Data Set Overview
    =================
      The gravitational signature of the Moon was determined from
      velocity perturbations of the Clementine spacecraft as measured
      from the Doppler shift of the S-band radio tracking signal.
      Clementine was tracked by NASA's Deep Space Network (DSN) at
      Goldstone, California, Canberra, Australia, Madrid, Spain, as
      well as by the Pomonkey, Maryland, tracking station operated by
      the Naval Research Laboratory.  The tracking data were used to
      determine the Clementine orbit about the Moon, as well as the
      lunar gravity field [ZUBERETAL1994].  A detailed description of
      how the Clementine orbits were computed and an assessment of
      their quality can be found in [LEMOINEETAL1995B].
 
      The Clementine data were combined with S-band tracking
      observations from Lunar Orbiters 1, 2, 3, 4, and 5 and from the
      Apollo 15 and 16 subsatellites [KONOPLIVETAL1993B].  With the
      exception of the Lunar Orbiter 4 and Lunar Orbiter 5
      spacecraft, these spacecraft lacked the global coverage of
      Clementine (LO-4 and LO-5 were placed in near polar, elliptical
      orbits of the Moon), but most had lower periapsis altitudes and
      thus provided distributed regions of short-wavelength
      resolution in the vicinity of spacecraft periapses (generally
      +/- 40 degrees latitude).
 
      There are seven gravity products in this archive.  These
      include a 70-th degree and order spherical harmonic
      gravitational field model, designated Goddard Lunar Gravity
      Model 2 (GLGM-2), and digital gridded maps of the Free-air
      gravity anomalies (at 1 and 0.25 degree resolution), Free-air
      gravity errors, Bouguer gravity anomalies, Geoid anomalies,
      Geoid anomaly errors, and effective crustal thicknesses.
 
 
    Data
    ====
      There are 3 data types for the gravity products found on this
      volume: tabular, array, and image data.  The file containing
      the spherical harmonic coefficients of the Moon's gravity field
      (GLGM-2) is in tabular format, with each row in the table
      containing the degree index m, the order index n, the
      coefficients Cmn and Smn, and the uncertainties in Cmn and Smn.
 
      The gridded digital maps of Free-air gravity anomalies (at 1
      and 0.25 degree resolution), Free-air gravity errors, Bouguer
      anomalies, Geoid anomalies, Geoid anomaly errors, and crustal
      thicknesses are ASCII 2-D data arrays.  There is also a
      byte-scaled image of each of the gridded products.
 
 
    Parameters
    ==========
      The gravitational signature of the Moon was determined from
      velocity perturbations of the Clementine spacecraft, Lunar
      Orbiters and Apollo 15 and 16 subsatellites as measured from
      the Doppler shift of the S-band radio tracking signal.  The
      Clementine Doppler data from the DSN stations were acquired
      with a count interval of 10 seconds.  Data from the Pomonkey
      station were also at a 10 second count interval.  Most of the
      historic Doppler data were at a count interval of 60 seconds.
 
      The Free-air gravity anomalies of the Moon (in milligals,
      mGals, where 1 mGal = 0.01 mm/s^2) are evaluated at the
      surface, and are determined from the GLGM-2 solution.  The
      Free-air gravity errors are also in mGals.  Bouguer anomalies,
      determined by subtracting the gravitational attraction of the
      surface topography from the free-air anomaly, are in mGals.
      Geoid anomalies and errors are in meters.  Crustal thicknesses,
      assuming a constant-density crust and mantle, are in
      kilometers.
 
 
    Processing
    ==========
      The GLGM-2 gravity solution consists of 708,854 observations,
      of which 361,794 were contributed by Clementine.  The data were
      divided into 392 spans or independent arcs based on
      considerations of data coverage and timing of maneuvers.  The
      table below summarizes the number of observations and arcs from
      each spacecraft:
 
      Satellite Number Avg.  Arc Total Observations of Arcs Length
      (hours)
 
      Lunar Orbiter-1 48 21.76 44,503 Lunar Orbiter-2 62 16.38 68,732
      Lunar Orbiter-3 68 17.77 61,852 Lunar Orbiter-4 11 70.16 48,734
      Lunar Orbiter-5 51 33.74 47,690 Apollo-15 subsatellite 81 16.76
      44,096 Apollo-16 subsatellite 35 4.55 31,453 Clementine 36
      44.16 361,794
 
      Total 392 708,854
 
 
      For each arc certain parameters were determined: the spacecraft
      state (position and velocity), a solar radiation pressure
      coefficient, Doppler biases for each station over the arc to
      account for frequency biases, and the mismodeling of the
      effects of the troposphere and ionosphere on the Doppler
      signal.  The a priori force model that was used included the
      [KONOPLIVETAL1993B] gravity model, and included the third-body
      perturbations due to the Sun, the Earth, and all the planets,
      the solar radiation pressure perturbation, the Earth-induced
      and solar-induced solid lunar tides (assuming a k2 value of
      0.027, as derived by previous investigators), and appropriate
      relativistic effects.  The DE200 set of planetary and lunar
      ephemerides was used in the analyses.
 
      The data in GLGM-2 were weighted at 1 to 3 cm/s, with the
      exception of the Clementine data, which had a data weight of
      0.5 cm/s (because of their high quality).  Although each data
      arc was typically fit to the level of a few mm/s, the data were
      downweighted in this fashion in order to attenuate the power of
      the high degree terms, and account for any systematic
      mismodeling that might still be present in the data.  The
      solution was also derived using a power law rule (Kaula
      constraint of 15 x 10e-5/L^2), where L is the spherical
      harmonic degree.  Without this constraint, the high degree
      terms develop excessive power.
 
      In the process of deriving GLGM-2, extensive experiments were
      performed in order to select the a priori weights for the sets
      of data in the solution - and care was taken to downweight or
      delete data that produced spurious signals in the anomaly maps.
      (GLGM-2 is the 309th in the series of lunar gravity solutions
      that have been developed in the course of this work since just
      prior to the Clementine mission).  The gravity anomalies in
      this model were evaluated at the lunar surface.
 
 
    Ancillary Data
    ==============
      N/A
 
 
    Coordinate System
    =================
      The coordinate system for the gravity data, and the
      coefficients in the GLGM-2 gravity field, is selenocentric,
      center of mass, longitude positive east.  The location of the
      pole and the prime meridian are defined as per the reference
      from [DAVIESETAL1992B], with corrections for two of the terms.
 
      alpha_0 = 270.000 + 0.003 T - 3.878 sin E1 - 0.120 sin E2 +
      0.070 sin E3 - 0.017 sin E4
 
      delta_0 = 66.541 + 0.013 T + 1.543 cos E1 + 0.024 cos E2 -
      0.028 cos E3 + 0.007 cos E4
 
      W = 38.317 + 13.1763582 d + 3.558 sin E1 + 0.121 sin E2 - 0.064
      sin E3 + 0.016 sin E4 + 0.025 sin E5
 
      E1 = 125.045 - 0.052992 d E2 = 250.090 - 0.105984 d E4 =
      176.625 + 13.340716 d
 
      The quantities E3 and E5 are listed incorrectly in the
      reference, and were corrected by [DAVIESETAL1993B, personal
      communication to the Clementine Science Team].  The correct
      values are:
 
      E3 = 260.008 + 13.012001 d E5 = 357.529 + 0.985600 d
 
      where T = interval in Julian centuries (36525 days) from the
      standard epoch.
 
      d = interval in days from the standard epoch.
 
      W = location of the prime meridian in degrees.
 
      alpha_0 and delta_0 are the standard equatorial coordinates, in
      degrees, with equinox J2000 at epoch J2000 (right ascension and
      declination).
 
      Standard Epoch is 2000 January 1.5 or Julian Date 2451545.0
      TBD.
 
 
    Software
    ========
      N/A
 
 
    Media/Format
    ============
      The Clementine gravity dataset will be available electronically
      via the World-Wide Web and anonymous FTP transfer.  File types
      include ASCII and binary formats.  Formats will be based on
      standards established by the Planetary Data System (PDS).