******************************************************************************** Giotto SPK file, Data for Closest Approach to Halley =========================================================================== Created by Samantha Krening, NAIF/JPL, November 9, 2011. Last edited by Samantha Krening on November 16, 2011. Objects in the Ephemeris ------------------------------------------------------------------- This file contains ephemeris data for the following: Body NAIF ID code ----------------- ----------------- Giotto probe -78 Halley's comet 1000036 Earth 399 Approximate Time Coverage ------------------------------------------------------------------- The Giotto, Halley, and Earth ephemerides provided in this file cover a twelve day interval during Giotto's closest approach to Halley's comet: COVERAGE BEGIN TIME (TDB): 1986 MAR 05 00:00:00.000 COVERAGE END TIME (TDB): 1986 MAR 16 23:06:40.000 Pedigree ------------------------------------------------------------------- This SP-kernel was made using position vectors from a document named epgiotto.doc, which was produced by Trevor Morley at ESOC. For more details on how the 'epgiotto' document was produced from the ESOC ephemeris data, please see the appendix below that contains the document's contents. The position vector components and time tags were truncated to 16 digits, which translates into tenths of a second and provides a very inaccurate input for SPK generation. The interpolation performed by the SPK subsystem of such inaccurate data can produce even more erroneous results. The time tags were reconstructed with more precision to obtain better results. Also, the 'epgiotto' document did not contain any velocity data, so the truncated positions were numerically differentiated to produce this file. Usage ------------------------------------------------------------------- An LSK file and an SPK file containing planet ephemeris information should be loaded together with this SPK to allow complex geometry computations. Contacts ------------------------------------------------------------------- If you have any question regarding this data contact NAIF at JPL: Samantha C. Krening (818)-354-6933 samantha.c.krening@jpl.nasa.gov Charles H. Acton, Jr (818)-354-3869 chuck.acton@jpl.nasa.gov Boris V. Semenov (818)-354-8136 boris.semenov@jpl.nasa.gov Appendix List ------------------------------------------------------------------- Appendix 1 : Data Source Appendix 2 : Data Parsing Appendix 3 : Converting Time Tags from MJD to ET Appendix 4 : Reconstruction of Time tags Appendix 5 : Calculating Positions with Respect to Sun Appendix 6 : Numerical Differentiation for Velocities Appendix 7 : SPK Creation using MKSPK Appendix 8 : SPK Verification: Comparison with epgiotto.doc Data Appendix 9 : SPK Verification: Comparison with Planetary Ephemeris Appendix 10: SPK Verification: Comparison with Horizons Ephemeris Appendix 11: epgiotto.doc Appendix 1: Data Source ------------------------------------------------------------------- The position components were taken from 'Appendix A1: The Position Data File' in 'epgiotto'. Please see Appendix 11 for the contents of 'epgiotto'. The 'epgiotto' document can also be found at the PDS Small Bodies Node. The document is in the same volume as the data set ID given below for the DID data, but is in the ephemeris directory instead of the DID directory. DATA_SET_ID: GIO-C-DID-3-RDR-HALLEY-V1.0 VOLUME_ID: HAL_0025 The direct link to the ephemeris directory is given below. http://pdssbn.astro.umd.edu/volume/hal_0025/giotto/ephemris/ Appendix 2: Data Parsing ------------------------------------------------------------------- The data from the 'epgiotto' document is comprised of two parts: a control record and position data. The control record is the first two lines of the data. The position data are the remaining lines of the data. Each position record spans three lines. The first line of a position record contains the ephemeris time in a Modified Julian Date format in which 14 March 1986 00:00:00 ET = MJD 13221, the three vector components of Giotto with respect to the solar system barycenter (SSB), and the first component of Halley with respect to the SSB. The second line of the position record contains the last two components of Halley's position with respect to the SSB, and all of the components of Earth's position with respect to the SSB. The third line of each position record contains the vector components of the Sun with respect to the SSB. It was determined that all of these position components are in the FK4 reference frame. Please see the following for details: http://naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/req/frames.html First, the Position Data File appendix in 'epgiotto' was copied into a text file. The data were parsed using a perl script. The regular expression that extracted the data from the first two lines of each position record was: $line =~ m/(.{16})(.{16})(.{16})(.{16})(.{16})/; while the regular expression for the third line of each position record was: $line =~ m/(.{16})(.{16})(.{16})/; After extracting the data from the 'epgiotto' format, the data was saved into a semi-colon delimited text file. Appendix 3: Converting Time Tags from MJD to ET ------------------------------------------------------------------- The parsed, semi-colon delimited file containing the position data from 'epgiotto' was loaded into MATLAB. The time tags from the file can be converted to ephemeris seconds past the J2000 epoch using a few steps. First, both Julian days and the Giotto mission's form of Modified Julian days are in units of days. The Julian date of 14 March 1986 is greater than the MJD, so the difference between these two time systems is the JD of 14 March 1986 minus 13221, which is the MJD of 14 March 1986. Remember: 'epgiotto' gave a time reference of 14 March 1986 ET = 13221 MJD. diff_JD_MJD = (JD of 14 March 1986) - 13221 Once the difference in these time systems was calculated, it was used to calculate the Julian Date of every time in the raw data file. JD = time_data + diff_JD_MJD The Julian Date was converted to ET using the SPICE function cspice_str2et. The Julian Date of 14 March 1986 was calculated using the cspice_str2et and cspice_timout functions from SPICE, and str2num from MATLAB. Appendix 4: Reconstructing Time Tags ------------------------------------------------------------------- There are 27 data records per day given in the 'epgiotto' document. Each data record should be 3200 seconds apart, or 0.037037037037 days. The time tags in 'epgiotto' were rounded to five decimals in units of days, which caused erroneous results. The time tags were recreated in a non-rounded format in MATLAB using the following: reconstructed_time = 13212 : (1/27) : 13224.034 The reconstructed times were printed out in a rounded form that exactly matched the data in 'epgiotto' using the following: fprintf ( '%10.5f\n', reconstructed_time ) Since the rounded time tags were exactly reproduced and the 'epgiotto' document states that there are 27 data records per day, a more-precise reconstructed time was used to create the SPK. The 'reconstructed_time' equation above was used for verification. The time tags used to make the SPK file were made in ephemeris seconds past the J2000 epoch (ET). Using a time step of 3200 seconds eliminates the precision issue. First, convert the start time from a string to ET. et_start = cspice_str2et ( '1986 Mar 5 00:00:00 TDB' ) Then, find the end time by adding 12 days worth of seconds to the start time. et_end = et_start + 12 * 24 * 60 * 60 The reconstructed array of time in ET seconds starts at 'et_start', increments by 3200 seconds, and ends 12 days later at 'et_end'. reconstructed_et = et_start : 3200 : et_end To print this into a readable string, the following was used. pic = 'YYYY Mon DD HR:MN:SC.#### ::TDB (TDB)' time_strings = cspice_timout ( reconstructed_et, pic ) Appendix 5: Calculating Positions with Respect to Sun ------------------------------------------------------------------- The position data from 'epgiotto' were with respect to the solar system barycenter. The vector from the SSB to the Sun plus the vector from the Sun to another body equals the vector from the SSB to the other body. Using this geometry, the vectors of Giotto, Halley, and the Earth with respect to the Sun were calculated by subtracting the Sun/SSB vector from the body/SSB vector. An example of this is shown below for Halley. pos_Halley_Sun = pos_Halley_SSB - pos_Sun_SSB Appendix 6: Numerical Differentiation for Velocities ------------------------------------------------------------------- The 'epgiotto' document did not provide velocity data. The velocities were needed to create an SPK. MATLAB was used to calculate the velocities by numerically differentiating the positions. In the following example, the velocities of Halley with respect to the Sun are 'vel_Halley_Sun', the the positions of Halley with respect to the Sun are 'pos_Halley_Sun', the ephemeris time in seconds past J2000 that corresponds to each position vector is 'time_ET', and 'diff' is a function in MATLAB. vel_Halley_Sun = diff(pos_Halley_Sun,1,1) ./ diff(time_ET) There are 325 position records. Numerically differentiating in this manner means that 324 velocity vectors were calculated. The last position record was omitted from the SPK since there is not a corresponding velocity. These 324 records of ephemeris time, position vectors, and velocity vectors were written to separate, semi-colon delimited text files for Giotto, Halley, and Earth. The picture used to output the ephemeris time was: picture = 'YYYY Mon DD HR:MN:SC.#### ::TDB (TDB)' Each line of the output files has ephemeris time in the first column, the position components in columns 2 - 4, and velocity components in columns 5 - 7. Appendix 7: SPK Creation using MKSPK ------------------------------------------------------------------- This SPK was created in three steps using the MKSPK command line utility. $ mkspk -setup spk_setup_giotto.txt $ mkspk -setup spk_setup_halley.txt $ mkspk -setup spk_setup_earth.txt For more information on the MKSPK utility, please visit the NAIF website at: http://naif.jpl.nasa.gov/naif/utilities.html The contents of the setup file for the Giotto segment are below. The setup files for Halley and Earth were the same, except for different input data files and sement IDs. Giotto MKSPK setup file (spk_setup_giotto.txt): -------------------------------------------------- INPUT_DATA_TYPE = 'STATES' OUTPUT_SPK_TYPE = 9 OBJECT_NAME = 'GIOTTO' CENTER_NAME = 'SUN' REF_FRAME_NAME = 'FK4' PRODUCER_ID = 'Samantha Krening, JPL' DATA_ORDER = 'epoch x y z vx vy vz' DATA_DELIMITER = ';' LEAPSECONDS_FILE = 'naif0009.tls' POLYNOM_DEGREE = 5 INPUT_DATA_FILE = 'giotto_input_states.txt' OUTPUT_SPK_FILE = 'giotto_spk_19860305_19860317.bsp' SEGMENT_ID = 'giotto_states_1986Mar5_1986Mar17' APPEND_TO_OUTPUT = 'YES' Appendix 8: SPK Verification: Comparison with epgiotto.doc Data ------------------------------------------------------------------- When the position data in this SPK was compared to the data in 'epgiotto', the two agreed with each other within 3E-8 in the first axis, and within 1E-8 in the second and third axes. This shows that the process of creating the SPK was internally valid. It does not show external validity, so the reference frame, and precision and accuracy of the initial data are not proven by this step. In the "Note added to explanation" section of 'epgiotto', it states that the data are consistent with a time of closest approach of 1986/03/14 00:02:59.5 UTC and a miss distance of 629 km. In March 1986, another analysis estimated the time of closest approach of 1986/03/14 00:03:00.4 UTC +/- 2 s (1-sigma) and 610 km +/- 40 km (1-sigma)). Another analysis using HMC data had best estimates of 1986/03/14 00:03:01.84 UTC +/- 0.2 s and 596 km +/- 2 km. Please see the 'epgiotto' document for details. To calculate the time and distance of the Giotto's closest approach to Halley, several SPICE functions were used. First, to find the time of closest approach, the function 'cspice_gfdist' was used. confine_window = cspice_wninsd( et_start, et_end ); closest_approach_time = cspice_gfdist ( 'Halley', 'None', 'Giotto', ... 'ABSMIN', 0, 0, 60, 100, ... confine_window ) To calculate the distance between Halley and Giotto at the time of closest approach, the SPICE function 'cspice_spkpos' was used. pos_halley_giotto_closest_none = cspice_spkpos ( 'Halley', ... closest_approach_time(1), ... 'FK4', 'None', 'Giotto' ) The results from these calculations are that the closest approach occured at 1986 Mar 14 00:02:59.50342 UTC at a distance of 629.2 km. This distance is from the center of the Giotto probe to the center of Halley, so the true miss distance would be less. The geometry represented by this SPK matches very well with the 'epgiotto' document, is within the 1-sigma range given by the analysis from March 1986, and matches with the HMC analysis as well as the 'epgiotto' document does. Appendix 9: SPK Verification: Comparison with Planetary Ephemeris ------------------------------------------------------------------- Using the SPKDIFF utility from SPICE, the planetary ephemeris kernel 'de421.bsp' was compared to this SPK. $ spkdiff -b1 earth -c1 sun -r1 fk4 -k naif0009.tls -b 1986-03-06 -e 1986-03-16 -s 30 -t stats de421.bsp giotto_19860305_19860317.bsp The maximum absolute difference of position of the down track direction is 5.77 km, the radial direction is 0.05 km, and the normal direction is 13.38 km. Using the SPKDIFF utility from SPICE, the older planetary ephemeris kernel 'de118.bsp' was compared to this SPK. The maximum absolute difference of position of the down track direction is 4.34 km, the radial direction is -0.021 km, and the normal direction is 1.87 km. This SPK matches very well with the older planetary ephemeris 'de118.bsp', and fairly well with the more accurate planetary ephemeris 'de421.bsp'. This SPK is fairly precise compared to the ephemeris available in 1986, but not as accurate as today's ephemeris. Appendix 10: SPK Verification: Comparison with Horizons Ephemeris ------------------------------------------------------------------- Using the SPKDIFF utility from SPICE, the expected ephemeris of Halley provided by the Horizons project was compared to this SPK. For more information on Horizons, please visit http://ssd.jpl.nasa.gov/x/spk.html. $ spkdiff -b1 halley -c1 sun -r1 fk4 -k naif0009.tls -b 1986-03-06 -e 1986-03-16 -s 30 -t stats halley_horizons.bsp giotto_19860305_19860317.bsp The maximum absolute difference of Halley's position from Horizons and this SPK is approximately 116 km in the down track direction, 107 km in the radial direction, and 100 km in the normal direction. The formal statistical uncertainties for the Halley Horizons data (1P/Halley solution J863/77 based on measurement uncertainties of Halley from 1835-1994) are about +- 120 km in the down track direction, +-75 km in the radial direction, and +- 20 km in the normal direction for a 3-sigma estimate. This SPK's down track component for Halley is within the 3-sigma range. The radial direction is a little larger than the 3-sigma range, and the normal direction is larger than the 3-sigma range. The statistical uncertainty of the data in 'epgiotto' was not provided, but it is a decent assumption that it is on the same order as the Halley Horizons solution from 1986. The differences between the Halley Horizons ephemeris and this SPK are on the expected order. Appendix 11: Appendix: epgiotto.doc ------------------------------------------------------------------- Only the body of the document and the A1 Appendix from 'epgiotto' are included here. Please see the 'epgiotto' document for more details. --------------------------------------------------------- ***** File EPGIOTTO.DOC GIOTTO EXPERIMENTER SUPPORT DATA. I. Abstract: A new experimenter support tape (EXSUP5) was made available to investigating teams and was provided for this disk by Trevor Morley. The Giotto Ephemeris on that tape represented the most recent predicted orbit. The Comet Halley orbit corresponded to the latest ephemeris estimated in ESOC 17.03.86. The documentation enclosed is adapted from the documentation for tape EXSUP5, which updated EXSUP4 with the following amendments:- a detailed tape layout, a sample listing of part of the position data file, and a sample of position/velocities. In addition, for EXSUP5, the subroutine PETRA, used to compute Kepler orbits at the home sites of experimenters, was contained on the tape and is provided here as a source listing found in appendix A4. II. Table of Contents: 1. Introduction. 2. Description of Tape EXSUP5. 3. The Position Data File. 3.1 The Control Record. 3.2 The Position Data Record. 4. The Interface/Auxiliary Software. 4.1 Subroutine GIODAT ( interface routine to the sequential formatted Position Data File ). 4.2 Subroutine TRAVEL ( generation of experimenter support data ). 4.3 Subroutine PETRA ( compute Kepler Orbits ). 5. Station Coordinates. 5.1 General. 5.2 Table of Station Coordinates. Appendix: A1 The Position Data File A2 Source listing of subroutine GIODAT. A3 Source listing of subroutine TRAVEL. A4 Source listing of subroutine PETRA. 1. Introduction. In this document, the Position Data, the interface routine to this data and the software for generation of experimenter support data, will be described. To ensure a safe 'transport' of the Position Data and to limit potential conversion problems between different computers it has been decided to deliver this as a sequential access file containing formatted data. In addition to this data file the following interface/auxiliary software can be found on the tape:- Software for:- - Acquisition of Position Data from the sequential file and determination of the approximate velocities derived from the position data. - Generation of Giotto experimenter support data ( signal travel time, etc. ). In order to reduce the processing time, the use of a binary direct access file for the Position Data is recommended. Software for generation of a direct access file from the formatted sequential file, and for acquisition of Position Data from this, is not included in this export package. Please note that the subroutine PETRA is now enclosed in this export package. See section 4.3 and Appendix A4. 2. Description of tape EXSUP5 Tape EXSUP5 is not described, since the Position data file and subroutine listings are included in the Appendices. 3. The Position Data File. In this section the data layout for the position data and control data for this will be described. 3.1 The Control Record. The logical Control Record consists of two physical records each totaling 80 characters per line as shown below by :- Variable Format Description -------------------------------------------------------- IY I5 Year in which the tape was generated. MO I5 Ditto for month. DA D16.10 Ditto for day. NS I5 Size of Position Record in characters. NR I5 Number of logical Position Records. --------------------------------------------------------- ET1 D16.10 Earliest Epoch - MJD ( E.T ) ET2 D16.10 Latest Epoch - MJD ( E.T ) SUTC D16.10 MJD ( E.T ) at which UTC jumps. ETUTC1 D16.10 E.T - UTC before SUTC. ETUTC2 D16.10 E.T - UTC after SUTC. ----------------------------------------------------------- Note: SUTC and ETUTC2 are T.B.D at present. SUTC is preset to mjd 13230 ( after latest epoch on file ). ETUTC2 is preset to ETUTC1. 3.2 The Position Data Record. The logical Position Data Record consists of three physical records each totaling 80 characters. Each logical Position Record is shown below by -: Variable Format Description ------------------------------------------------------------------------ ET D16.10 Epoch = MJD ( E.T ) PG(1) D16.10 Component of position vector of the Giotto probe at ET. PG(2) D16.10 Component of position vector of the Giotto probe at ET. PG(3) D16.10 Component of position vector of the Giotto probe at ET. PH(1) D16.10 Component of position vector of the Giotto for Halley's comet. ------------------------------------------------------------------------ PH(2) D16.10 Component of position vector of the Giotto for Halley's comet. PH(3) D16.10 Component of position vector of the Giotto for Halley's comet. PE(1) D16.10 Component of position vector of the Giotto for Earth. PE(2) D16.10 Component of position vector of the Giotto for Earth. PE(3) D16.10 Component of position vector of the Giotto for Earth. ------------------------------------------------------------------------ PS(1) D16.10 Component of position vector of the Giotto for Sun. PS(2) D16.10 Component of position vector of the Giotto for Sun. PS(3) D16.10 Component of position vector of the Giotto for Sun. ------------------------------------------------------------------------ Note: Reference frame: M.E.S of 1950. Origin = solar system barycenter. Position units: km Time units: days The Position Data File is stored in Appendix A1. 4. Interface/Auxiliary Software. In this section the auxiliary software found on the tape will be described. 4.1 Subroutine GIODAT ( interface routine to the sequential formatted Position Data File). Input variable: TUTC : Universal coordinated time since 1950.0 in days. Output variables: PVG(1-3) : Position of the Giotto probe at time TUTC ( units: km ). PVG(4-6) : Approximate velocity of the Giotto probe at time TUTC ( units: km/s ). PVH(1-3) : PVH(4-6) : Ditto for Halley's comet. PVE(1-3) : PVE(4-6) : Ditto for Earth. PVS(1-3) : PVS(4-6) : Ditto for Sun. The positions will be acquired from the sequential file using quadratic interpolation. For the Position Records on the file a time step size was selected which will give an accuracy better than 1 sigma-error limit. The approximate velocities are derived from the position data. A source listing of subroutine GIODAT can be seen in Appendix A2. 4.2 Subroutine TRAVEL ( generation of Experimenter Support Data ). Subroutine TRAVEL provides the signal travel time between a station of Earth and the Giotto S/C as well as position of station and S/C at the times of signal reception and transmission. The states of the Giotto S/C, the Earth and the sun are acquired from the formatted Position Data File on unit 7 ( described in section 3 ) via subroutine GIODAT (described in section 4.1 ). The station coordinates are computed without precession. Thus an accuracy of approx. 1 msec for the travel times computed can be expected. Input variables: TUTC : Signal reception time ( Universal Coordinated Time since 1950.0 in days ). S(3) : Cartesian Coordinates of station in the body fixed system at Epoch TUTC ( units: km ). Output variables: DTG : Signal travel time ( sec ) Giotto S/C - Station P(1-3): Position of station at TUTC in Heliocentric EME50 ( units: km ). G(1-3): Ditto for the Giotto S/C at TUTC-DTG. See Appendix A3 for a source listing of subroutine TRAVEL. 4.3 Subroutine PETRA ( computing of Kepler Orbits ). About one day prior to the encounter, position and velocity data for the relevant bodies as well as misc. data, was sent to the experimenters. Subroutine PETRA can be used to compute a Kepler orbit, thus obtaining position/velocities at the Encounter Epoch. See Appendix A4 for a source listing. 5. The Station Coordinates. In this section some general comments on station coordinates will be given as well as a table of coordinates for stations relevant to the Giotto mission. 5.1 General. Section 5.2 contains a table with the coordinates of some stations that are involved in the Giotto mission. These coordinates are needed in the computation of the signal travel times between the Giotto S/C and the station ( see also subroutine TRAVEL ). The coordinates are Cartesian position vectors ( X,Y,Z ) in the Body Fixed System. The X-Y plane of this system is the equatorial plane of the Earth with the X-axis going through the Greenwich Meridian. 5.2 Table of Station Coordinates. Station name X ( km ) Y ( km ) Z ( km ) Carnarvon -2328 5302 -2666 Tidbinbilla -4461 2682 -3675 Madrid 4847 -370 4117 Goldstone -2350 -4652 3666 ********************************************************************** Note added to explanation: The orbital data applicable to P/Halley encounter were set up using exactly the same ESOC orbit files as were used at the time for providing the data tapes to the experimenters. However, for your purposes, I have increased the number of steps per day (to 27) and restricted the interval to 5 - 17 March. So that there is no misunderstanding concerning our definition of MJD: 14 March 1986 = MJD 13221. Logically speaking, the data set consists of one header record and 325 data records. The total number of physical records is thus 977, each 80 bytes long. Use of the interpolation routine GIODAT will result in small differences compared with the data on the original ESOC files. I have tested this over the interval and find the average differences to be 7 km for both the spacecraft and the Earth, 10 km for the comet and only 3 m for the Sun. Around the time of closest approach, because of the way the ESOC files were set up, these differences are much smaller than the average, being only a fraction of a km (negligible for the Sun). To give you a better idea of the accuracy of the data, they are consistent with a time of closest approach of 1986/03/14 00:02:59.5 UTC and a miss distance of 629 km. (In March 1986 we did some detailed analysis, not reflected by the data on the orbit files, and made a best estimate of 1986/03/14 00:03:00.4 UTC +/- 2 s (1-sigma) and 610 km +/- 40 km (1-sigma)). According to W. Curdt et al. in A & A 191, L1-L3, 1998, using the HMC data the best estimates are 1986/03/14 00:03:01.84 UTC +/- 0.2 s and 596 km +/- 2 km. Trevor Morley ESOC ************************************************************************* Appendix A1 The Position Data File 1992 40.3000000000D+01 208 325 0.1321200000D+050.1322400000D+050.1323000000D+050.6387037038D-030.6387037038D-03 0.1321200000D+05-.9601636683D+08-.7906490418D+08-.3867273476D+08-.4678284441D+08 -.9843252167D+08-.3689730827D+08-.1427640334D+090.3939800010D+080.1707778408D+08 -.4190252668D+060.1003521211D+070.4287756995D+06 0.1321203704D+05-.9596091678D+08-.7914441085D+08-.3870579532D+08-.4692866173D+08 -.9843528587D+08-.3693827435D+08-.1427925150D+090.3931374281D+080.1704125398D+08 -.4190536459D+060.1003491221D+070.4287636026D+06 0.1321207407D+05-.9590541005D+08-.7922391260D+08-.3873873515D+08-.4707443852D+08 -.9843796341D+08-.3697920787D+08-.1428209374D+090.3922946927D+080.1700471679D+08 -.4190820230D+060.1003461230D+070.4287515053D+06 0.1321211111D+05-.9584984160D+08-.7930336248D+08-.3877164966D+08-.4722017473D+08 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