were accommodated on a full scale Huygens Probe mockup and launched by a stratospheric balloon that reached a maximum altitude of approximately 30 km. The Huygens mission at Titan was simulated by separating the probe from the balloon, and descending to the surface under parachute. Atmospheric reconstruction activities were conducted during both balloon ascent and parachute descent. Since GPS receivers were included as part of the instrument payload and the trajectory is therefore very well known, the HASI balloon flight data will provide another important test of the Huygens reconstruction algorithm. A very important test will be the reconstruction of the Huygens entry and descent trajectory utilizing a properly timed and formatted synthetic data set. An extensive effort is devoted to the preparation of this data set that will be representative of all the measurement parameters of the various Huygens instruments contributing to the DTWG reconstruction effort (Pe´rez-Ayu´car et al., 2004). This data set will serve as the main test bed for the final implementation of the full reconstruction algorithm.
ARTICLE IN PRESS 592
D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593
By comparing the trajectory reconstructed from the synthetic data with the known input atmosphere and trajectory, the effect of errors, data dropouts, and instrument failures will be tested.
8. Reconstruction of probe attitude Similar to MPF, the Huygens Probe is not equipped with onboard gyroscopes which therefore precludes a direct reconstruction of the probe attitude during entry. However, the spin of the probe about its symmetry axis will be directly measured by the RASU. From the ratio of the measured normal and axial aerodynamic accelerations (measured by the HASI and CASU accelerometers), the Huygens Probe’s angle of attack during entry can be reconstructed using the aerodynamic database (see Section 5). A probable slight misalignment between the vehicle’s body axes (defined by the probe/aeroshell axis of symmetry) and the principal axes (defined by the probe/aeroshell mass distribution) will cause a coning of the vehicle about its principal axis. This coning motion was observed in the MPF normal acceleration measurements even prior to atmospheric entry (Spencer et al., 1999) and will likely be visible in slight oscillations of the Huygens Probe normal acceleration measurements. During the descent phase the probe attitude will be reconstructed from DISR images. A dedicated algorithm is currently under development by the instrument Principal Investigator at the Lunar and Planetary Laboratory of the University of Arizona, USA (Rizk, 2002). Furthermore, the DWE and the SSP will also provide data to support the reconstruction of the probe descent attitude (Atkinson, 2003). 9. Summary The ESA Huygens Probe with a suite of six instruments will enter the atmosphere of Titan in January, 2005. For the correct scientific interpretation and correlation of the different measurements a single and common entry and descent profile is needed that is consistent with all available probe science and engineering data. The Huygens DTWG is developing trajectory and attitude reconstruction methodologies, including a dedicated reconstruction algorithm. Standard techniques of entry probe accelerometry will provide an entry and descent trajectory that is maximally consistent with all the experiment data. The algorithm will be tested on existing data sets from past planetary probe missions and synthetic data sets that are representative of the format and data sampling rates of the various Huygens instruments.
Acknowledgements The authors would like to acknowledge support from ESA under a Huygens Science Operations Contract, and DHA also acknowledges support provided by NASA JPL as a Co-Investigator on the Huygens Doppler Wind Experiment. Additionally, the authors thank Bill Clabough, Erica Lively, and Ben Pollard at the University of Idaho for many useful discussions. References Atkinson, D., 2003. Report of the Huygens Descent Trajectory Working Group. Technical Report Review 3, University of Idaho. Bird, M.K., Dutta-Roy, R., Heyl, M., Allison, M., Asmar, S.W., Folkner, W.M., Preston, R.A., Atkinson, D.H., Edenhofer, P., Plettemeier, D., Wohlmuth, R., Iess, L., Tyler, G.L., 2002. The Huygens doppler wind experiment—Titan Winds derived from probe radio frequency measurements. Space Sci. Rev. 104, 611–638. Clausen, K.C., Hassan, H., Verdant, M., Couzin, P., Huttin, G., Brisson, M., Sollazzo, C., Lebreton, J.-P., 2002. The Huygens probe system design. Space Sci. Rev. 104, 155–189. Duxbury, E.D., Schofield, J.T., 1998. MPFL-M-ASIMET-2/3-EDR/ RDR- EDL-V1.0, Data set information. Technical Report, NASAPDS File: edlerds.cat. Dymond, J.H., Smith, E.B., 1992. The Virial Coefficients of Pure Gases and Mixtures, a Critical Compilation. Oxford University Press, Oxford. Fulchignoni, M., Ferri, F., Angrilli, F., Bar-Nun, A., Barucci, M.A., Bianchini, G., Borucki, W., Coradini, M., Coustenis, A., Falkner, P., Flamini, E., Grard, R., Hamelin, M., Harri, A.M., Leppelmeier, G.W., Lopez-Moreno, J.J., McDonnell, J.A.M., McKay, C.P., Neubauer, F.H., Pedersen, A., Picardi, G., Pirronello, V., Rodrigo, R., Schwingenschuh, K., Seiff, A., Svedhem, H., Vanzani, V., Zarnecki, J., 2002a. The characterisation of Titan’s atmospheric physical properties by the Huygens Atmospheric Structure Instrument (HASI). Space Sci. Rev. 104, 397–434. Fulchignoni, M., Gaborit, V., Aboudam, A., Angrilli, F., Antonello, M., Bastianello, S., Bettanini, C., Bianchini, G., Colombatti, G., Ferri, F., Lion Stoppato, P., 2002b. Huygens Atmospheric Structure Instrument (HASI) test by a stratospheric balloon experiment. AAS/Division for Planetary Sciences Meeting 34. Gaborit, V., 2004. Procedure development for the trajectory reconstruction of a probe descending in a planetary atmosphere: application to Galileo and HASI balloon tests. In: ESA SP-544: Planetary Probe Atmospheric Entry and Descent Trajectory Analysis and Science. Gnoffo, P.A., Weilmuenster, K.J., Braun, R.D., Cruz, C.I., 1996. Influence of sonic-line location on Mars Pathfinder probe aerothermodynamics. J. Spacecraft Rockets 33 (2), 167–177. Israel, G., Cabane, M., Brun, J.-F., Niemann, H., Way, S., Riedler, W., Steller, M., Raulin, F., Coscia, D., 2002. Huygens probe aerosol collector pyrolyser experiment. Space Sci. Rev. 104, 433–468. Kazeminejad, B., 2005. Methodology development for the reconstruction of the ESA Huygens probe entry and descent trajectory. Ph.D. Thesis, Karl-Franzens University Graz. Kazeminejad, B., Atkinson, D.H., 2004. The ESA Huygens probe entry and descent trajectory reconstruction. In: ESA SP-544: Planetary Probe Atmospheric Entry and Descent Trajectory Analysis and Science, pp. 137–149. Kazeminejad, B., Pe´rez-Ayu´car, M., Lebreton, J.-P., Sanchez-Nogales, M., Bello´-Mora, M., Strange, N., Roth, D., Popken, L., Clausen,
ARTICLE IN PRESS D.H. Atkinson et al. / Planetary and Space Science 53 (2005) 586–593 K., Couzin, P., 2004. Simulation and analysis of the revised Huygens probe entry and descent trajectory and radio link modelling. Planet. Space Sci. 52, 799–814. Lebreton, J.-P., Matson, D.L., 2002. The Huygens probe: science, payload and mission overview. Space Sci. Rev. 104, 59–100. Lo´pez-Moreno, J.J., Molina-Cuberos, G.J., Hamelin, M., Brown, V.J.G., Ferri, F., Grard, R., Jernej, I., Jero´nimo, J.M., Leppelmeier, G.W., Ma¨kinen, T., Rodrigo, R., Sabau, L., Schwingenschuh, K., Svedhem, H., Zarnecki, J., Fulchignoni, M., 2002. The Comas sola mission to test the HUYGENS/HASI instrument on board a stratospheric balloon. Adv. Space Res. 30, 1359–1364. Magalha˜es, J.A., Schofield, J.T., Seiff, A., 1999. Results of the Mars Pathfinder atmospheric structure investigation. J. Geophys. Res. 104, 8943–8956. Mahaffy, P.R., Niemann, H.B., Alpert, A., Atreya, S.K., Demick, J., Donahue, T.M., Harpold, D.N., Owen, T.C., 2000. Noble gas abundance and isotope ratios in the atmosphere of Jupiter from the Galileo probe Mass Spectrometer. J. Geophys. Res. 105, 15061–15072. Moss, J., Blanchard, R.C., Wilmoth, R.G., Braun, R.D., 1998. Mars Pathfinder Rarefied Aerodynamics: Computations and Measurements. AIAA 98-0298. Niemann, H.B., Atreya, S.K., Bauer, S.J., Biemann, K., Block, B., Carignan, G.R., Donahue, T.M., Frost, R.L., Gautier, D., Haberman, J.A., Harpold, D., Hunten, D.M., Israel, G., Lunine, J.I., Mauersberger, K., Owen, T.C., Raulin, F., Richards, J.E., Way, S.H., 2002. The gas chromatograph mass spectrometer for the Huygens probe. Space Sci. Rev. 104, 551–590. Pe´rez-Ayu´car, M., Witasse, O., Lebreton, J.-P., Kazeminejad, B., Atkinson, D.H., 2004. A simulated dataset of the Huygens mission.
593
In: ESA SP-544: Planetary Probe Atmospheric Entry and Descent Trajectory Analysis and Science, pp. 343–349. Rizk, B., 2002. Using DISR SLI strip data to reconstruct the Huygens probe attitude—progress. Technical Report DTWG5: Power Point Presentation, LPL, University of Arizona. Schipper, A., 2002. Private Communication. Seiff, A., Knight, T.C.D., 1992. The Galileo probe atmosphere structure instrument. Space Sci. Rev. 60, 203–232. Spencer, D.A., Blanchard, R.C., Braun, R.D., Kallemeyn, P.H., Thurmann, S.W., 1999. Mars Pathfinder entry, descent, and landing reconstruction. J. Spacecraft Rockets 36 (3), 357–366. Steiner, G., Bauer, S.J., 1990. Molecular and eddy diffusion in the atmosphere of Titan. Ann. Geophys. 8, 473–476. Strobel, D.F., Summers, M.E., Zhu, X., 1992. Titan’s upper atmosphere—structure and ultraviolet emissions. Icarus 100, 512–526. Tomasko, M.G., Buchhauser, D., Bushroe, M., Dafoe, L.E., Doose, L.R., Eibl, A., Fellows, C., Farlane, E.M., Prout, G.M., Pringle, M.J., Rizk, B., Sec, C., Smith, P.H., Tsetsenekos, K., 2002. The descent imager/spectral radiometer (DISR) experiment on the Huygens entry probe of Titan. Space Sci. Rev. 104, 467–549. Withers, P., Towner, M.C., Hathi, B., Zarnecki, J.C., 2003. Analysis of entry accelerometer data: a case study of Mars Pathfinder. Planet. Space Sci. 51, 541–561. Yelle, R.V., Strobell, D.F., Lellouch, E., Gautier, D., 1997. The Yelle Titan atmosphere engineering models. In: Wilson, A. (Ed.), Huygens: Science, Payload and Mission, ESA SP-1177, pp. 243–256. Zarnecki, J.C., Leese, M.R., Garry, J.R.C., Ghafoor, N., Hathi, B., 2002. Huygens’ surface science package. Space Sci. Rev. 104, 591–609.