| SPKDIFF User's Guide |
Table of ContentsSPKDIFF User's Guide Abstract Summary Usage Specifying Options vs. Defaults Options/Defaults for Body, Center, and Frame Options/Defaults for Comparison Time Boundaries and Step Options/Defaults for Output Report Type Option for Specifying Additional Kernels Output Report Types Usage display Comparison Information Header Basic Report (no ``-t'' option or ``-t basic'') View Frame Statistics Report (``-t stats'') Difference Dump Report (``-t dump'') View Frame Difference Dump Report (``-t dumpvf'') Troubleshooting Examples Do Two SPK Files Provide the Same Trajectory for a Spacecraft? Do SPK files Differ Enough to Matter? What Is the Down Track Timing Error? How Does the Difference Change with Time? SPKDIFF User's Guide
Abstract
Summary
Usage
> spkdiff [options] <first SPK file> <second SPK file>
where options are:
-b1 <first body name or ID>
-c1 <first center name or ID>
-r1 <first reference frame name>
-b2 <second body name or ID>
-c2 <second center name or ID>
-r2 <second reference frame name>
-k <other kernel file name(s)>
-b <interval begin time>
-e <interval end time>
-s <time step in seconds>
-n <number of states: 2 to 1000000 (default: 1000)>
-f <output time format (default: TDB seconds past J2000)>
-t <report type: basic|stats|dump|dumpvf (default: basic)>
The names of the two SPK files to be compared are required while none of
the other options are. The order of options and case of the option keys
are not significant. The values provided after the option keys must be
separated from keys by one or more spaces. Un-recongnized options are
not specifically checked for; instead they are treated as continuation
of the value provided with the preceeding reconginized option.
Either physical object names or NAIF IDs can be provided using the ``-b1'', ``-c1'', ``-b2'', and ``-c2'' options to identify the bodies and centers to be used for each of the two SPK files. If the names provided using these options do not belong to the set of name/ID mappings built into SPICE, a text kernel(s) containing name/ID mappings for these names must be provided using the ``-k'' option. The reference frame names provided using the ``-r1'' and ``-r2'' options must be for any of the frames built into SPICE; otherwise a frame kernel(s) defining these frames must be provided using the ``-k'' option. The comparison interval begin and end times specified using the ``-b'' and ``-e'' options must be in any of the formats accepted by SPICE STR2ET routine (see STR2ET header for details). If one or both of these times are provided, the name of an LSK file must also be provided using the ``-k' option. The output time format to be used in ``dump'' reports, provided using the ``-f'' option must be given in any of the forms acceptable to the SPICE TIMOUT routine (see TIMOUT header for details). Specifying Options vs. Defaults
Options/Defaults for Body, Center, and Frame
This set of simple rules determines which body, center, and frame combination SPKDIFF uses when calling SPKGEO for each of the two SPK files, given a particular set of options and defaults determined by examining the data in the SPK files. The rules for picking bodies to be used in calls to SPKGEO to sample states from the SPK files are:
Options/Defaults for Comparison Time Boundaries and Step
As with the body, center, frame combinations, in some cases no command line options defining the comparison window boundaries and time step need to be specified because the combination of defaults picked by SPKDIFF by examining the SPK files and using internal parameters produces the desired result. In other cases, though, specifying one or both comparison window end points and/or the time step on the command line may be required to perform a comparison only over a time period of interest or get a more ``refined'' result by using a smaller time step. This set of rules determines which comparison window begin and end times SPKDIFF uses given a particular set of options and defaults determined by examining the data in the files. It is important to note that the default time coverage information is obtained from the SPK files using the corresponding body, center, and frame combinations provided on the command line and/or determined earlier from the files.
A few scenarios below illustrate when some or all of the options specifying the comparison time window and time step can be omitted and when they should be provided to achieve the desired result:
Options/Defaults for Output Report Type
If the ``-t'' option is omitted or if it is followed by the value ``basic'', the program generates a ``Basic Report'' showing only the absolute and relative maximum and average differences in magnitude of position and velocity vectors. This type of output is useful for a quick assessment of whether the two SPK files are different and finding the maximum magnitude of this difference. If the ``-t'' option is followed by the value ``stats'' the program generates a ``View Frame Statistics Report'' including a set of values resulting from statistical analysis of the state differences rotated into the view frame -- +X down track along velocity vector, +Y normal to the orbit plane, computed as the cross product of position and velocity vectors, and +Z in the orbit plane, completing the right handed frame -- based on the state computed from the first SPK file. Among values included in this report are the average and RMS view frame components of the differences as well as the view frame components for maximum relative and maximum absolute differences. This report is useful for obtaining a more useful assessment of the differences between trajectories, for which using the view frame is appropriate. If the ``-t'' option is followed by the value ``dump'' the program generates a ``Difference Dump Report'' containing a table with time tagged differences between individual states computed from the two SPK files. This report is useful for subsequent plotting of the difference between trajectories over time. If the ``-t'' option is followed by the value ``dumpvf'' the program generates a ``View Frame Difference Dump Report'' containing a table with time tagged differences between individual states computed from the two SPK files, rotated into the view frame based on states computed from the first SPK file. This report is useful for plotting of the difference between trajectories expressed in the view frame, as a function of time. Each of these reports is described in detail in the section ``Output Report Types'' later in this User's Guide. Option for Specifying Additional Kernels
The set of other kernels may include any number of SPK files as long as these additional SPK files do not provide enough data for computing states anywhere within the comparison window for the body, center, frame combinations applicable to either of the SPK files to be compared. This restriction is important to ensure that the states being compared are indeed computed using the data from the two SPK files of interest but not from the additional SPK files provided to support the program run. There are some special cases when a kernel(s) of a particular type must be provided in order for SPKDIFF to proceed. Among such cases are:
Output Report Types
Usage display
spkdiff -- Version 1.0.0, April 25, 2006 -- Toolkit Version N0060
spkdiff computes differences between geometric states obtained from
two SPK files and either displays these differences or shows
statistics about them (see the User's Guide for more details). The
program usage is:
% spkdiff [options] <first SPK file> <second SPK file>
Options are shown below. Order and case of keys are not
significant. Values must be space-separated from keys, i.e.
'-n 10', not '-n10'.
-b1 <first body name or ID>
-c1 <first center name or ID>
-r1 <first reference frame name>
-b2 <second body name or ID>
-c2 <second center name or ID>
-r2 <second reference frame name>
-k <other kernel file name(s)>
-b <interval start time>
-e <interval stop time>
-s <time step in seconds>
-n <number of states: 2 to 1000000 (default: 1000)>
-f <output time format (default: TDB seconds past J2000)>
-t <report type: basic|stats|dump|dumpvf (default: basic)>
Comparison Information Header
# # Comparison of N_POINTS 'FRAME1_NAME'-referenced geometric states # # of 'BOD1_NAME' (BOD1_ID) relative to 'CEN1_NAME' (CEN1_ID) # from SPK 'SPK1_NAME' # # with N_POINTS 'FRAME2_NAME'-referenced geometric states # # of 'BOD2_NAME' (BOD2_ID) relative to 'CEN2_NAME' (CEN2_ID) # from SPK 'SPK2_NAME' # # evenly-spaced with STEP_SECONDS second (STEP_DDHRMNSC) step size # within the time interval # # from 'BEGIN_TIME' (BEGIN_ET_SEC TDB seconds) # to 'END_TIME' (END_ET_SEC TDB seconds) # # using additional data from these kernels # # KERNEL_LIST #where
Note that each line of the ``Comparison Information Header'' has
#as the first character. This allows common plotting programs, such as GNUPLOT, to skip these header lines when plotting the ``dump''-type reports generated by SPKDIFF. Basic Report (no ``-t'' option or ``-t basic'')
Relative differences in state vectors:
maximum average
Position: n.nnnnnnnnnnnnnE-nn n.nnnnnnnnnnnnnE-nn
Velocity: n.nnnnnnnnnnnnnE-nn n.nnnnnnnnnnnnnE-nn
Absolute differences in state vectors:
maximum average
Position (km): n.nnnnnnnnnnnnnE-nn n.nnnnnnnnnnnnnE-nn
Velocity (km/s): n.nnnnnnnnnnnnnE-nn n.nnnnnnnnnnnnnE-nn
where ``n.nnnnnnnnnnnnnE-nn'' are the relative and absolute maximum and
average differences in magnitude of position and velocity vectors.
It is important to remember that these maximum values are picked from the sets of states sampled from the SPK files within the given/default comparison windows using the given/default time step, rather than by a true search for the maximum within the window. Thus any change in the window begin and end time and/or time step will result in a different set of states being sampled at different times and then used in the comparison, leading to different maximum and average values appearing in the report. View Frame Statistics Report (``-t stats'')
The view frame into which the differences between states are rotated for statistical analysis is based on states computed using the first SPK file and is defined as follows:
1) Average components of position difference vectors in view
frame coordinates:
1a) Down track (km): n.nnnnnnnnnnnnnn
1b) In orbit plane (km): n.nnnnnnnnnnnnnn
1c) Normal to orbit plane (km): n.nnnnnnnnnnnnnn
1d) Average delta time down track (sec): n.nnnnnnnnnnnnnn
2) Average |components| of position difference vectors in view
frame coordinates:
2a) Down track (km): n.nnnnnnnnnnnnnn
2b) In orbit plane (km): n.nnnnnnnnnnnnnn
2c) Normal to orbit plane (km): n.nnnnnnnnnnnnnn
2d) Average |delta time| down track (sec): n.nnnnnnnnnnnnnn
3) RMS of position difference vectors in view frame coordinates:
3a) Down track (km): n.nnnnnnnnnnnnnn
3b) In orbit plane (km): n.nnnnnnnnnnnnnn
3c) Normal to orbit plane (km): n.nnnnnnnnnnnnnn
3d) RMS delta time down track (sec): n.nnnnnnnnnnnnnn
4) Components of the position difference vector in view frame
coordinates for the states with the MAXIMUM RELATIVE
difference in position:
4a) Down track (km): n.nnnnnnnnnnnnnn
4b) In orbit plane (km): n.nnnnnnnnnnnnnn
4c) Normal to orbit plane (km): n.nnnnnnnnnnnnnn
4d) Delta time down track (sec): n.nnnnnnnnnnnnnn
4e) Epoch (TDB, seconds past J2000): nnnnnnnnn.nnnnnn
4f) Epoch (TDB, calendar format): YYYY-MON-DD-HR:MN:SC
5) Components of the position difference vector in view frame
coordinates for the states with the MAXIMUM ABSOLUTE
difference in position:
5a) Down track (km): n.nnnnnnnnnnnnnn
5b) In orbit plane (km): n.nnnnnnnnnnnnnn
5c) Normal to orbit plane (km): n.nnnnnnnnnnnnnn
5d) Delta time down track (sec): n.nnnnnnnnnnnnnn
5e) Epoch (TDB, seconds past J2000): nnnnnnnnn.nnnnnn
5f) Epoch (TDB, calendar format): YYYY-MON-DD-HR:MN:SC
In addition to the average, average of absolute values, RMS, maximum
relative, and maximum absolute down track, in orbit plane and normal to
orbit plane components, the program includes in each category a delta
time down track in seconds. For the maximum relative and maximum
absolute differences the report also provides the times -- as calendar
format TDB and TDB seconds past J2000 -- at which these states were
computed.
As with the basic report the statistically determined maximum values are based on the sets of states sampled from the SPK files within the given/default comparison windows using the given/default time step rather than by a true search for the maximum within the window. Thus any change in the window begin and end time and/or time step will result in a different set of states being sampled at different times and then used in the comparison, leading to different maximum and average values appearing in the report. While this type of report can be requested for any combination of body, center, and frame, for some of them the notion of the view frame would not be applicable because the motion of the body with respect to the center would be too different from the ``normal'' orbital motion for which using the view frame makes the most sense. In such cases this report may contain meaningless or even incomprehensible numbers. There is also a possibility that the view frame simply cannot be constructed for one or more states computed from the first SPK file because position and velocity components of this state are linearly dependent. In such cases the program reports this fact and does not generate the report. To facilitate parsing, each of the items included in this report is provided on a separate line tagged with a distinct item ``identifier'' (1a, 2b, 5d, etc.), with the value appearing as the last word on the line. Difference Dump Report (``-t dump'')
# time, (x1-x2), (y1-y2), (z1-z2), (vx1-vx2), (vy1-vy2), (vz1-vz2) TIME DELTA_X DELTA_Y DELTA_Z DELTA_VX DELTA_VY DELTA_VZ TIME DELTA_X DELTA_Y DELTA_Z DELTA_VX DELTA_VY DELTA_VZ ... ... ... ... ... ... ... TIME DELTA_X DELTA_Y DELTA_Z DELTA_VX DELTA_VY DELTA_VZThe first line of the report ``names'' the items provided in the table. As for the lines of the ``Comparison Information Header'' that this line immediately follows, it is prefixed using the
#character in order to be ignored by common plotting utilities. Each of the subsequent lines contains seven space-delimited items -- a time tag in the format specified using the ``-f'' option (if ``-f'' was not provided the time tag is the number of TDB seconds past J2000) followed by the X, Y, Z, Vx, Vy, and Vz components of the difference between the state computed from the first SPK file and the state computed from the second SPK file. The position component differences are provided in kilometers, the velocity component differences in kilometers per second. All differences are printed in scientific notation, +n.nnnnnnnnnnnnnE+nn. View Frame Difference Dump Report (``-t dumpvf'')
# time, down_track_p_diff, normal_to_plane_p_diff, in_plane_p_diff, down_track_v_diff, normal_to_plane_v_diff, in_plane_v_diff TIME DELTA_DT DELTA_NTP DELTA_IP DELTA_VDP DELTA_VNTP DELTA_VIP TIME DELTA_DT DELTA_NTP DELTA_IP DELTA_VDP DELTA_VNTP DELTA_VIP ... ... ... ... ... ... ... TIME DELTA_DT DELTA_NTP DELTA_IP DELTA_VDP DELTA_VNTP DELTA_VIPThe first line of the report (which is shown as two lines above to fit into the width of the page) ``names'' the items provided in the table. As for the lines of the ``Comparison Information Header'' that this line immediately follows, it is prefixed using the
#character in order to be ignored by common plotting utilities. Each of the subsequent lines contains seven space-delimited items -- a time tag in the format specified using the ``-f'' option (if the ``-f'' option was not provided the time tag is the number of TDB seconds past J2000) followed by the down track, normal to orbit plane, in orbit plane, down track velocity, normal to orbit plane velocity, and in orbit plane velocity components of difference between the state computed from the first SPK file and the state computed from the second SPK file, rotated into the view frame. The position component differences are provided in kilometers, the velocity component differences in kilometers per second. All differences are printed in scientific notation, +n.nnnnnnnnnnnnnE+nn. While this type of report can be requested for any combination of body, center, and frame, for some of them the notion of the view frame would not be applicable because the motion of the body with respect to the center would be too different from the ``normal'' orbital motion for which using the view frame makes the most sense. In such cases this report may contain meaningless or even incomprehensible numbers. There is also a possibility that the view frame simply cannot be constructed for one or more states computed from the first SPK file because position and velocity components of this state are linearly dependent. In such cases the program reports this fact and does not generate the report. Troubleshooting
Examples
Do Two SPK Files Provide the Same Trajectory for a Spacecraft?
In most cases spacecraft SPK files that are checked for ``sameness'' have the same attributes -- storing spacecraft trajectory with respect to the same center in the same frame -- and need to be compared during the whole period of overlap between their coverages. Therefore, SPKDIFF can be run with ``bare minimum'' inputs -- just the names of the SPK files -- and be allowed to use defaults obtained by examining the files and/or hard-coded into the program. Below, SPKDIFF is invoked to answer this question for a regular, reconstructed OD solution SPK file and a merged reconstructed SPK file for Mars Global Surveyor. With just the SPK file names provided on the command line:
> spkdiff spk_m_060508_OD32021-32092_rec_V1.bsp mgs_map_rec.bspthe program produces the following output:
#
# Comparison of 1000 'J2000'-referenced geometric states
#
# of 'MGS' (-94) relative to 'MARS BARYCENTER' (4)
# from SPK 'spk_m_060508_OD32021-32092_rec_V1.bsp'
#
# with 1000 'J2000'-referenced geometric states
#
# of 'MGS' (-94) relative to 'MARS BARYCENTER' (4)
# from SPK 'mgs_map_rec.bsp'
#
# evenly-spaced with 507.387 second (0d 00h 08m 27.387s) step size
# within the time interval
#
# from '2006 MAY 08 15:22:00.000 TDB' (200373720.0 TDB seconds)
# to '2006 MAY 14 12:10:00.000 TDB' (200880600.0 TDB seconds)
#
Relative differences in state vectors:
maximum average
Position: 0.0000000000000E+00 0.0000000000000E+00
Velocity: 0.0000000000000E+00 0.0000000000000E+00
Absolute differences in state vectors:
maximum average
Position (km): 0.0000000000000E+00 0.0000000000000E+00
Velocity (km/s): 0.0000000000000E+00 0.0000000000000E+00
The fact that all differences in the output are zero means that both
files provide the same trajectory for MGS relative to Mars Barycenter
for the whole period of overlap (which should be the case because the
regular reconstructed OD solution SPK file is one of the files that was
used to create the merged SPK file).
Do SPK files Differ Enough to Matter?
As in the previous example, the SPK files that are compared probably have the same attributes -- storing the spacecraft trajectory with respect to the same center in the same frame -- but the comparison window of interest is likely to be narrower than the whole overlap between the file coverages (for example only during closest approach or during a time window around pericenter). Thus, SPKDIFF should be allowed to get most defaults from the files but should be provided with the comparison window begin and end times on the command line. Below, SPKDIFF is run to check how different the reconstructed MGS trajectories provided by the Mars Global Surveyor Navigation team and the JPL Gravity Group are during the 30 minute window from 2001 APR 04 02:30 to 03:30 UTC (a part of illuminated portion of the MGS orbit 9266). SPKDIFF, invoked with the comparison window boundaries, LSK file name (to support conversion of boundary UTC times to ET), and SPK file names:
> spkdiff -b 2001 APR 04 02:30 -e 2001 APR 04 03:00 \
-k naif0008.tls \
mgs_ext2.bsp mgs_ext2_ipng_mgs75d.bsp
produces the following output:
#
# Comparison of 1000 'J2000'-referenced geometric states
#
# of 'MGS' (-94) relative to 'MARS BARYCENTER' (4)
# from SPK 'mgs_ext2.bsp'
#
# with 1000 'J2000'-referenced geometric states
#
# of 'MGS' (-94) relative to 'MARS BARYCENTER' (4)
# from SPK 'mgs_ext2_ipng_mgs75d.bsp'
#
# evenly-spaced with 1.801 second (0d 00h 00m 01.801s) step size
# within the time interval
#
# from '2001 APR 04 02:30' (39623464.185 TDB seconds)
# to '2001 APR 04 03:00' (39625264.185 TDB seconds)
#
# using additional data from these kernels
#
# 'naif0008.tls'
#
Relative differences in state vectors:
maximum average
Position: 1.5585888672802E-05 7.4593186410629E-06
Velocity: 1.7161324644915E-05 1.4552469606438E-05
Absolute differences in state vectors:
maximum average
Position (km): 5.9196225803226E-02 2.8215203092988E-02
Velocity (km/s): 5.7990372644310E-05 4.9083689420832E-05
The report shows that the maximum difference in position is about 60
meters, which, given uncertainties in other data (timing, attitude,
etc), may be deemed unimportant in processing data from a low resolution
instrument.
What Is the Down Track Timing Error?
Below, SPKDIFF is run to determine the down track timing error during the 10 minute window around pericenter of the MEX orbit 3040 ( 2006 MAY 23 21:46 ... 21:56 UTC) for trajectories provided by long-term and short-term predicted SPK files. SPKDIFF, invoked with the comparison window boundaries, LSK file name (to support conversion of boundary UTC times to ET), report type ``stats'', and SPK file names:
> spkdiff -b 2006 MAY 23 21:46 -e 2006 MAY 23 21:56 \
-k NAIF0008.TLS \
-t stats
ORMM__060501000000_00253.BSP ORMF_______________00185.BSP
produces the following output:
#
# Comparison of 1000 'J2000'-referenced geometric states
#
# of 'MARS EXPRESS' (-41) relative to 'MARS' (499)
# from SPK 'ORMM__060501000000_00253.BSP'
#
# with 1000 'J2000'-referenced geometric states
#
# of 'MARS EXPRESS' (-41) relative to 'MARS' (499)
# from SPK 'ORMF_______________00185.BSP'
#
# evenly-spaced with 0.600 second (0d 0h 0m 0.600000s) step size
# within the time interval
#
# from '2006 MAY 23 21:46' (201692825.18509 TDB seconds)
# to '2006 MAY 23 21:56' (201693425.18509 TDB seconds)
#
# using additional data from these kernels
#
# 'NAIF0008.TLS'
#
1) Average components of position difference vectors in view
frame coordinates:
1a) Down track (km): 30.552115284475
1b) In orbit plane (km): 1.2710676287493
1c) Normal to orbit plane (km): -0.011807645604121
1d) Average delta time down track (sec): 7.1913943821391
2) Average |components| of position difference vectors in view
frame coordinates:
2a) Down track (km): 30.552115284475
2b) In orbit plane (km): 1.2710676287493
2c) Normal to orbit plane (km): 0.011807645604121
2d) Average |delta time| down track (sec): 7.1913943821391
3) RMS of position difference vectors in view frame coordinates:
3a) Down track (km): 30.553065680244
3b) In orbit plane (km): 1.2720138468831
3c) Normal to orbit plane (km): 0.012788802634391
3d) RMS delta time down track (sec): 7.1917249241123
4) Components of the position difference vector in view frame
coordinates for the states with the MAXIMUM RELATIVE
difference in position:
4a) Down track (km): 30.708369357832
4b) In orbit plane (km): 1.2758338375402
4c) Normal to orbit plane (km): -0.011447894251492
4d) Delta time down track (sec): 7.1972290201441
4e) Epoch (TDB, seconds past J2000): 201693107.46737
4f) Epoch (TDB, calendar format): 2006-MAY-23-21:51:47
5) Components of the position difference vector in view frame
coordinates for the states with the MAXIMUM ABSOLUTE
difference in position:
5a) Down track (km): 30.767205150213
5b) In orbit plane (km): 1.3086257963549
5c) Normal to orbit plane (km): -0.0080797486007561
5d) Delta time down track (sec): 7.2439115051116
5e) Epoch (TDB, seconds past J2000): 201692992.15206
5f) Epoch (TDB, calendar format): 2006-MAY-23-21:49:52
As seen in the report, the maximum down track timing error is about 7.2
seconds at 2006-MAY-23-21:49:52 TBD.
How Does the Difference Change with Time?
Below SPKDIFF is run to generate a view frame difference table for Phobos ephemerides provided by the previous and the latest Martian satellite ephemeris files produced by the Solar System Dynamics group at JPL. To get detailed information on short-term difference trends, the comparison is done over 1 day, which is about three Phobos orbits, using a 30 minute time step (time boundaries and step specified using the ``-b'', ``-e'', and ``-s'' options). Since both SPK files contain data for multiple natural bodies, the body name is explicitly specified on the command line using the ``-b1'' option. Because the trajectory difference with respect to Mars is of interest, Mars is specified as the center using the ``-c1'' option. The time tag format for the output is set to the Julian date TDB using the ``-f'' option. SPKDIFF, run with the all of these options and the names of the SPK files:
> spkdiff -b 2006 MAY 10 -e 2006 MAY 11 \
-s 1800 \
-k naif0008.tls \
-b1 PHOBOS -c1 MARS \
-t dumpvf \
-f 'JULIAND.######## ::TDB' \
mar033_2000-2025.bsp mar063.bsp
produces the following output:
# # Comparison of 49 'J2000'-referenced geometric states # # of 'PHOBOS' (401) relative to 'MARS' (499) # from SPK 'mar033_2000-2025.bsp' # # with 49 'J2000'-referenced geometric states # # of 'PHOBOS' (401) relative to 'MARS' (499) # from SPK 'mar063.bsp' # # evenly-spaced with 1800.0 second (0d 0h 30m 0.0000s) step size # within the time interval # # from '2006 MAY 10' (200491265.18535 TDB seconds) # to '2006 MAY 11' (200577665.18533 TDB seconds) # # using additional data from these kernels # # 'naif0008.tls' # # time, along_track_P_diff, normal_to_plane_P_diff, in_plane_P_di ff, along_track_V_diff, normal_to_plane_V_diff, in_plane_V_diff 2453865.50075450 -3.4E+0 +1.1E-1 +1.1E+0 +1.6E-3 -1.9E-4 +1.2E-3 2453865.52158780 -4.5E+0 -2.3E-1 +1.7E+0 +1.5E-3 -2.0E-4 +1.3E-3 2453865.54242110 -6.1E+0 -5.5E-1 +2.1E+0 +1.4E-3 -1.6E-4 +1.5E-3 2453865.56325450 -7.9E+0 -7.7E-1 +2.0E+0 +1.2E-3 -1.0E-4 +1.6E-3 2453865.58408780 -9.5E+0 -8.6E-1 +1.8E+0 +1.2E-3 -3.0E-5 +1.8E-3 2453865.60492110 -1.0E+1 -8.1E-1 +1.1E+0 +1.2E-3 +5.1E-5 +1.9E-3 2453865.62575450 -1.1E+1 -6.2E-1 +3.2E-1 +1.3E-3 +1.2E-4 +1.9E-3 2453865.64658780 -1.1E+1 -3.4E-1 -5.4E-1 +1.5E-3 +1.7E-4 +2.0E-3 2453865.66742110 -1.0E+1 -1.5E-2 -1.3E+0 +1.7E-3 +2.0E-4 +1.9E-3 2453865.68825450 -9.0E+0 +3.2E-1 -1.9E+0 +1.9E-3 +1.9E-4 +1.8E-3 2453865.70908780 -7.3E+0 +6.0E-1 -2.0E+0 +2.2E-3 +1.5E-4 +1.6E-3 2453865.72992110 -5.6E+0 +7.9E-1 -1.9E+0 +2.2E-3 +8.8E-5 +1.4E-3 2453865.75075450 -4.1E+0 +8.4E-1 -1.6E+0 +2.1E-3 +6.2E-6 +1.2E-3 2453865.77158780 -3.1E+0 +7.6E-1 -8.8E-1 +2.0E-3 -7.7E-5 +1.1E-3 2453865.79242110 -2.8E+0 +5.4E-1 +6.4E-2 +1.8E-3 -1.4E-4 +1.1E-3 2453865.81325450 -3.2E+0 +2.3E-1 +8.8E-1 +1.4E-3 -1.9E-4 +1.2E-3 2453865.83408780 -4.1E+0 -1.1E-1 +1.5E+0 +1.2E-3 -2.0E-4 +1.2E-3 2453865.85492110 -5.6E+0 -4.4E-1 +2.0E+0 +1.0E-3 -1.8E-4 +1.4E-3 2453865.87575450 -7.4E+0 -7.0E-1 +2.1E+0 +9.0E-4 -1.2E-4 +1.6E-3 2453865.89658780 -9.0E+0 -8.5E-1 +1.9E+0 +1.0E-3 -5.4E-5 +1.8E-3 2453865.91742110 -1.0E+1 -8.5E-1 +1.3E+0 +1.2E-3 +2.7E-5 +1.9E-3 2453865.93825450 -1.1E+1 -7.2E-1 +6.0E-1 +1.5E-3 +1.0E-4 +1.9E-3 2453865.95908780 -1.1E+1 -4.8E-1 -3.6E-1 +1.8E-3 +1.6E-4 +2.0E-3 2453865.97992110 -1.0E+1 -1.5E-1 -1.0E+0 +2.1E-3 +1.9E-4 +1.9E-3 2453866.00075450 -9.4E+0 +1.8E-1 -1.7E+0 +2.2E-3 +1.9E-4 +1.8E-3 2453866.02158780 -7.8E+0 +5.0E-1 -2.1E+0 +2.1E-3 +1.6E-4 +1.6E-3 2453866.04242110 -6.2E+0 +7.3E-1 -2.0E+0 +2.1E-3 +1.1E-4 +1.5E-3 2453866.06325450 -4.6E+0 +8.5E-1 -1.6E+0 +1.9E-3 +3.3E-5 +1.4E-3 2453866.08408780 -3.3E+0 +8.1E-1 -1.1E+0 +1.6E-3 -4.9E-5 +1.1E-3 2453866.10492110 -2.7E+0 +6.4E-1 -2.7E-1 +1.5E-3 -1.2E-4 +1.0E-3 2453866.12575450 -3.0E+0 +3.5E-1 +5.6E-1 +1.3E-3 -1.7E-4 +1.1E-3 2453866.14658780 -3.9E+0 +1.0E-2 +1.2E+0 +1.2E-3 -2.0E-4 +1.3E-3 2453866.16742110 -5.1E+0 -3.4E-1 +1.9E+0 +1.3E-3 -1.8E-4 +1.3E-3 2453866.18825450 -6.7E+0 -6.3E-1 +2.3E+0 +1.4E-3 -1.4E-4 +1.5E-3 2453866.20908780 -8.5E+0 -8.1E-1 +2.0E+0 +1.3E-3 -8.0E-5 +1.7E-3 2453866.22992110 -9.9E+0 -8.6E-1 +1.4E+0 +1.3E-3 -1.1E-6 +1.8E-3 2453866.25075450 -1.0E+1 -7.6E-1 +8.4E-1 +1.5E-3 +7.7E-5 +2.0E-3 2453866.27158780 -1.1E+1 -5.4E-1 +3.4E-2 +1.6E-3 +1.4E-4 +2.0E-3 2453866.29242110 -1.0E+1 -2.3E-1 -8.5E-1 +1.7E-3 +1.8E-4 +1.9E-3 2453866.31325450 -9.8E+0 +1.1E-1 -1.5E+0 +1.7E-3 +1.9E-4 +1.8E-3 2453866.33408780 -8.4E+0 +4.3E-1 -2.0E+0 +1.8E-3 +1.7E-4 +1.7E-3 2453866.35492110 -6.7E+0 +6.9E-1 -2.1E+0 +1.8E-3 +1.2E-4 +1.5E-3 2453866.37575450 -5.0E+0 +8.2E-1 -1.9E+0 +1.9E-3 +5.8E-5 +1.4E-3 2453866.39658780 -3.7E+0 +8.2E-1 -1.3E+0 +2.0E-3 -2.5E-5 +1.2E-3 2453866.41742110 -3.0E+0 +6.8E-1 -5.7E-1 +1.9E-3 -1.0E-4 +1.1E-3 2453866.43825450 -2.8E+0 +4.1E-1 +3.5E-1 +1.9E-3 -1.6E-4 +1.1E-3 2453866.45908780 -3.4E+0 +8.1E-2 +1.1E+0 +1.7E-3 -2.0E-4 +1.2E-3 2453866.47992110 -4.6E+0 -2.6E-1 +1.7E+0 +1.4E-3 -1.9E-4 +1.3E-3 2453866.50075440 -6.2E+0 -5.6E-1 +2.1E+0 +1.1E-3 -1.6E-4 +1.5E-3(To fit into the page width, the format for the difference columns in the output above was changed from n.nnnnnnnnnnnnnE-nn to n.nE-n). The table above shows that differences in Phobos' position provided by the previous and latest SPK file oscillates with Phobos orbital motion, with the down track component ranging from -11 km to -3 km, normal to orbit plane from -0.9 to 0.9 km, and in orbit plane from -2 to 2 km.
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