PDS_VERSION_ID        = PDS3

RECORD_TYPE           = STREAM

RECORD_BYTES          = 80

OBJECT                = TEXT

  PUBLICATION_DATE      = 2008-07-28

  NOTE                        = "Software Interface Specification for

                                 the Radio Science Digital Map Product

                                 (RSDMAP) file.  Formatted for display

                                 or printing at 58 lines per page with

                                 up to 78 constant width characters

                                 per line."

END_OBJECT            = TEXT

END

 

 

 

 

 

 

 

 

 

 

 

SOFTWARE INTERFACE SPECIFICATION

 

 

RADIO SCIENCE  DIGITAL MAP (RSDMAP) PRODUCTS

 

 

 

 

 

 

prepared  by

 

Richard A. Simpson

Packard Building - Room 332

Stanford University

Stanford, CA

94305

 

Peggy L. Jester

SGT, Inc / Code 614.1

NASA GSFC / Wallops Flight Facility

Wallops Island, VA 23337 USA

 

 

 

Version 3.2

13 October 2010

 

 

 

 

 

 

 

 

                               PREFACE

 

|====================================================================|

|                                                                    |

|                        DOCUMENT CHANGE LOG                         |

|                                                                    |

|====================================================================|

|REVISION|REVISION|  SECTION   |               REMARKS               |

| NUMBER |  DATE  |  AFFECTED  |                                     |

|--------+--------+------------+-------------------------------------|

|   2.0  |98/04/20|     All    |Adapted from V1.0.2 for MGS and Lunar|

|        |        |            | Prospector.                         |

|--------+--------+------------+-------------------------------------|

|  2.0.1 |98/12/16|    4.2.1   |Change MGS DATA_SET_ID to            |

|        |        |            |  MGS-M-RSS-5-SDP-V1.0               |

|--------+--------+------------+-------------------------------------|

|  2.0.1 |98/12/16| Appendix B |Added examples in B.1 and B.2        |

|--------+--------+------------+-------------------------------------|

|  2.0.2 |99/03/09|Distribution|Update list of PDS recipients        |

|--------+--------+------------+-------------------------------------|

|  2.0.2 |99/03/09|Acr & Abbrev|Changed "LPX" to "LP" for Lunar      |

|        |        |     1.2    | Prospector                          |

|--------+--------+------------+-------------------------------------|

|  2.0.2 |99/03/09|     2.3    |Generalized use of "nnnnvv" string in|

|        |        |            | file naming.                        |

|--------+--------+------------+-------------------------------------|

|  2.0.2 |99/03/09| Fig. 4-2-3 |Generalized value for pointer        |

|        |        |            | ^DATA_SET_MAP_PROJECTION            |

|--------+--------+------------+-------------------------------------|

|  2.0.2 |99/03/09| Fig. 4-2-2 |Removed keyword UNIT from IMAGE      |

|        |        |     B.1    | object definition                   |

|--------+--------+------------+-------------------------------------|

|  2.0.2 |99/03/09|   1.5.4.1  |Substituted 7-bit ASCII characters   |

|        |        |   1.5.4.2  | for 8-bit versions                  |

|--------+--------+------------+-------------------------------------|

|   3.0  |06/03/15|     All    |Adapted from V2.0.2 for Messenger and|

|        |        |            | MRO.  Streamlined format, omitting  |

|        |        |            | obsolete distribution list and table|

|        |        |            | of Items to be                      |

|--------+--------+------------+-------------------------------------|

|   3.1  |08/07/28|     2.3    |Updated file naming convention       |

|        |        |            |  for MRO                            |

|--------+--------+------------+-------------------------------------|

|   3.2  |10/13/10|     2.3    |Updated file naming convention       |

|        |        |            | to include more characters to       |

|        |        |            | describe solution of the field      |

|========|========|============|=====================================|

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                               Contents

 

 

Preface.............................................................ii

  Document Change Log...............................................ii

  Contents.........................................................iii

  Acronyms and Abbreviations.........................................v

 

1. General Description...............................................1

  1.1. Overview......................................................1

  1.2. Scope.........................................................1

  1.3. Applicable Documents..........................................1

  1.4. System Siting.................................................1

    1.4.1. Interface Location and Medium.............................1

    1.4.2. Data Sources, Transfer Methods, and Destinations..........1

    1.4.3. Generation Method and Frequency...........................2

  1.5. Assumptions and Constraints...................................2

    1.5.1. Usage Constraints.........................................2

    1.5.2. Priority Phasing Constraints..............................2

    1.5.3. Explicit and Derived Constraints..........................2

    1.5.4. Documentation Conventions.................................2

      1.5.4.1. Data Format Descriptions..............................2

      1.5.4.2. Time Standards........................................3

      1.5.4.3. Coordinate Systems....................................3

      1.5.4.4. Limits of This Document...............................3

      1.5.4.5. Typographic Conventions...............................3

 

2. Interface Characteristics.........................................4

  2.1. Hardware Characteristics and Limitations......................4

    2.1.1. Special Equipment and Device Interfaces...................4

    2.1.2. Special Setup Requirements................................4

  2.2. Volume and Size...............................................4

  2.3. Labeling and Identification...................................4

  2.4. Interface Medium Characteristics..............................5

  2.5. Failure Protection, Detection, and Recovery Procedures........5

  2.6. End-of-File Conventions.......................................5

 

3. Access............................................................6

  3.1. Programs Using the Interface..................................6

  3.2. Synchronization Considerations................................6

    3.2.1. Timing and Sequencing Considerations......................6

    3.2.2. Effective Duration........................................6

    3.2.3. Priority Interrupts.......................................6

  3.3. Input/Output Protocols, Calling Sequences.....................6

 

4. Detailed Interface Specifications.................................7

  4.1. Structure and Organization Overview...........................7

  4.2. Detached PDS Label............................................7

    4.2.1. Label Header..............................................7

    4.2.2. Image Object Definition...................................9

    4.2.3. Image Map Projection Object Definition...................10

  4.3. Data File....................................................11

 

5. Support Staff and Cognizant Personnel............................12

 

 

 

 

Appendix A.  Binary Data Format.....................................13

  A.1. IEEE Integer Fields..........................................13

  A.2. IEEE Floating-Point Fields...................................13

  A.3. VAX Integer Fields...........................................14

  A.4. VAX Floating-Point Fields....................................15

 

Appendix B.  Example Data Products..................................16

  B.1. Example Label................................................16

  B.2. Example Data Object..........................................17

 

Figures

  4-2-1. RSDMAP Label Header.........................................7

  4-2-2. RSDMAP Image Object Definition..............................9

  4-2-3. RSDMAP Image Map Projection Definition.....................10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Acronyms and Abbreviations

      ANSI      American National Standards Institute

      APL       Applied Physics Laboratory

      ARC       Ames Research Center

      ARCDR     MGN Altimetry and Radiometry Composite Data Record

      ASCII     American Standard Code for Information Interchange

      ASU       Arizona State University

      CD-WO     compact-disc write-once

      CNES      Centre National d'Etudes Spatiales

      CR        Carriage return (ASCII character)

      dB        Decibel

      DEC       Digital Equipment Corporation

      DSN       Deep Space Network

      DVD       Digital Video Disc or Digital Versatile Disc

      EGM96     Earth Gravitational Model 1996

      FEA       Front End Assembly

      GSFC      Goddard Space Flight Center

      IEEE      Institute of Electrical and Electronic Engineers

      IAU       International Astronomical Union

      JHU       Johns Hopkins University

      JPL       Jet Propulsion Laboratory

      J2000     IAU Official Time Epoch

      K         Degrees Kelvin

      kB        kilobytes

      km        Kilometers

      LAST      Laser Altimeter Science Team (Messenger)

      LF        Line feed (ASCII character)

      LP        Lunar Prospector (mission or spacecraft)

      MESSENGER MErcury Surface Space ENvironment, GEochemistry,

                        and Ranging (acronym for mission to Mercury)

      MGN       Magellan (project or spacecraft)

      MGS       Mars Global Surveyor

      MIT       Massachusetts Institute of Technology

      MLA       MESSENGER Laser Altimeter

      MO        Mars Observer

      MRO       Mars Reconnaissance Orbiter

      NAIF      Navigation and Ancillary Information Facility

      NASA      National Aeronautics and Space Administration

      NAV       Navigation Subsystem/Team

      ODL       Object Definition Language (PDS)

      PDS       Planetary Data System

      RS        Radio Science

      RSDMAP    Radio Science Digital Map Product

      RSS       Radio Science Subsystem

      RST       Radio Science Team

      SCET      Space Craft Event Time

      SHADR     Spherical Harmonic ASCII Data Record

      SHBDR     Spherical Harmonic Binary Data Record

      SHM       Spherical Harmonic Model

      SIS       Software Interface Specification

      SOPC      Science Operations Planning Computer

      SPARC     Sun Scaleable Processor Architecture

      SPK       Spacecraft and Planet Kernel Format, from NAIF

      TBD       To Be Determined

      TDB       Temps Dynamique Barycentrique - IAU Standard Ephemeris

                         Time

      TES       Thermal Emission Spectrometer

      UTC       Universal Time Coordinated

1.  General Description

 

1.1.   Overview

 

      This Software Interface Specification (SIS) describes Radio

Science Digital Map (RSDMAP) files.  The RSDMAP product was designed

for geoid, isostatic anomaly, Bouguer anomaly, or other digital maps

derived primarily from Radio Science data [1].  Use of the RSDMAP format

is not limited to Radio Science data, however.

 

1.2.   Scope

 

      The format and content specifications in this SIS apply to all

phases of a project for which RSDMAP products are produced.

 

      The RSDMAP product was defined initially for free air gravity

maps derived from Magellan (MGN) and Mars Observer (MO) radio tracking

data, but the format is more generally useful.  It was adapted in 1999

for Mars Global Surveyor (MGS) and Lunar Prospector (LP) radio data with options for MGS Thermal Emission Spectrometer (TES) data.  In this revision it is adapted for Mars Reconnaissance Orbiter (MRO) [6,7] and the MESSENGER [8,9] missions.

 

      The Magellan, Mars Observer, Mars Global Surveyor, and Mars Reconnaissance Orbiter missions are or were managed by the Jet Propulsion Laboratory (JPL) for the National Aeronautics and Space Administration (NASA).  Lunar Prospector was managed by the Ames Research Center (ARC) for NASA.  MESSENGER is managed by the Johns Hopkins University Applied Physics Laboratory (APL), in Laurel Maryland.

 

1.3.   Applicable Documents

 

[1] Tyler, G.L., G. Balmino, D.P. Hinson, W.L. Sjogren, D.E. Smith,

     R. Woo, S.W. Asmar, M.J. Connally, C.L. Hamilton, and R.A.

     Simpson, Radio Science Investigations with Mars Observer, J.

     Geophys. Res., 97, 7759-7779, 1992.

 

[2] MGN 630-7, Rev. D, Magellan Planetary Constants and Models, D.T.

     Lyons, Mission Design, Jet Propulsion Laboratory, 9 January 1991.

 

[3] MO 642-321, Mars Observer Planetary Constants and Models, JPL

     D-3444, November 1990.

 

[4] D-7116, Rev. D, Planetary Science Data Dictionary Document, 

     Jet Propulsion Laboratory, 28 August 2002.

 

[5] D-7669 Part 2, Planetary Data System Standards Reference, PDS

     Version 3.6, Jet Propulsion Laboratory, 1 August 2003.

 

[6] Mars Reconnaissance Orbiter Mission Plan, Revision C: July 2005,

    prepared by Robert Lock Document JPL D-22239, MRO-31-201.

 

[7] MRO-D-22685, Rev B., Planetary Constants and Models, 05-15-2003.

 

[8] McAdams, J. V. (JHU/APL), MESSENGER mission overview and trajectory

    design, American Institute of Aeronautics and Astronautics,

    American  Astronautical Society (AIAA/AAS) Astrodynamics  Specialist 

    Conference, Paper AAS 03-541, 20 pp., Big Sky, MT, August 3-7, 2003.

 

[9] McAdams, J. V., D. W. Dunham, R. W. Farquhar (all at JHU/APL),

    A. H. Taylor, and B. G.  Williams (both at KinetX, Inc.), Trajectory

    design and maneuver strategy for the MESSENGER mission to Mercury,

    15th American Astronautical Society (AAS)/American Institute of

    Aeronautics and Astronautics (AIAA) Space Flight Mechanics Conf.,

    Paper AAS 05-173, 21 pp., Copper Mountain, CO, January 23-27, 2005.

 

[10] Wessel, P. and W. H. F. Smith, Free software helps map and display data,

    EOS Trans. AGU, 72, 441, 1991.

 

[11] Generic Mapping Tools website: http://gmt.soest.hawaii.edu/.

 

 

1.4.   System Siting

 

1.4.1.   Interface Location and Medium

 

      RSDMAP files are created at the institution conducting the

science analysis.  RSDMAP files are electronic files.

 

1.4.2.   Data Sources, Transfer Methods, and Destinations

 

      RSDMAP files are created from radio tracking, vertical sounding,

in situ, and/or other measurements at the institution conducting the

scientific data analysis.  They are transferred to and deposited in a

data system specified by the managing institution.

 

      RSDMAP files will be delivered to users via electronic networks and

on compact-disc write-once volumes (CD-WO).

 

1.4.3.   Generation Method and Frequency

 

      RSDMAP files are developed separately at each institution

conducting scientific analyses on raw data.  Each digital map meets

criteria specified by the investigators conducting the analysis. 

Each digital map typically requires data from a large number of

latitudes and longitudes, so that RSDMAP files will be issued

infrequently and on schedules which cannot be predicted.

 

 

1.5.   Assumptions and Constraints

 

1.5.1.   Usage Constraints

 

      None.

 

1.5.2.   Priority Phasing Constraints

 

      None.

 

 

1.5.3.   Explicit and Derived Constraints

 

      None.

 

1.5.4.   Documentation Conventions

 

1.5.4.1.   Data Format Descriptions

 

      The reference data unit is the byte. Data may be stored in

fields with various sizes and formats, viz. one-, two-, and four-byte

binary integers, four- and eight-byte binary floating-point numbers,

and character strings. Data are identified throughout this document as

 

          char         8 bits      character

          uchar        8 bits      integer

          short       16 bits      integer

          long        32 bits      integer

          float       32 bits      floating point (sign, exponent, and

                                      mantissa)

          double      64 bits      floating point (sign, exponent, and

                                      mantissa)

          u (prefix)               unsigned (as with ulong  for

                                      unsigned 32-bit integer)

          other                    special data structures such as

                                      time, date, etc. which are

                                      described within this document

 

The detailed formats of the numeric fields are defined in Appendix A.

 

      If a field is described as containing n bytes of ASCII character

string data, this implies that the leftmost (lowest numbered) byte

contains the first character, the next lowest byte contains the second

character, and so forth.

 

      An array of n elements is written as array[n]; the first element

is array[0], and the last is array[n-1]. Array[n][m] describes an n by

m element array, with first element array[0][0], second element

array[0][1], and so forth. 

 

1.5.4.2.   Time Standards

 

      RSDMAP files use the January 1.5, 2000 epoch as the standard

time.  Within the data files, all times are reported in Universal

Coordinated Time (UTC) as strings of 23 ASCII characters.  The time

format is  "YYYY-MM-DDThh:mm:ss.fff", where "-", "T", ":", and "." are

fixed delimiters; "YYYY" is the year "19nn" or "20nn"; "MM" is a two-

digit month of year; "DD" is a two-digit day of month; "T" separates

the date and time segments of the string; "hh" is hour of day; "mm" is

the minutes of hour (00-59); "ss" is the seconds of hour (00-59); and

"fff" is in milliseconds.

 

      The date format is "YYYY-MM-DD", where the components are

defined as above.

 

1.5.4.3.   Coordinate Systems

 

      Coordinate systems for RSDMAP products are specified in the

IMAGE_MAP_PROJECTION definition in the PDS label (see Section 4.2.3).

These may be described more fully in other documents -- e.g. [2,3].

 

1.5.4.4.   Limits of This Document

 

      This document applies only to RSDMAP data files.

 

1.5.4.5.   Typographic Conventions

 

      This document has been formatted for simple electronic file

transfer and display.  Line lengths are limited to 80 ASCII

characters, including line delimiters.  No special fonts or structures

are included within the file.  Constant width characters are assumed

for display.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.  Interface Characteristics

 

2.1.   Hardware Characteristics and Limitations

 

2.1.1.   Special Equipment and Device Interfaces

 

      Users of the RSDMAP product must have access to the data system

(or to backup media) on which RSDMAP files are stored.

 

2.1.2.   Special Setup Requirements

 

      None.

 

2.2.   Volume and Size

 

      RSDMAP products have variable length depending on the resolution

of the map, the number of quantities represented in the image, and the

format of the individual data points.  A rectangular map of resolution

1 degree in both latitude and longitude with a single parameter given

as a double precision floating point number requires about 520 kB

total.  The same map in one-byte integers would require about 65 kB.

 

 

2.3.   Labeling and Identification

 

      The length of file names is limited to 27 or less characters before the period delimeter and 3 characters after the period delimeter.

 

      Each file has a name which describes its contents. The name

includes the following structure which uniquely identifies it among

RSDMAP products.  Beginning with the MRO gravity products the following file naming convention is used:

 

                               GTsss_ffff_nnnn_cccc.IMG

 

where 

 

      "G"       denotes the generating institution

                      "A"      for Arizona State University

                      "J"      for the Jet Propulsion Laboratory

                      "G"      for Goddard Space Flight Center

                      "C"      for Centre National d'Etudes Spatiales

                      "S"      for Stanford University

 

      "T"       indicates the type of mission data represented

                      "G" for gravity field

                      "T" for topography

                      "M" for magnetic field

 

      "sss"     is a 3-character modifier specified by the data

                producer. This modifier is used to indicate the source

                spacecraft or project, such as MRO for the Mars

                Reconnaisance Orbiter.

 

      "_"       the underscore character is used to delimit information

                in the file name for clarity.

 

      "ddddff"  is a 4- to 6-character modifier specified by the data

                producer to indicate the degree and order of the

                solution for the gravity field, topography or magnetic

                field.

 

      "_"       the underscore character is used to delimit information

                in the file name for clarity.

 

     "nnnn"     is a 4- to 8-character modifier indicating the type

                of data represented

                      "ANOM"      for free air gravity anomalies

                      "ANOMERR"   for free air gravity anomaly

                                  errors (1)

                      "GEOID"     for geoid

                      "GEOIDERR"  for geoid errors (1)

                      "BOUG"      for Bouguer anomaly

                      "ISOS"      for isostatic anomaly

                      "TOPO"      for topography

                      "MAGF"      for magnetic field

 

               (1) Geoid and gravity anomaly errors are computed

                   from a mapping of the error covariance matrix

                   of the gravity field solution.

 

    "_"       the underscore character is used to delimit information

              in the file name for clarity.

 

         "cccc"    is a 2- to 4-character modifier specified by the data producer

  to indicate the degree and order to which the potential

  solution  (gravity, topography or magnetic field) has

  been evaluated. In the case of the error maps for the

  gravity anomalies or geoid, this field indicates to

  which maximum degree and order the error covariance was '

  used to propagate the spatial errors

 

   ".IMG"     indicates the data is stored as an image.

 

 

      Each RSDMAP file is accompanied by a detached PDS label; that label is a file in its own right with name GTsss_ffff_nnnn_cccc.LBL

 

 

 

2.4.   Interface Medium Characteristics

 

      RSDMAP products are electronic files.

 

2.5.   Failure Protection, Detection, and Recovery Procedures

 

      None.

 

2.6.   End-of-File Conventions

 

      End of file labeling complies with standards of the data system

or medium on which they are stored.

 

 

 

 

3.   Access

 

3.1.   Programs Using the Interface

 

      Data contained in RSDMAP files will be accessed by programs at

the home institutions of science investigators.  Those programs

cannot be identified here.

 

3.2.   Synchronization Considerations

 

3.2.1.   Timing and Sequencing Considerations

 

      N/A

 

3.2.2.   Effective Duration

 

      N/A

 

3.2.3.   Priority Interrupts

 

      None.

 

3.3.   Input/Output Protocols, Calling Sequences

 

      None.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.   Detailed Interface Specifications

 

4.1.   Structure and Organization Overview

 

      The RSDMAP is a file generated by software at the institution

conducting scientific data analysis.  Each RSDMAP file is

accompanied by a detached PDS label.

 

4.2. Detached PDS Label

 

      The detached PDS label has three parts -- a header, an IMAGE

object definition, and an IMAGE_MAP_PROJECTION definition.  The header

contains information about the origin of the file and its general

characteristics such as record type and size.  The IMAGE object definition contains information about the image -- lines, pixels, scaling of pixel values, etc.  The IMAGE_MAP_PROJECTION definition describes how one should display the image.

 

      Each detached PDS label is constructed of ASCII records;

each record contains exactly 80 characters.  The last two characters

in each record are the carriage-return (ASCII 13) and line-feed

(ASCII 10) characters.

 

      An example of a complete label is given in Appendix B.

 

4.2.1 Label Header

 

      The structure of the label file header is illustrated in

Figure 4-2-1.  Keyword definitions are given below. 

 

|====================================================================|

|                                                                    |

|                 Figure 4-2-1  RSDMAP Label Header                  |

|                                                                    |

|====================================================================|

|                                                                    |

|  PDS_VERSION_ID = PDS3                                             |

|  RECORD_TYPE = FIXED_LENGTH                                        |

|  RECORD_BYTES = nnn                                                |

|  FILE_RECORDS = nnn                                                |

|  ^IMAGE = "GTnnnnvv.IMG"                                           |

|  INSTRUMENT_HOST_NAME = "cccccccccccccccccccc"                     |

|  TARGET_NAME = "cccc"                                              |

|  INSTRUMENT_NAME = "ccccccccccccccccccccccc"                       |

|  DATA_SET_ID = "ccccccccccccccccccccccc"                           |

|  ORIGINAL_PRODUCT_ID = "ccccccccccccccc"                           |

|  PRODUCT_ID = "GTnnnnvv.IMG"                                       |

|  PRODUCT_RELEASE_DATE = YYYY-MM-DD                                 |

|  DESCRIPTION = "cccccccccccccccccc"                                |

|  START_ORBIT_NUMBER = nnnn                                         |

|  STOP_ORBIT_NUMBER = nnnn                                          |

|  START_TIME = YYYY-MM-DDThh:mm:ss.fff                              |

|  STOP_TIME = YYYY-MM-DDThh:mm:ss.fff                               |

|  SOFTWARE_NAME = "ccccccc;Vn.m"                                    |

|  PRODUCT_CREATION_TIME = YYYY-MM-DDThh:mm:ss.fff                   |

|  PRODUCER_ID = "ccccccc"                                           |

|                                                                    |

|====================================================================|

 

PDS_VERSION_ID =          The version of the Planetary Data System for

                          which these data have been prepared (set to

                          PDS3 by agreement between the Mars Global

                          Surveyor Project and PDS).

 

RECORD_TYPE =             The type of record.  Set to  "FIXED_LENGTH"

                          to indicate that all logical records have

                          the same length.

 

RECORD_BYTES =            The number of bytes per (fixed-length)

                          record.

 

FILE_RECORDS =            The number of records in the RSDMAP file;

                          instance dependent.

 

^IMAGE =                  File name of the RSDMAP file in the form

                          "GTnnnnvv.IMG", where the structure is

                          explained in Section 2.3.

 

INSTRUMENT_HOST_NAME =    Name of the spacecraft; acceptable names

                          include "MARS GLOBAL SURVEYOR", "LUNAR

                          PROSPECTOR", "MARS RECONNAISSANCE ORBITER",

                          and "MESSENGER".

 

TARGET_NAME =             A character string which identifies the

                          target body.  For MGS and MRO RSDMAP files,

                          the character string "MARS".  For Lunar

                          Prospector RSDMAP files, the character

                          string "MOON".  For MESSENGER RSDMAP files,

                          the character string "MERCURY".

 

INSTRUMENT_NAME =         Name of the instrument; set to "RADIO

                          SCIENCE SUBSYSTEM" for products generated

                          from radio science data, or to other

                          instrument names as appropriate.

 

DATA_SET_ID =             Identifier for the data set of which this

                          RSDMAP product is a member.  Set to "MGS-M-

                          RSS-5-SDP-Vn.m" for Mars Global Surveyor

                          RSDMAP products, where "Vn.m" indicates the

                          version number of the data set. Set to

                          "MRO-M-RSS-5-SDP-Vn.m" for MRO.  Set to

                          "MESS-H-RSS-5-SDP-Vn.m" for MESSENGER.

                          Set to "LP-L-RSS-5-SHGBDR-L2-Vn.m"

                          for Lunar Prospector;

 

ORIGINAL_PRODUCT_ID =      Optional.  An identifier for the product

                           provided by the producer.  Generally a

                           file name, different from PRODUCT_ID, which

                           would be recognized at the producer's

                           institution.

 

PRODUCT_ID =              A unique identifier for the product within

                          the collection identified by DATA_SET_ID.

                          Usually the same as the value for ^IMAGE.

                          The naming convention is defined in

                          Section 2.3.

 

PRODUCT_RELEASE_DATE =    The date on which the product was released

                          to the Planetary Data System; entered in the

                          format "YYYY-MM-DD", where components are

                          defined in Section 1.5.4.2.

 

DESCRIPTION =             A short description of the RSDMAP product.

 

START_ORBIT_NUMBER =      Optional.  The first orbit represented in

                          the RSDMAP product.  An integer.

 

STOP_ORBIT_NUMBER =       Optional.  The last orbit represented in

                          the RSDMAP product.  An integer.

 

START_TIME =              The Earth Receive Time at which the first

                          sample was acquired, expressed in the format

                          "YYYY-MM-DDThh:mm:ss.fff"  where the

                          components are defined in Section 1.5.4.2.

 

STOP_TIME =               The Earth Receive Time at which the last

                          sample was acquired, expressed in the format

                          "YYYY-MM-DDThh:mm:ss.fff"  where the

                          components are defined in Section 1.5.4.2.

 

SOFTWARE_NAME =           The name and version number of the program

                          creating this RSDMAP file; expressed as a

                          character string in the format

                          "PROGRAM_NAME;n.mm" where "PROGRAM_NAME" is

                          the name of the software and "n.mm" is the

                          version number.

 

PRODUCT_CREATION_TIME =   The time at which this RSDMAP was created;

                          expressed in the format "YYYY-MM-

                          DDThh:mm:ss.fff"  where the components are

                          defined in Section 1.5.4.2.

 

PRODUCER_ID =             The entity responsible for creation of the

                          RSDMAP product; for products generated by the

                          Mars Global Surveyor Radio Science Team, set

                          to "MGS RST".

 

4.2.2.  Image Object Definition

 

      The Image Object Definition in the label completely describes

the accompanying Digital Map.  It immediately follows the label

header and has the format shown in Figure 4-2-2.

 

Keywords are defined in [4].  There is no requirement within

this document that there be any relationship among RECORD_BYTES,

LINE_SAMPLES, and SAMPLE_BITS other than that the number of bytes

in an image line be an integral multiple of RECORD_BYTES (Section

4.2.1).  It is strongly recommended, however, that producers of

RSDMAP files make the line lengths identically equal to RECORD_BYTES

to ensure maximum compatibility with existing image processing

software.  For compatibility, producers are also encouraged to use

8- or 16-bit integer pixels rather than longer formats.

 

 

|====================================================================|

|                                                                    |

|            Figure 4-2-2  RSDMAP Image Object Definition            |

|                                                                    |

|====================================================================|

|                                                                    |

|  OBJECT               = IMAGE                                      |

|    LINES                      = nnnn                               |

|    LINE_SAMPLES               = nnnn                               |

|    SAMPLE_TYPE                = nnnn                               |

|    SAMPLE_BITS                = nnnn                               |

|    OFFSET                     = nnn.ff                             |

|    SCALING_FACTOR             = nnn.ff                             |

|    DESCRIPTION                = "cccccccccccccc"                   |

|  END_OBJECT           = IMAGE                                      |

|                                                                    |

|====================================================================|

 

 

4.2.3. Image Map Projection Object Definition

 

      The Image Map Projection Object Definition specifies the map

projection for an RSDMAP product.  It is used for interpretation of

the RSDMAP data; it is not required for understanding the structure

of the file.  It immediately follows the Image Object Definition and

has the form shown in Figure 4-2-3.

 

|====================================================================|

|                                                                    |

|        Figure 4-2-3  RSDMAP Image Map Projection Definition        |

|                                                                    |

|====================================================================|

|                                                                    |

|  OBJECT               = IMAGE_MAP_PROJECTION                       |

|    ^DATA_SET_MAP_PROJECTION     = "cccccccc.CAT"                   |

|    COORDINATE_SYSTEM_NAME       = ccccccccccccc                    |

|    COORDINATE_SYSTEM_TYPE       = ccccccccccccc                    |

|    MAP_PROJECTION_TYPE          = "ccccccccccc"                    |

|    A_AXIS_RADIUS                = nnn.ff <unit>                    |

|    B_AXIS_RADIUS                = nnn.ff <unit>                    |

|    C_AXIS_RADIUS                = nnn.ff <unit>                    |

|    FIRST_STANDARD_PARALLEL      = "N/A"                            |

|    SECOND_STANDARD_PARALLEL     = "N/A"                            |

|    POSITIVE_LONGITUDE_DIRECTION = ccccccccccccc                    |

|    CENTER_LATITUDE              = nnn.ff <unit>                    |

|    CENTER_LONGITUDE             = nnn.ff <unit>                    |

|    REFERENCE_LATITUDE           = "N/A"                            |

|    REFERENCE_LONGITUDE          = "N/A"                            |

|    LINE_FIRST_PIXEL             = nnn                              |

|    LINE_LAST_PIXEL              = nnn                              |

|    SAMPLE_FIRST_PIXEL           = nnn                              |

|    SAMPLE_LAST_PIXEL            = nnn                              |

|    MAP_PROJECTION_ROTATION      = nnn.ff <unit>                    |

|    MAP_RESOLUTION               = nnn.ff <unit>                    |

|    MAP_SCALE                    = "N/A"                            |

|    MAXIMUM_LATITUDE             = nnn.ff <unit>                    |

|    MINIMUM_LATITUDE             = nnn.ff <unit>                    |

|    EASTERNMOST_LONGITUDE        = nnn.ff <unit>                    |

|    WESTERNMOST_LONGITUDE        = nnn.ff <unit>                    |

|    LINE_PROJECTION_OFFSET       = nnn.ff                           |

|    SAMPLE_PROJECTION_OFFSET     = nnn                              |

|  END_OBJECT           = IMAGE_MAP_PROJECTION                       |

|                                                                    |

|====================================================================|

 

      Keywords are defined, and standard values are given, in [4].

For Mars Global Surveyor, Mars Reconnaissance Orbiter, and Messenger RSDMAP

products, the following are required:

 

         COORDINATE_SYSTEM_NAME       = "PLANETOCENTRIC"

         COORDINATE_SYSTEM_TYPE       = "BODY-FIXED ROTATING"

         POSITIVE_LONGITUDE_DIRECTION = "EAST"

 

DSMP.CAT  is a file stored elsewhere (in the CATALOG directory); it specifies the map projection more explicitly.

 

4.3   Data File

 

      The data file is the Image Object, defined in 4.2.2 and

presumed to contain the digital map.

 

      Each map comprises LINES rows of LINE_SAMPLES pixels; each

pixel occupies SAMPLE_BITS bits.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. Support Staff and Cognizant Personnel

 

 

      The following persons may be contacted for information.

     

 

      Mars Global Surveyor Radio Science Team:

 

            Richard A. Simpson

            Packard Building - Room 332

            Stanford University

            Stanford, CA  94305

            Phone:  650-723-3525

            FAX:    650-723-9251

            Electronic mail:  rsimpson@magellan.stanford.edu

 

      Mars Reconnaissance Orbiter Gravity Science Team:

                                                                     

            Frank G. Lemoine

            Code 698, Planetary Geodynamics Laboratory

            NASA Goddard Space Flight Center

            Greenbelt, Maryland 20771 U.S.A.

            Phone:  301-614-6109                                              

            FAX:    301-614-6522                                             

            Electronic mail:  Frank.Lemoine@gsfc.nasa.gov

 

      Messenger Laser Altimeter Science Team:

 

            Maria T. Zuber

            Department of Earth, Atmospheric, and Planetary

             Sciences

            Massachusetts Institute of Technology

            54-918

            Cambridge, MA 02139-4307

            Phone: 617-253-0149

            FAX:   617-253-8298

 

      Planetary Data System:

 

            PDS Operator

            Planetary Data System

            MS 202-101

            Jet Propulsion Laboratory

            4800 Oak Grove Drive

            Pasadena, CA  91109-8099

 

            Phone:  818-354-4321

            Electronic Mail:  pds_operator@jpl.nasa.gov

 

 

 

 

 

 

 

 

 

 

Appendix A. Binary Data Format

 

A.1. IEEE Integer Fields

 

 0       7                                      1-byte (char; uchar)

 ---------

|   [0]   |

 ---------

 

 0                15                            2-byte (short; ushort)

 --------- ---------

|   [0]   |   [1]   |

 --------- ---------

 

 0                                    31        4-byte (long; ulong)

 --------- --------- --------- ---------

|   [0]   |   [1]   |   [2]   |   [3]   |

 --------- --------- --------- ---------

 

 

IEEE binary integers are stored in one, two, or four consecutive 8-bit

bytes. Unsigned integers uchar, ushort, ulong, which always represent

positive values, contain 8, 16, or 32 binary bits, respectively. As

illustrated above, the significance increases from the rightmost bit

to the leftmost (bit 0). Signed integers (char, short, long) are

stored in the same way, except that negative values are formed by

taking the corresponding positive value, complementing each bit, then

adding unity -- known as "two's complement" format. As a consequence,

a negative value always has bit 0 set "on". Integers are written

externally in increasing byte-number order, i.e. [0], [1], etc., so

that more significant bits always precede less significant ones. For

example, the short value -2 is stored as a pair of bytes valued  0xff,

0xfe.

 

A.2. IEEE Floating-Point Fields

 

 0 1       8 9                        31               4-byte (float)

 --------- --------- --------- ---------

| |  [0]  | |  [1]  |   [2]   |   [3]   |

 --------- --------- --------- ---------

 

 0 1       8 9                        31               8-byte (double)

 --------- --------- --------- ---------

| |  [0]  | |  [1]  |   [2]   |   [3]   |

 --------- --------- --------- ---------

           32                                   63

           --------- --------- --------- ---------

          |   [4]   |   [5]   |   [6]   |   [7]   |

           --------- --------- --------- ---------

 

 

IEEE single- (double-) precision floating point numbers (known to IEEE

enthusiasts as E-type floating-point formats, respectively) are stored

in four (eight) consecutive bytes. Bit number 0 contains a sign

indicator, S. Bits 1 through 8 (11) contain a binary exponent, E. The

significance increases from bit 8 (11) through bit 1. Bits 9 (12)

through 31 (63) contain a mantissa M, a 23-bit (52-bit) binary

fraction whose binary point lies immediately to the left of bit 9

(12). The significance increases from bit 31 (63) through bit 9 (11).

The value of the  single-precision field is given by

 

                             S  E-127

                         (-1) *2     *(1+M)

 

The value of the  double-precision field is given by

 

                             S  E-1023

                         (-1) *2      *(1+M)

 

The numbers are stored externally in increasing byte-number order,

i.e. [0], [1], etc. For example, the maximum single-precision float

value +3.40282347E+38 is stored as four bytes valued 0x7f, 0x7f, 0xff,

0xff.

 

Special single-precision float values are represented as +Infinity

(0x7f800000), -Infinity (0xff800000), quiet NaN (not a number)

(0xffffffff), and signaling NaN (0x7f800001).

 

A.3. VAX Integer Fields

 

 0       7                                      1-byte (char; uchar)

 ---------

|   [0]   |

 ---------

 

 0                15                            2-byte (short; ushort)

 --------- ---------

|   [1]   |   [0]   |

 --------- ---------

 

 0                                    31        4-byte (long; ulong)

 --------- --------- --------- ---------

|   [3]   |   [2]   |   [1]   |   [0]   |

 --------- --------- --------- ---------

 

      VAX binary integers are stored in one, two, or four consecutive

8-bit bytes. Unsigned integers uchar, ushort, and ulong (which always

represent positive values) contain 8, 16, or 32 binary bits,

respectively.  As illustrated above, the significance increases from

the rightmost bit to the leftmost (bit 0).  Signed integers (char,

short, long) are stored in the same way, except that negative values

are formed by taking the corresponding positive value, complementing

each bit, then adding unity -- known as "two's complement" format. As

a consequence, a negative value always has bit 0 set or "on." 

Integers are written externally in increasing byte-number order, i.e.

[0], [1], etc., so that less significant bits always precede more

significant ones.  For example, the short value -2 is stored as a pair

of bytes valued 0xfe, 0xff.  (This section has been adapted from a

description by P.G. Ford in the Magellan ARCDR SIS).

 

 

 

 

 

 

 

A.4. VAX Floating-Point Fields

 

 0 1       8 9                        31               4-byte (float)

 --------- --------- --------- ---------

| |  [1]  | |  [0]  |   [3]   |   [2]   |

 --------- --------- --------- ---------

 

 0 1       8 9                        31               8-byte (double)

 --------- --------- --------- ---------

| |  [1]  | |  [0]  |   [3]   |   [2]   |

 --------- --------- --------- ---------

           32                                   63

           --------- --------- --------- ---------

          |   [5]   |   [4]   |   [7]   |   [6]   |

           --------- --------- --------- ---------

 

      VAX single- (double-) precision floating point numbers (known to

VAX enthusiasts as F-type and D-type floating-point formats,

respectively) are stored in four (eight) consecutive bytes.  Bit

number 0 contains a sign indicator, S.  Bits 1 through 8 contain a

binary exponent, E.  The significance increases from bit 8 through bit

1.  Bits 9 through 31 (63) contain a mantissa M, a 23-bit (55-bit)

binary fraction whose binary point lies immediately to the left of bit

9.  The significance increases from bit 31 (63) through bit 9.  The

value of the field is given by

 

                              S  E-129

                          (-1) *2     *(1+M)

 

The numbers are stored externally in increasing byte-number order,

i.e. [0], [1], etc.  For example, the float value +1.0 is stored as

four bytes valued 0x80, 0x40, 0x00, 0x00.  (This section has been

adapted from a description by P.G. Ford in the Magellan ARCDR SIS).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix B.   Example RSDMAP Label and Data Object

 

B.1  Example Label

 

PDS_VERSION_ID               = PDS3                                          

RECORD_TYPE                  = FIXED_LENGTH                                  

RECORD_BYTES                 = 2880                                          

FILE_RECORDS                 = 180                                           

^IMAGE                       = "GG041A60.IMG"                               

INSTRUMENT_HOST_NAME         = "MARS RECONNAISSANCE ORBITER"                 

TARGET_NAME                  = "MARS"                                        

INSTRUMENT_NAME              = "RADIO SCIENCE SUBSYSTEM"                     

DATA_SET_ID                  = "MRO-M-RSS-5-SDP-V1.0"                        

ORIGINAL_PRODUCT_ID          = "MGM1041A.ANOMALY"                            

PRODUCT_ID                   = "GG041A60.IMG"                                 

PRODUCT_RELEASE_DATE         = 2006-02-23                                    

DESCRIPTION                  = "                                             

 This file contains a digital map of the gravity anomalies derived from        

 the MGM1041A model of the Mars gravity field.  Each point gives the         

 Mars gravity anomaly in milligals, which is the difference of the           

 model gravity on the geoid from the normal gravity on a reference           

 ellipsoid with                                                               

         semi-major-axis = 3397.0 km,                                        

         GM              = 42828.37024 km**3/s**2,                           

         1/flattening    = 196.877360, and                                    

         rotation rate   = 7.08821806630385e-5 rad/s.                        

 

 The GG041A60 gravity anomaly map is computed from a truncated MGM1041A      

 solution (from degree 2 up to degree 60) where 'GD' in the file name        

 indicates it is Gravity anomaly data, '041A' indicates the MGM1041A         

 solution is used, and '60' indicates the maximum degree of the field        

 used to create the map.                                                     

                                                                              

 The map was produced by the Mars Global Surveyor Gravity Science Team       

 at GSFC under the direction of David E. Smith, by Frank G. Lemoine.         

 

 This anomaly map contains 64800 values.

 Location of minimum and maximum anomalies in this file:

  Minimum: -507.752 mGals; Longitude = 313.50 E; Latitude 15.50 S

  Maximum: 2977.960 mGals; Longitude = 226.50 E; Latitude 18.50 N 


The binary data format are big endian (binary style on SUN OS type workstations).

 

START_ORBIT_NUMBER           = "N/A"                                         

STOP_ORBIT_NUMBER            = "N/A"                                         

START_TIME                   = 1997-10-13T00:00:00.000                        

STOP_TIME                    = 2002-05-27T23:59:59.000                       

SOFTWARE_NAME                = "HIGEN;V9.0"                                  

PRODUCT_CREATION_TIME        = 2006-02-23T17:50:00.000                       

PRODUCER_ID                  = "MRO GST"                                     

 

/* Structure Objects */                                                      

                                                                             

OBJECT                       = IMAGE                                         

  LINES                        = 180                                         

  LINE_SAMPLES                 = 360                                         

  SAMPLE_TYPE                  = "IEEE REAL"                                 

  SAMPLE_BITS                  = 64                                          

  OFFSET                       = 0.0E+00                                     

  SCALING_FACTOR               = 1.0E+00                                      

  DESCRIPTION                = "The Digital Map contains                     

   values of the gravity anomaly.  The values can be obtained                

   by multiplying the sample in the map by SCALING_FACTOR                     

   and then adding OFFSET.  One milligal equals 0.01 mm/s/s."                

END_OBJECT                   = IMAGE                                         

                                                                             

OBJECT                       = IMAGE_MAP_PROJECTION                          

  ^DATA_SET_MAP_PROJECTION     = "DSMAP2.CAT"                                

  COORDINATE_SYSTEM_TYPE       = "BODY-FIXED ROTATING"                       

  COORDINATE_SYSTEM_NAME       = "PLANETOCENTRIC"                              

  MAP_PROJECTION_TYPE          = "SIMPLE CYLINDRICAL"                        

  A_AXIS_RADIUS                = 3397.00 <KM>                                 

  B_AXIS_RADIUS                = 3397.00 <KM>                                  

  C_AXIS_RADIUS                = 3379.75 <KM>                                 

  FIRST_STANDARD_PARALLEL      = "N/A"                                       

  SECOND_STANDARD_PARALLEL     = "N/A"                                        

  POSITIVE_LONGITUDE_DIRECTION = "EAST"                                      

  CENTER_LATITUDE              = 0.0 <DEGREES>                               

  CENTER_LONGITUDE             = 180.0 <DEGREES>                            

  REFERENCE_LATITUDE           = 0.0 <DEGREES>                               

  REFERENCE_LONGITUDE          = 0.0 <DEGREES>                               

  LINE_FIRST_PIXEL             = 1                                           

  LINE_LAST_PIXEL              = 180                                         

  SAMPLE_FIRST_PIXEL           = 1                                           

  SAMPLE_LAST_PIXEL            = 360                                         

  MAP_PROJECTION_ROTATION      = 0.0 <DEGREES>                                

  MAP_RESOLUTION               = 1.0E+00                                     

  MAP_SCALE                    = "N/A"                                       

  MAXIMUM_LATITUDE             = 89.5 <DEGREES>                               

  MINIMUM_LATITUDE             = -89.5 <DEGREES>                             

  EASTERNMOST_LONGITUDE        = 359.5 <DEGREES>                             

  WESTERNMOST_LONGITUDE        = 0.5 <DEGREES>                            

  LINE_PROJECTION_OFFSET       = 89.5                                        

  SAMPLE_PROJECTION_OFFSET     = -0.5                                       

END_OBJECT                   = IMAGE_MAP_PROJECTION                          

                                                                              

END                                                                          

 

 

 

 

B.2      Example Data Object                                                 

                                                                              

      The list below contains the ascii dump of the first and last record

or the map file cited in B.1. The first record consists of the map data

at the northernmost latitude (89.5 degrees), sequentially from longitude

0.5 to 359.5 degrees. The last record contains the map data for the southern-

most latitude (-89.5 deg) from longitude 0.5 to 359.5 degrees.

 

      A convenient way to read the image data for the

example givien in Appendix B.1  is with a fortran program

that has the following statements:

    ......................................

       implicit double precision(a-h,o-z)

       dimension rec(360)

       dminlon = 0.5d0

       dmaxlat = +89.5d0

 

       open(10,file='gg041a60.img',recl=2880,access='direct')

       line=1

       do 5 line=1,180

 10    read(10,rec=line)rec

 

       do 20 i=1,360

        dlon = dminlon + dfloat(i-1)

        dlat = dmaxlat - dfloat(line-1)

        write(6,30)dlon,dlat,rec(i)

 20    continue

 30    format(1x,2f15.5,e20.8)

 5     continue

 99    stop

       end

   ........................................

 

The image file may also be read directly into a GMT (Generic

Mapping Tools) [10,11] grd file  using the following command:

(noting that the command wraps around onto a second line in

 this document).

 

xyz2grd gg041a60.img -ZTLd -Gmgm1041a.grd -I1/1 -R0.5/359.5/-89.5/89.5

 -Ddeg/d eg/milligals/1/0/" Gravity Anomaly to 60" –V

 

A generic GMT script to plot the img file is given below:

========================================================

   set -x

   rm –f mgm1041a.grd out.ps tmp.cpt

   xyz2grd gg041a60.img -ZTLd -Gmgm1041a.grd -I1/1 -R0.5/359.5/-89.5/89.5

  -Ddeg/d eg/milligals/1/0/" Gravity Anomaly to 60" –V

   grd2cpt mgm1041a.grd –Chaxby –L-600/600 –S-600/600/100 –Z –V > tmp.cpt

   grdimage mgm1041a.grd –Ctmp.cpt –JM8.0i –R0/360/-70/70 –B30g30/30g30 –K > out.ps

   grdinfo –M mgm1041a.grd

   psscale –Ctmp.cpt –D11.0/14.0/16.0/0.3h –B:.ÓGMM-2B Gravity Anomalies (60x60) (mGals)Ó: -O >>out.ps

   ps2pdf out.ps


 

 

 

 

......

Sample records from gg041a60.img

 rec =  1

   39.426   39.303   39.186   39.074   38.968   38.867   38.772   38.683

   38.599   38.521   38.448   38.381   38.319   38.264   38.213   38.169

   38.129   38.096   38.068   38.045   38.028   38.017   38.011   38.010

   38.016   38.026   38.042   38.064   38.091   38.123   38.161   38.204

   38.252   38.306   38.365   38.430   38.500   38.575   38.655   38.741

   38.832   38.928   39.029   39.136   39.247   39.364   39.485   39.612

   39.743   39.880   40.022   40.168   40.319   40.476   40.637   40.802

   40.973   41.148   41.328   41.512   41.701   41.894   42.092   42.294

   42.501   42.712   42.927   43.147   43.371   43.598   43.830   44.066

   44.306   44.549   44.797   45.048   45.303   45.562   45.824   46.089

   46.358   46.631   46.907   47.186   47.468   47.753   48.041   48.332

   48.626   48.923   49.223   49.525   49.830   50.137   50.447   50.759

   51.073   51.389   51.708   52.028   52.350   52.674   53.000   53.328

   53.657   53.987   54.319   54.652   54.987   55.322   55.659   55.996

   56.334   56.673   57.013   57.353   57.694   58.035   58.377   58.718

   59.060   59.402   59.744   60.085   60.426   60.767   61.107   61.447

   61.787   62.125   62.463   62.799   63.135   63.470   63.803   64.135

   64.466   64.795   65.122   65.448   65.772   66.094   66.414   66.733

   67.048   67.362   67.673   67.982   68.289   68.592   68.893   69.191

   69.487   69.779   70.068   70.354   70.636   70.915   71.191   71.463

   71.732   71.996   72.257   72.514   72.767   73.016   73.261   73.501

   73.737   73.969   74.196   74.418   74.636   74.849   75.057   75.260

   75.458   75.651   75.839   76.021   76.199   76.371   76.537   76.698

   76.853   77.003   77.147   77.285   77.417   77.544   77.664   77.779

   77.887   77.989   78.086   78.175   78.259   78.336   78.407   78.472

   78.530   78.581   78.626   78.665   78.697   78.722   78.741   78.753

   78.758   78.757   78.749   78.734   78.713   78.685   78.650   78.608

   78.559   78.504   78.442   78.373   78.297   78.215   78.126   78.030

   77.927   77.818   77.702   77.580   77.450   77.315   77.172   77.023

   76.868   76.706   76.538   76.364   76.183   75.996   75.803   75.603

   75.398   75.186   74.969   74.746   74.517   74.282   74.041   73.795

   73.543   73.286   73.024   72.757   72.484   72.206   71.923   71.636

   71.343   71.046   70.745   70.439   70.128   69.814   69.495   69.173

   68.846   68.516   68.182   67.845   67.504   67.160   66.813   66.464

   66.111   65.755   65.397   65.037   64.674   64.309   63.943   63.574

   63.204   62.832   62.458   62.084   61.708   61.331   60.953   60.575

   60.196   59.817   59.438   59.058   58.679   58.299   57.920   57.542

   57.164   56.787   56.410   56.035   55.661   55.288   54.917   54.547

   54.179   53.813   53.449   53.087   52.727   52.370   52.015   51.663

   51.313   50.966   50.622   50.282   49.944   49.610   49.279   48.951

   48.627   48.307   47.990   47.678   47.369   47.064   46.764   46.468

   46.176   45.888   45.605   45.326   45.052   44.782   44.517   44.257

   44.002   43.751   43.506   43.265   43.029   42.799   42.573   42.353

   42.138   41.928   41.724   41.524   41.330   41.142   40.958   40.780

   40.608   40.441   40.279   40.123   39.973   39.828   39.688   39.554

 

 rec =  180

  137.311  137.340  137.364  137.382  137.395  137.402  137.404  137.401

  137.392  137.378  137.359  137.334  137.303  137.268  137.227  137.181

  137.129  137.073  137.011  136.944  136.872  136.795  136.713  136.625

  136.533  136.436  136.334  136.227  136.116  136.000  135.879  135.753

  135.623  135.488  135.349  135.206  135.058  134.905  134.749  134.588

  134.424  134.255  134.082  133.906  133.725  133.541  133.353  133.161

  132.966  132.767  132.565  132.359  132.150  131.938  131.723  131.505

  131.283  131.059  130.832  130.602  130.369  130.134  129.896  129.656

  129.413  129.168  128.920  128.671  128.419  128.165  127.910  127.652

  127.393  127.132  126.869  126.604  126.339  126.071  125.803  125.533

  125.261  124.989  124.716  124.441  124.166  123.890  123.613  123.336

  123.058  122.779  122.500  122.221  121.941  121.661  121.381  121.101

  120.821  120.541  120.261  119.981  119.701  119.422  119.143  118.865

  118.587  118.310  118.034  117.759  117.484  117.210  116.937  116.666

  116.395  116.126  115.858  115.591  115.326  115.062  114.799  114.539

  114.280  114.022  113.767  113.513  113.262  113.012  112.765  112.519

  112.276  112.035  111.797  111.561  111.327  111.096  110.867  110.641

  110.418  110.198  109.980  109.766  109.554  109.345  109.140  108.938

  108.738  108.542  108.350  108.161  107.975  107.793  107.614  107.439

  107.267  107.100  106.936  106.776  106.619  106.467  106.319  106.174

  106.034  105.898  105.766  105.638  105.515  105.395  105.281  105.170

  105.064  104.963  104.865  104.773  104.685  104.602  104.523  104.449

  104.380  104.315  104.255  104.200  104.150  104.105  104.065  104.029

  103.998  103.973  103.952  103.936  103.925  103.919  103.919  103.923

  103.932  103.946  103.965  103.990  104.019  104.053  104.093  104.137

  104.186  104.241  104.300  104.364  104.434  104.508  104.587  104.671

  104.760  104.854  104.953  105.057  105.165  105.278  105.396  105.519

  105.646  105.778  105.914  106.056  106.201  106.351  106.506  106.665

  106.828  106.996  107.168  107.344  107.524  107.709  107.897  108.090

  108.286  108.487  108.691  108.899  109.110  109.326  109.545  109.767

  109.993  110.222  110.455  110.690  110.929  111.172  111.417  111.665

  111.916  112.169  112.426  112.685  112.947  113.211  113.478  113.747

  114.018  114.291  114.567  114.845  115.124  115.405  115.688  115.973

  116.260  116.547  116.837  117.127  117.419  117.712  118.006  118.301

  118.596  118.893  119.190  119.488  119.786  120.085  120.384  120.683

  120.982  121.282  121.581  121.880  122.179  122.477  122.775  123.073

  123.369  123.665  123.961  124.255  124.548  124.840  125.131  125.420

  125.708  125.995  126.280  126.563  126.844  127.124  127.401  127.677

  127.950  128.221  128.489  128.756  129.019  129.280  129.538  129.793

  130.046  130.295  130.541  130.785  131.025  131.261  131.494  131.724

  131.950  132.172  132.391  132.606  132.816  133.023  133.226  133.425

  133.620  133.810  133.996  134.177  134.355  134.527  134.695  134.859

  135.018  135.172  135.321  135.465  135.605  135.739  135.869  135.994

  136.113  136.228  136.337  136.441  136.540  136.633  136.722  136.805

  136.883  136.955  137.022  137.084  137.140  137.191  137.236  137.276