KPL/IK MARSIS Instrument Kernel =========================================================================== This instrument kernel (I-kernel) contains references to mounting alignment, operating modes, and timing as well as internal and FOV geometry for the Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS). Version and Date ----------------------------------------------------------------------------- Version 0.2 -- May 17, 2021 -- Alfredo Escalante Lopez, ESAC/ESA Marc Costa Sitja, NAIF Fixed minor typos and updated contact information. Version 0.1 -- March 24, 2020 -- Marc Costa Sitja, ESAC/ESA Incorporated Apparent Field-of-View definition and addendum with information provided by Roberto Orosei (ISAF) after several iterations with Alejandro Cardesin (ESAC/ESA) and corrected by Boris Semenov (NAIF). Version 0.0 -- January 13, 2019 -- Marc Costa Sitja, ESAC/ESA First draft. References ----------------------------------------------------------------------------- 1. ``Kernel Pool Required Reading'' 2. ``Frames Required Reading'' 3. ``C-Kernel Required Reading" 4. Mars Express Spacecraft Frames Definition Kernel 5. ``MARSIS: Mars Advanced Radar for Subsurface and Ionospheric Sounding'', J.J. Plaut, G. Picardi, et al, European Space Agency, (Special Publication) ESA SP, 2004. 6. ``MARSIS Flight User Manual'', D. Calabrese, F. Bernardini, E. Zampolini, FAUSTINIID-MAR-0008-INF, December 2003. 7. ``How to compute size and orientation of the MARSIS footprint'', R. Orosei provided in an e-mail communication. Contact Information ----------------------------------------------------------------------------- If you have any questions regarding this file contact the ESA SPICE Service support at ESAC: Alfredo Escalante Lopez (+34) 91-8131-429 spice@sciops.esa.int, or NAIF at JPL: Boris Semenov (818) 354-8136 Boris.Semenov@jpl.nasa.gov Implementation Notes ----------------------------------------------------------------------------- This file is used by the SPICE system as follows: programs that make use of this frame kernel must "load" the kernel normally during program initialization. Loading the kernel associates the data items with their names in a data structure called the "kernel pool". The SPICELIB routine FURNSH loads a kernel into the pool as shown below: FORTRAN: (SPICELIB) CALL FURNSH ( frame_kernel_name ) C: (CSPICE) furnsh_c ( frame_kernel_name ); IDL: (ICY) cspice_furnsh, frame_kernel_name MATLAB: (MICE) cspice_furnsh ( 'frame_kernel_name' ) PYTHON: (SPICEYPY)* furnsh( frame_kernel_name ) In order for a program or routine to extract data from the pool, the SPICELIB routines GDPOOL, GIPOOL, and GCPOOL are used. See [2] for more details. This file was created and may be updated with a text editor or word processor. * SPICEYPY is a non-official, community developed Python wrapper for the NAIF SPICE toolkit. Its development is managed on Github. It is available at: https://github.com/AndrewAnnex/SpiceyPy Naming Conventions ----------------------------------------------------------------------------- Data items are specified using ''keyword=value'' assignments [1]. All keywords referencing values in this I-kernel start with the characters `INS' followed by the NAIF MEX instrument ID code, constructed using the spacecraft ID number (-41) followed by the NAIF three digit ID number for one of the MARSIS data item. These IDs are as follows Instrument name ID ------------------------ ------ MEX_MARSIS -41300 MEX_MARSIS_1800KHZ_500KM -41301 MEX_MARSIS_3MHZ_500KM -41302 MEX_MARSIS_4MHZ_500KM -41303 MEX_MARSIS_5MHZ_500KM -41304 The remainder of the name is an underscore character followed by the unique name of the data item. For example, the MARSIS boresight direction in the frame MEX_MARSIS_BASE frame (see [2]) is specified by: INS-41300_BORESIGHT The upper bound on the length of the name of any data item identifier is 32 characters. If the same item is included in more than one file, or if the same item appears more than once within a single file, the latest value supersedes any earlier values. Overview ----------------------------------------------------------------------------- MARSIS (Mars Advanced Radar for Subsurface and Ionosphere Sounding) is a subsurface radar sounder with a 40-meter (130-foot) antenna on the Mars Express orbiter that is searching for water and study the atmosphere. MARSIS is a low frequency, nadir-looking pulse limited radar sounder and altimeter with ground penetration capabilities, which uses synthetic aperture techniques and a secondary receiving antenna to isolate subsurface reflections. From [5]: MARSIS is the first radar to collect data from Mars orbit. MARSIS is a multi-frequency synthetic aperture orbital sounding radar (Picardi et al., 2004) that operates in two modes, subsurface sounding and ionospheric sounding. In both modes, MARSIS acquires data in the conventional fashion of a radar, in which pulses of electromagnetic radio waves are transmitted, interact with a target, and the echoes are received and recorded by the instrument. MARSIS differs from most orbital radars in the frequencies of the radar signal. MARSIS operates in the range 0.1-5.5 MHz, which corresponds to wavelengths of tens to hundreds of metres. These long wavelengths were chosen, in the case of the subsurface sounder, to maximise the penetration of the signal into the subsurface of Mars. In the case of the ionospheric sounder, the selected frequencies are in the range where some waves reflect from the topside of the ionosphere, depending on the electron plasma frequency, while others penetrate through to be reflected at the surface or subsurface. The primary goal of the MARSIS subsurface experiment is to detect material discontinuities in the subsurface of Mars in order to understand the distribution of water, both solid and liquid, in the upper crust. The experiment is also probing for other discontinuities in the subsurface, related to geological units and structures. Finally, the subsurface mode obtains information in its surface echoes on the electromagnetic, topographic and roughness properties of the Mars surface. The goals of the ionospheric sounding experiment are to characterise the upper portions of the atmosphere (the ionosphere) and its interactions with solar radiation and particles. From [6]: MARSIS has 5 subsurface sounding modes (passive ionosphere sounding embedded) with dual frequency and/or dual antenna capability. Spatial sampling rate of ~5 to 10 km (depending on the altitude). Active ionosphere sounding mode. Vertical resolution of 15 km, spatial sampling step of ~30 km. The following table lists the principal parameters for the Subsurface and the Ionosphere Sounding Operative modes of MARSIS: Parameter | Value ------------------------------+----------------- Subsounding Operative mode | | Center Frequencies | 1.8 MHz | 3.0 MHz | 4.0 MHz | 5.0 MHz | Bandwidth | 1.0 MHz | Irradiated Power | Band 1 | 1.5 Watt Band 2 | 5.0 Watt Band 3 | 5.0 Watt Band 4 | 5.0 Watt | Transmit Pulse Width | 250 (30 in mode SS5) | microsecond | PRF | 130 Pulses Per Second | Minimum Altitude | 250 kilometer Maximum Altitude | subsurface sounding | 800 kilometer ionosphere sounding | 1200 kilometer | Receive Window Size per | 350 microsecond channel (baseline) | | Analog to Digital | Conversion Rate | 2.8 MHz Digital Conversion | 8 Bit | Number of Processed | 4 (max) Channels | | Maximum Number of | 2 Simultaneous Frequencies | | Radiation Gain | 2.1 dB | Dipole Antenna Length | 20 meter Monopole Antenna Length | 7 meter Data Rate Output | 18 (min) - 75 (max) kbps | Data Volume | 285(max) Mbit/day Mass (CBE) | 17 kg Power | 64.5 Watt (max including margins) | | Ionosphere Sounding Mode | Start Frequency | 100 kHz End Frequency | 5.4 MHz Number of Frequencies | 160 Transmit Pulse Length | 91.43 microsecond Frequency Step | 10.937 kHz PRF | 130 Pulses Per Second Frequency Sweep Duration | 7.38 Second From [5]: MARSIS data are collected when the elliptical orbit of Mars Express brings the spacecraft to an altitude of 250-1400 km above the surface; this condition is met during about 45 min of each 6.7 h orbit. Subsurface sounding data may be collected when the altitude is below 1000 km. In the subsurface modes, MARSIS operates in four frequency bands between 1.3 and 5.5 MHz, with a 1 MHz instantaneous bandwidth that provides free-space range resolution of approximately 150 m. Lateral spatial resolution depends on surface roughness characteristics, but for most Mars surfaces the cross-track footprint is 10-30 km and the along-track footprint, narrowed by onboard synthetic aperture processing, is 5-10 km. Mounting Alignment ----------------------------------------------------------------------------- Refer to the latest version of the Mars Express Frames Definition Kernel (FK) [4] for the MARSIS reference frame definitions and mounting alignment information. MARSIS Apparent Field-of-View Layout ----------------------------------------------------------------------------- The antenna of MARSIS is a dipole with negligible directivity, meaning that it emits radiation in every direction. Thus, the MARSIS footprint is not the intersection of a conical beam with a spherical planet, but rather a circle whose edge has a distance from the spacecraft equal to the spacecraft altitude plus the range resolution of MARSIS. This is called a pulse-limited footprint: __ ####--|__|-#### MEX S/C /\ Altimeter / \ / \ / \ / \ Radar phase / .--\----- Pulse-limited measurement front . / / \ level surface | / | \ '-----> . V . Mars surface -------------------' ######### '----------------------------- #### The radius of the pulse-limited footprint Rop can be computed through the following formula: Rop = ( 2 * C * H / B ) ^ 0.5 where H is the altitude over Mars in Km B is the bandwidth of the MARSIS pulse (``chirp''), which is equal to 1 MHz. C is the speed of light in Km/s Footprint size is improved in the along-track direction through on-board processing. The coherent summing of several tens (up to two hundreds or more, depending on altitude and frequency) reduces the effective footprint size in the along-track direction only, that is in the direction of spacecraft motion. The along-track footprint size can be computed through the following formula: Rpl = ( LAN * H / 2 ) ^ 0.5 where LAN is the wavelength: C/F H is the altitude over Mars in Km F is the operational frequency in MHz (e.g.: 1.8, 3, 4, 5) C is the speed of light in Km/s This formula corresponds to the so-called Fresnel radius, i.e. the size of the area illuminated by the radar on a perfectly specular surface (as opposed to the pulse-limited footprint size, which assumes that the surface is rough). The actual resolution of the radar is half its footprint size (two separate targets can be distinguished when their distance is equal to the footprint radius). Thus, Rpl and Rop can be directly used to compute the MARSIS resolution cell size respectively in the across-track and along-track direction: A = atan( Rpl / H ) B = atan( Rol / H ) where A and B are the subtended view angles. The orientation of the resolution cell follows the projection of the spacecraft velocity vector on the surface, that is the ground track. +Y ^ along-track . . . | (cross-product of nadir and +X ) . ' ^ ' . | ' | B ' | '< - - - - - - - - - >' o--------> +X cross-track '. A | .' +Z (~ S/C ground track velocity) ' . v . ' Nadir ' ' ' MARSIS dipole Field of View Definition ------------------------------------------------------------------------------ This section contains assignments defining an apparent or approximated MARIS FOVs. These definitions are based on the apparent FOV parameters provided in the previous sections and are provided in a format consistent with/required by the SPICE TOOLKIT function GETFOV. The radiation pattern of the MARSIS dipole is is a toroid around the antenna's cylindrical tube. We use the apparent Field of View defined in the previous section to describe a footprint in the ground. Because of the operational altitude dependency and due to the fact that an IK cannot accommodate a dynamic FOV definition, a limited number of FOV definitions are provided. From the information of the previous paragraph we generate five apparent ellipsoidal Field of Views: we use an altitude of 500 Km for each of the radar frequencies: 1.8, 3, 4 and 5 MHz. This FOV definition corresponds to the NAIF Body Names: MEX_MARSIS_1800KHZ_500KM, MEX_MARSIS_3MHZ_500KM, MEX_MARSIS_4MHZ_500KM and MEX_MARSIS_5MHZ_500KM. \begindata INS-41300001_NAME = 'MEX_MARSIS_1800KHZ_500KM' INS-41300001_BORESIGHT = ( 0.0 0.0 1.0 ) INS-41300001_FOV_SHAPE = 'ELLIPSE' INS-41300001_FOV_FRAME = 'MEX_MARSIS' INS-41300001_FOV_CLASS_SPEC = 'ANGLES' INS-41300001_FOV_REF_VECTOR = ( 1.0 0.0 0.0 )' INS-41300001_FOV_REF_ANGLE = 0.7393883820929412 INS-41300001_FOV_CROSS_ANGLE = 1.9833048415704062 INS-41300001_FOV_ANGLE_UNITS = 'DEGREES' INS-41300002_NAME = 'MEX_MARSIS_3MHZ_500KM' INS-41300002_BORESIGHT = ( 0.0 0.0 1.0 ) INS-41300002_FOV_SHAPE = 'ELLIPSE' INS-41300002_FOV_FRAME = 'MEX_MARSIS' INS-41300002_FOV_CLASS_SPEC = 'ANGLES' INS-41300002_FOV_REF_VECTOR = ( 1.0 0.0 0.0 )' INS-41300002_FOV_REF_ANGLE = 0.5727404951968748 INS-41300002_FOV_CROSS_ANGLE = 1.9833048415704062 INS-41300002_FOV_ANGLE_UNITS = 'DEGREES' INS-41300003_NAME = 'MEX_MARSIS_4MHZ_500KM' INS-41300003_BORESIGHT = ( 0.0 0.0 1.0 ) INS-41300003_FOV_SHAPE = 'ELLIPSE' INS-41300003_FOV_FRAME = 'MEX_MARSIS' INS-41300003_FOV_CLASS_SPEC = 'ANGLES' INS-41300003_FOV_REF_VECTOR = ( 1.0 0.0 0.0 )' INS-41300003_FOV_REF_ANGLE = 0.49601194885975425 INS-41300003_FOV_CROSS_ANGLE = 1.9833048415704062 INS-41300003_FOV_ANGLE_UNITS = 'DEGREES' INS-41300004_NAME = 'MEX_MARSIS_5MHZ_500KM' INS-41300004_BORESIGHT = ( 0.0 0.0 1.0 ) INS-41300004_FOV_SHAPE = 'ELLIPSE' INS-41300004_FOV_FRAME = 'MEX_MARSIS' INS-41300004_FOV_CLASS_SPEC = 'ANGLES' INS-41300004_FOV_REF_VECTOR = ( 1.0 0.0 0.0 )' INS-41300004_FOV_REF_ANGLE = 0.44364879069526447 INS-41300004_FOV_CROSS_ANGLE = 1.9833048415704062 INS-41300004_FOV_ANGLE_UNITS = 'DEGREES' \begintext MARSIS Field-of-View Definitions Addendum ----------------------------------------------------------------------------- Given that the MARSIS dipole FOV definition depends on the operational altitude, a unique FOV model cannot be provided; because of that section ``MARSIS dipole Field of View Definition'' provides a limited number of FOV definitions for a representative altitude (500 Km) for the four operational frequencies. This addendum provides the information needed by the user to generate FOV for an arbitrary altitude-frequency combination. The variable INS-41300_FOV_DEFINITIONS defined below provides possible MARSIS Field-of-View definitions for different altitudes, from 300 Km to 900 Km in steps of 10 Km, and operational frequencies, 2MHz (synonym for 1.8MHz), 3MHz, 4MHz, and 5MHz. For a given ``i'' row the variable provides: DEFS(i)(0): Operational frequency in MHz, used to generate the FOV name. DEFS(i)(1): Operational altitude in Km, used to generate the FOV name. DEFS(i)(2): FOV reference angle, to be used in the FOV definition. DEFS(i)(2): FOV cross angle, to be used in the FOV definition. In order to create a standard FOV definition keyword set for the i-th row, the DEFS values from that row should be incorporated into the keyword names and values as follows (data items to be introduced by users are shown in brackets): INS-41300[iii]_NAME = 'MEX_MARSIS_[DEFS(i)(0)]_[DEFS(i)(1)]KM' INS-41300[iii]_BORESIGHT = ( 0.0 0.0 1.0 ) INS-41300[iii]_FOV_SHAPE = 'ELLIPSE' INS-41300[iii]_FOV_FRAME = 'MEX_MARSIS' INS-41300[iii]_FOV_CLASS_SPEC = 'ANGLES' INS-41300[iii]_FOV_REF_VECTOR = ( 1.0 0.0 0.0 ) INS-41300[iii]_FOV_REF_ANGLE = [DEFS(i)(2)] INS-41300[iii]_FOV_CROSS_ANGLE = [DEFS(i)(3)] INS-41300[iii]_FOV_ANGLE_UNITS = 'DEGREE NAIF_BODY_NAME += ( 'MEX_MARSIS_[DEFS(i)(0)]_[DEFS(i)(1)]KM' ) NAIF_BODY_CODE += ( -41300[iii] ) where ``iii'' is ``i'' in three-digit format, left-padded with ``0'' for ``000'' to ``243'' full range. Please note that if the user needs to incorporate an altitude that is not provided, he/she can interpolate lines or use the formulas provided in section ``MARSIS Apparent Field-of-View Layout''. Please note that the data provided below can be accessed with the SPICE routine GDPOOL. \begindata INS-41300_FOV_DEFINITIONS = ( 2 300 0.9545109751 2.5597542649 2 310 0.9389922390 2.5181834946 2 320 0.9242066210 2.4785744370 2 330 0.9100981594 2.4407775044 2 340 0.8966166961 2.4046586059 2 350 0.8837171248 2.3700971434 2 360 0.8713587553 2.3369843139 2 370 0.8595047725 2.3052216668 2 380 0.8481217748 2.2747198713 2 390 0.8371793773 2.2453976577 2 400 0.8266498705 2.2171809059 2 410 0.8165079250 2.1900018564 2 420 0.8067303344 2.1637984254 2 430 0.7972957925 2.1385136077 2 440 0.7881846976 2.1140949550 2 450 0.7793789807 2.0904941177 2 460 0.7708619554 2.0676664422 2 470 0.7626181845 2.0455706154 2 480 0.7546333621 2.0241683502 2 490 0.7468942095 2.0034241062 2 500 0.7393883821 1.9833048416 2 510 0.7321043867 1.9637797915 2 520 0.7250315072 1.9448202706 2 530 0.7181597388 1.9263994953 2 540 0.7114797279 1.9084924251 2 550 0.7049827188 1.8910756190 2 560 0.6986605057 1.8741271067 2 570 0.6925053887 1.8576262723 2 580 0.6865101345 1.8415537481 2 590 0.6806679409 1.8258913198 2 600 0.6749724039 1.8106218394 2 610 0.6694174887 1.7957291461 2 620 0.6639975023 1.7811979947 2 630 0.6587070693 1.7670139897 2 640 0.6535411094 1.7531635255 2 650 0.6484948171 1.7396337317 2 660 0.6435636423 1.7264124225 2 670 0.6387432739 1.7134880505 2 680 0.6340296233 1.7008496649 2 690 0.6294188099 1.6884868719 2 700 0.6249071480 1.6763897988 2 710 0.6204911343 1.6645490615 2 720 0.6161674361 1.6529557329 2 730 0.6119328813 1.6416013156 2 740 0.6077844483 1.6304777149 2 750 0.6037192568 1.6195772152 2 760 0.5997345597 1.6088924572 2 770 0.5958277351 1.5984164169 2 780 0.5919962794 1.5881423863 2 790 0.5882377998 1.5780639556 2 800 0.5845500089 1.5681749961 2 810 0.5809307182 1.5584696445 2 820 0.5773778331 1.5489422885 2 830 0.5738893474 1.5395875531 2 840 0.5704633388 1.5304002879 2 850 0.5670979644 1.5213755548 2 860 0.5637914567 1.5125086175 2 870 0.5605421191 1.5037949305 2 880 0.5573483229 1.4952301297 2 890 0.5542085038 1.4868100229 2 900 0.5511211582 1.4785305812 3 300 0.7393883821 2.5597542649 3 310 0.7273663079 2.5181834946 3 320 0.7159122063 2.4785744370 3 330 0.7049827188 2.4407775044 3 340 0.6945389838 2.4046586059 3 350 0.6845460541 2.3700971434 3 360 0.6749724039 2.3369843139 3 370 0.6657895104 2.3052216668 3 380 0.6569714951 2.2747198713 3 390 0.6484948171 2.2453976577 3 400 0.6403380084 2.2171809059 3 410 0.6324814450 2.1900018564 3 420 0.6249071480 2.1637984254 3 430 0.6175986105 2.1385136077 3 440 0.6105406463 2.1140949550 3 450 0.6037192568 2.0904941177 3 460 0.5971215144 2.0676664422 3 470 0.5907354594 2.0455706154 3 480 0.5845500089 2.0241683502 3 490 0.5785548753 2.0034241062 3 500 0.5727404952 1.9833048416 3 510 0.5670979644 1.9637797915 3 520 0.5616189812 1.9448202706 3 530 0.5562957946 1.9263994953 3 540 0.5511211582 1.9084924251 3 550 0.5460882890 1.8910756190 3 560 0.5411908299 1.8741271067 3 570 0.5364228157 1.8576262723 3 580 0.5317786428 1.8415537481 3 590 0.5272530414 1.8258913198 3 600 0.5228410505 1.8106218394 3 610 0.5185379947 1.7957291461 3 620 0.5143394639 1.7811979947 3 630 0.5102412937 1.7670139897 3 640 0.5062395485 1.7531635255 3 650 0.5023305054 1.7396337317 3 660 0.4985106396 1.7264124225 3 670 0.4947766113 1.7134880505 3 680 0.4911252530 1.7008496649 3 690 0.4875535586 1.6884868719 3 700 0.4840586729 1.6763897988 3 710 0.4806378817 1.6645490615 3 720 0.4772886035 1.6529557329 3 730 0.4740083808 1.6416013156 3 740 0.4707948728 1.6304777149 3 750 0.4676458482 1.6195772152 3 760 0.4645591789 1.6088924572 3 770 0.4615328338 1.5984164169 3 780 0.4585648734 1.5881423863 3 790 0.4556534441 1.5780639556 3 800 0.4527967739 1.5681749961 3 810 0.4499931674 1.5584696445 3 820 0.4472410019 1.5489422885 3 830 0.4445387234 1.5395875531 3 840 0.4418848427 1.5304002879 3 850 0.4392779322 1.5213755548 3 860 0.4367166225 1.5125086175 3 870 0.4341995995 1.5037949305 3 880 0.4317256015 1.4952301297 3 890 0.4292934165 1.4868100229 3 900 0.4269018799 1.4785305812 4 300 0.6403380084 2.5597542649 4 310 0.6299261603 2.5181834946 4 320 0.6200062239 2.4785744370 4 330 0.6105406463 2.4407775044 4 340 0.6014957692 2.4046586059 4 350 0.5928413248 2.3700971434 4 360 0.5845500089 2.3369843139 4 370 0.5765971176 2.3052216668 4 380 0.5689602379 2.2747198713 4 390 0.5616189812 2.2453976577 4 400 0.5545547543 2.2171809059 4 410 0.5477505610 2.1900018564 4 420 0.5411908299 2.1637984254 4 430 0.5348612648 2.1385136077 4 440 0.5287487129 2.1140949550 4 450 0.5228410505 2.0904941177 4 460 0.5171270811 2.0676664422 4 470 0.5115964467 2.0455706154 4 480 0.5062395485 2.0241683502 4 490 0.5010474768 2.0034241062 4 500 0.4960119489 1.9833048416 4 510 0.4911252530 1.9637797915 4 520 0.4863801993 1.9448202706 4 530 0.4817700747 1.9263994953 4 540 0.4772886035 1.9084924251 4 550 0.4729299111 1.8910756190 4 560 0.4686884916 1.8741271067 4 570 0.4645591789 1.8576262723 4 580 0.4605371198 1.8415537481 4 590 0.4566177503 1.8258913198 4 600 0.4527967739 1.8106218394 4 610 0.4490701413 1.7957291461 4 620 0.4454340331 1.7811979947 4 630 0.4418848427 1.7670139897 4 640 0.4384191615 1.7531635255 4 650 0.4350337653 1.7396337317 4 660 0.4317256015 1.7264124225 4 670 0.4284917773 1.7134880505 4 680 0.4253295498 1.7008496649 4 690 0.4222363153 1.6884868719 4 700 0.4192096011 1.6763897988 4 710 0.4162470565 1.6645490615 4 720 0.4133464459 1.6529557329 4 730 0.4105056407 1.6416013156 4 740 0.4077226138 1.6304777149 4 750 0.4049954328 1.6195772152 4 760 0.4023222545 1.6088924572 4 770 0.3997013201 1.5984164169 4 780 0.3971309495 1.5881423863 4 790 0.3946095377 1.5780639556 4 800 0.3921355498 1.5681749961 4 810 0.3897075177 1.5584696445 4 820 0.3873240359 1.5489422885 4 830 0.3849837586 1.5395875531 4 840 0.3826853962 1.5304002879 4 850 0.3804277121 1.5213755548 4 860 0.3782095204 1.5125086175 4 870 0.3760296830 1.5037949305 4 880 0.3738871073 1.4952301297 4 890 0.3717807436 1.4868100229 4 900 0.3697095832 1.4785305812 5 300 0.5727404952 2.5597542649 5 310 0.5634276263 2.5181834946 5 320 0.5545547543 2.4785744370 5 330 0.5460882890 2.4407775044 5 340 0.5379981240 2.4046586059 5 350 0.5302571855 2.3700971434 5 360 0.5228410505 2.3369843139 5 370 0.5157276222 2.3052216668 5 380 0.5088968528 2.2747198713 5 390 0.5023305054 2.2453976577 5 400 0.4960119489 2.2171809059 5 410 0.4899259807 2.1900018564 5 420 0.4840586729 2.1637984254 5 430 0.4783972379 2.1385136077 5 440 0.4729299111 2.1140949550 5 450 0.4676458482 2.0904941177 5 460 0.4625350344 2.0676664422 5 470 0.4575882049 2.0455706154 5 480 0.4527967739 2.0241683502 5 490 0.4481527720 2.0034241062 5 500 0.4436487907 1.9833048416 5 510 0.4392779322 1.9637797915 5 520 0.4350337653 1.9448202706 5 530 0.4309102857 1.9263994953 5 540 0.4269018799 1.9084924251 5 550 0.4230032932 1.8910756190 5 560 0.4192096011 1.8741271067 5 570 0.4155161825 1.8576262723 5 580 0.4119186966 1.8415537481 5 590 0.4084130611 1.8258913198 5 600 0.4049954328 1.8106218394 5 610 0.4016621900 1.7957291461 5 620 0.3984099163 1.7811979947 5 630 0.3952353858 1.7670139897 5 640 0.3921355498 1.7531635255 5 650 0.3891075242 1.7396337317 5 660 0.3861485786 1.7264124225 5 670 0.3832561258 1.7134880505 5 680 0.3804277121 1.7008496649 5 690 0.3776610088 1.6884868719 5 700 0.3749538041 1.6763897988 5 710 0.3723039955 1.6645490615 5 720 0.3697095832 1.6529557329 5 730 0.3671686636 1.6416013156 5 740 0.3646794233 1.6304777149 5 750 0.3622401339 1.6195772152 5 760 0.3598491469 1.6088924572 5 770 0.3575048888 1.5984164169 5 780 0.3552058573 1.5881423863 5 790 0.3529506164 1.5780639556 5 800 0.3507377935 1.5681749961 5 810 0.3485660754 1.5584696445 5 820 0.3464342049 1.5489422885 5 830 0.3443409782 1.5395875531 5 840 0.3422852419 1.5304002879 5 850 0.3402658899 1.5213755548 5 860 0.3382818616 1.5125086175 5 870 0.3363321389 1.5037949305 5 880 0.3344157445 1.4952301297 5 890 0.3325317396 1.4868100229 5 900 0.3306792219 1.4785305812 ) \begintext End of IK file.