Dawn Vesta Gravity Science Derived Data Bundle Description
==========================================================

References
==========

- Asmar, S.W., R.G. Herrera, and T. Priest, Radio Science Handbook, 
JPL D-7938 Vol. 6, Jet Propulsion Laboratory, Pasadena, CA, 1995.

- Asmar, S.W., and N.A. Renzetti, The Deep Space Network as an 
Instrument for Radio Science Research, Jet Propulsion Laboratory 
Publication 80-93, Rev. 1, 1993.

- Bini, A., I. Ficai-Veltroni, S. Pieraccini, G. Cherubini, 
M. Benetello, and M. Giustini, Instrument system description, 
VID-GAF-RP-002, 2005.

- Deep Space Network Telecommunications Link Design Handbook, 
JPL-E-810-005 Jet Propulsion Laboratory, Pasadena, CA, 2013.

- H.&B.S. Jeffreys, Methods of Mathematical Physics, Third Edition. 
Cambridge University Press, 1962, 269 p.

- Deep Space Mission System (DSMS) External Interface Specification 
(820-013, JPL D-16765), Radio Science Receiver Standard Formatted 
Data Unit (SFDU), Jet Propulsion Laboratory, Pasadena, CA, 2001.

- Konopliv, A.S., S.W. Asmar, B.G. Bills, N. Mastrodemos, R.S. Park,
C.A. Raymond, D.E. Smith, and M.T. Zuber, The Dawn Gravity Investigation
at Vesta and Ceres, Space Science Reviews, 163, 461-486, 2011.

- Konopliv, A.S., S.W. Asmar, R.S. Park, B.G. Bills, F. Centinello, 
A.B. Chamberlin, A. Ermakov, R.W. Gaskell, N. Rambaux, C.A. Raymond, 
C.T. Russell, D.E. Smith, P. Tricarico, and M.T. Zuber, The Vesta
gravity field, spin pole and rotation period, landmark positions, 
and ephemeris from the Dawn tracking and optical data, Icarus 240, 
103-117, doi:10.1016/j.icarus.2013.09.005, 2014.

- Moyer, T.D., Mathematical Formulation of the Double-Precision Orbit
Determination Program (DPODP), TR 32-1527, Jet Propulsion Laboratory,
Pasadena, CA, 1971.

- Prettyman, T.H., W.C. Feldman, F.P. Ameduri, B.L. Barraclough, 
E.W. Cascio, K.R. Fuller, H.O. Funsten, D.J. Lawrence, G.W. McKinney, 
C.T. Russell, S.A. Soldner, S.A. Storms, C. Szeles, and R.L. Tokar,
Gamma-ray and neutron spectrometer for the Dawn mission to 1 Ceres and 
4 Vesta, IEEE Trans. Nucl. Sci., Volume 50, Issue 4, pp. 1190-1197, 
August 2003, doi:10.1109/TNS.2003.815156

- Prettyman, T.H., W.C. Feldman, H.Y. McSween, Jr., R.D. Dingler, 
D.C. Enemark, D.E. Patrick, S.A. Storms, J.S. Hendricks, J.P. Morgenthaler, 
K.M. Pitman, R.C. Reedy, Dawn's Gamma Ray and Neutron Detector, Space Sci. 
Rev. (2011) 163:371-459, doi:10.1007/s11214-011-9862-0

- Rayman, M.D., T.C. Fraschetti, C.A. Raymond, and C.T. Russell, Dawn: A 
mission in development for exploration of main belt asteroids Vesta and Ceres,
Acta Astronautica 58, 605-616, 2006.

- Raymond, C.A., Dawn Science Plan, JPL D-31827, 2007.

- Russell, C.T., and C.A. Raymond,
The Dawn Mission to Vesta and Ceres, Space Science
Reviews, 163, 3-23, 2011.

- Schroeder, S.E. and P. Gutierrez-Marques, Calibration Pipeline,
MPS report DA-FC-MPAE-RP-272, Issue 2, Rev. a, 20 July 2011.

- Thornton, C.L. and J.S. Border,
Radiometric Tracking Techniques for Deep Space Navigation, John Wiley
and Sons, Hoboken, NY, 2003.

- 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, Journal of Geophysical
Research, 97, 7759-7779, 1992.

Collections Overview
====================

The Dawn Vesta Gravity Archive Data Collection of Science Data Products 
(SDP) includes data products generated from gravity investigations
conducted by members of the Dawn Gravity Team while the spacecraft
was in orbit around the asteroid Vesta. Radio measurements were made
using the Dawn spacecraft and Earth-based stations of the NASA Deep
Space Network (DSN).

Gravity SDPs include spherical harmonic models of Vesta's gravity field, 
maps or images of those models, and possibly line-of-sight acceleration 
profiles. A group at the Jet Propulsion Laboratory JPL under the direction 
of Sami Asmar produced spherical harmonic models and maps. These results 
were derived from raw radio tracking data.

At Vesta, the mission was divided into three science orbits.
All the orbits were polar. The Survey orbit was performed at
a nominal altitude of 2735 km. The High Altitude Mapping
Orbit, or HAMO, was performed at a nominal altitude of 685 km.
The Low Altitude Mapping Orbit, or LAMO, was performed at a
nominal altitude of 200 km. The spacecraft spent 20 days in
Survey orbit, 34 days in HAMO-1, 141 days in LAMO, and another
40 days in HAMO-2. Between these science orbits, the spacecraft
was in a transfer phase using the electric ion engines
(Russell & Raymond, 2011).

Parameters
==========

Spherical harmonic models are tables of coefficients GM, Cmn,
and Smn -- as in equation (1) of (Tyler et al., 1992). These can
be used to represent gravitational potential of Vesta, for
example. ASCII (data type SHA) formatted spherical harmonics
are defined. Each file contains up to four tables: 
a header table containing general parameters for
the model (gravitational constant, its uncertainty, degree 
and order of the field, normalization state, reference longitude,
and reference latitude); a names table, giving the order in
which coefficients appear; a coefficients table (degree m,
order n, coefficients Cmn and Smn, and their uncertainties).

Radio Science Digital Map files are image representations
of gravity and other parameters. Free air gravity, geoid,
Bouguer anomaly, isostatic anomaly, and topographic values
may be displayed using this data type. Data are formatted
as PDS image objects. Provided in this bundle are several 
map types including a map of radial acceleration using the 
VESTA20H field with the J2 coefficient removed.

Processing
==========

Spherical harmonic models, maps, and line-of-sight acceleration
profiles are derived from raw radio tracking data in several
steps.

The tracking data are processed in large orbit determination
programs that integrate the equations of motion (DPODP at JPL
(Moyer, 1971)), and model mathematically the radio science observables
(ramped Doppler and range data). The observations are related to
the geophysical parameters through the numerical integration and the
detailed mathematical modeling of the radio science observables, and of
all forces acting on the spacecraft trajectory, including 
planetary and third body gravity, solar radiation pressure, 
planetary radiation pressure, atmospheric drag, solid body tides,
and relativity, where applicable.

The gravity field coefficients are obtained by accumulating
normal equations from often hundreds of data arcs, and
solving these systems of linear equations with thousands of unknowns.
The unknowns include arc parameters, particular to one data arc (such
as the spacecraft state, radiation pressure scale factors,
atmospheric drag scale factors, etc.) and common parameters
(such as the gravity coefficients, the planetary gravitational
constant or GM). Radio tracking data are processed in arcs delimited by 
propulsive maneuvers, occultations, etc. 

The spacecraft periodically performed angular momentum
desaturation maneuvers. These maneuvers allowed the reaction
wheels to spin down to avoid damage, but they had be countered
the use of thrusters. Arcs may be delimited by these maneuvers.
The details of each of these maneuvers specified in the small forces
file of the Dawn Vesta Gravity Science Raw Data Archive.

Useful references which describe the procedures applied in
general to processing Vesta orbiter tracking data include
(Konopliv et al., 2014).  

(Thornton & Border, 2003) is a general reference for Orbit Determination.

Data
====
Data are available online through the Planetary Data System
(http://pds.nasa.gov).

ASCII spherical harmonic models are stored in the data-shadr/ directory
with file names of the form GTDWN_nnnnvv_SHA.TAB where:

  'G'   denotes the generating institution
                  'J'       for the Jet Propulsion Laboratory
  'T'         indicates the type of data represented
                  'G'       for gravity field
  'DWN'    all products use this.
  '_'      the underscore character is used to delimit modifiers in
           the file name for clarity.
  'nnnvvv' is a 6-character modifier specified by the data
           producer.  Among other things, this modifier may be used to
           indicate the target body, whether the SHADR contains primary
           data values as specified by 'T' or uncertainties/errors,
           and/or the version number.  For Dawn, this specifies the
           degree and version of the field.
   '_'     the underscore character is used to delimit information in
           the file name for clarity.
   'SHA'   denotes that this is an ASCII file of Spherical Harmonic
           coefficients
   '.TAB'  indicates the data is stored in tabular form.

Each SHADR file is accompanied by a detached PDS label; that label is
a file in its own right, having the name GTsss_nnnnvv_SHA.xml.

Binary spherical harmonic models are stored in the data-shbdr/ directory
with file names of the form GTsss_nnnnvv_SHB.DAT where:

  'G'   denotes the generating institution
                  'J'       for the Jet Propulsion Laboratory
  'T'         indicates the type of data represented
                  'G'       for gravity field
  'DWN'    all products use this.
  '_'      the underscore character is used to delimit modifiers in
           the file name for clarity.
  'nnnvvv' is a 6-character modifier specified by the data
           producer.  Among other things, this modifier may be used to
           indicate the target body, whether the SHBDR contains primary
           data values as specified by 'T' or uncertainties/errors,
           and/or the version number.  For Dawn, this specifies the
           degree and version of the field.
   '_'     the underscore character is used to delimit information in
           the file name for clarity.
   'SHB'   denotes that this is an Binary file of Spherical Harmonic
           coefficients and covariance
   '.DAT'  indicates the data is stored in a binary data file.

Each SHBDR file is accompanied by a detached PDS label; that label is
a file in its own right, having the name GTsss_nnnnvv_SHB.xml.

Radio Science Digital Map products are stored in the maps/
directory with file names of the form GTsss_ffff_nnnn_cccc.IMG where:

    'G'       denotes the generating institution
                    'J'      for the Jet Propulsion Laboratory
    'T'       indicates the type of mission data represented
                    'G' for gravity field
    'DWN'    all products use this.
    '_'       the underscore character is used to delimit information
              in the file name for clarity.
    'ffff'    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)
                    'BOU'      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 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 error, 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.xml.



SHADR Files Descriptions
------------------------


# SHADR Header Table Description

The SHADR header includes
descriptive information about the spherical harmonic
coefficients which follow in SHADR_COEFFICIENTS_TABLE.
The header consists of a single record of eight (delimited)
data columns requiring 137 bytes, a pad of 105 unspecified
ASCII characters, an ASCII carriage-return, and an ASCII
line-feed.


# SHADR Coefficients Table Description

The SHADR coefficients table
contains the coefficients for the spherical harmonic model.
Each row in the table contains the degree index m, the
order index n, the coefficients Cmn and Smn, and the
uncertainties in Cmn and Smn.  The (delimited) data
require 107 ASCII characters; these are followed by a pad
of 13 unspecified ASCII characters, an ASCII carriage-
return, and an ASCII line-feed.



# JGDWN_VES20H_SHA File Description

This file contains coefficients and related data for the
VESTA20H spherical harmonic gravity model of Vesta.

VESTA20H is a 20th degree and order model obtained from radiometric
tracking (Doppler and range data) and optical landmarks of the
Dawn spacecraft in orbit about Vesta. The gravity model includes
data from the Approach phase to the end of the HAMO-2 orbit.
The data span is July 13, 2011 to July 25, 2012. Optical landmark
tracking is included for the Survey, HAMO and LAMO phases.
Optical tracking is yet to be included for HAMO-2.

Some details describing this model are:
   The spherical harmonic coefficients are fully normalized.
   The associated GM = 17.2882449693 km^3/s^2
   The reference radius = 265.0 km
   The Vesta-fixed reference frame prime meridian and pole
      location in IAU coordinates is given by
         Right ascension = 309.05870 degrees (estimated)
         RA rate         = -0.207 degrees/cty (fixed)
         Declination     =   42.23190 degrees (estimated)
         Dec rate        = -0.048 degrees/cty (fixed)
         Prime Meridian  = 284.59521 degrees (fixed)
         Rotation rate   = 1617.3331279 degrees/day (estimated)
   The pole location and rotation rate are estimated jointly with the
   gravity field. The motion of the pole in inertial space is given
   by the modeled precession and nutation for a homogeneous Vesta and
   is not estimated. The prime meridian epoch value is chosen
   to match the Vesta LAMO shape model from Bob Gaskell on
   June 1, 2012 (Claudia is rotated to 146 deg E). This shape model
   includes images from the HAMO-2 phase and fills the previous gap
   in the shape model of the northern polar region.
   The uncertainties of the pole and rotation rate (5x formal) for
   this solution are
         Right ascension = 0.000043 degrees
         Declination     = 0.000031 degrees
         Rotation rate   = 0.00000087 degrees/day

The reference for this gravity field is Konopliv et al.,
The Vesta gravity field, spin pole and rotation, landmark
positions, and ephemeris from the Dawn tracking and optical data,
Icarus, 2013, http://dx.doi.org/10.1016/j.icarus.2013.09.005.
(Konopliv et al., 2014).

The original published gravity field is in the Claudia coordinate
system with the prime meridian location defined by the Claudia crater.
To be consistent with IAU standards, this version of the VESTA20H
gravity field has been rotated by 210 degrees to be similar to the
Claudia double-prime coordinate system. The difference between the
Claudia coordinate system and Claudia double-prime coordinate system is
documented in the document collection, VESTA_COORDINATES_131018.PDF. 
Note that because the pole and spin rate are jointly estimated with 
the gravity field, the coordinate system used in this map differs 
slightly from the official Claudia double-prime coordinate system. 
For details about the gravity coordinate frame, see the details above.

Observations for the gravity field consist of Doppler and
range measurements from Deep Space Network (DSN) tracking.

The count time for the Doppler observations is 60 seconds.
The typical accuracy for the Doppler is 0.02 mm/s for the
60 second sample time. The range accuracy is about 2 meters
and is limited by the station calibration accuracy. The actual
rms scatter is less than 0.3 meters in spacecraft position.

This product is a set of two ASCII tables: a header table and
a coefficients table with 252 coefficients and a GM value.
Definitions of the tables follow.

The VESTA20H gravity model is delivered as a Spherical Harmonics
Gravity ASCII Data Record (SHADR) and is produced by the JPL
Dawn Gravity Science Team (Alex Konopliv, Ryan Park, Sami Asmar).



# JGDWN_VES26J_SHA File Description

This file contains coefficients and related data for the 
VESTA26J spherical harmonic gravity model of Vesta. 

VESTA26J is a 26th degree and order model obtained from radiometric
tracking (Doppler and range data) and optical landmarks of the
Dawn spacecraft in orbit about Vesta. The gravity model includes
data from the Approach phase to the end of the HAMO-2 orbit.
The data span is July 23, 2011 to July 25, 2012. Optical landmark
tracking is included for the Survey, HAMO, HAMO-2 and LAMO phases.

Some details describing this model are:
   The spherical harmonic coefficients are fully normalized.
   The associated GM = 17.2882844211 km^3/s^2
   The reference radius = 265.0 km
   The Vesta-fixed reference frame prime meridian and pole 
      location in IAU coordinates is given by 
         Right ascension = 309.06110 degrees (estimated)
         RA rate         = -0.225213 degrees/cty (estimated with MOI)
         RA acceleration =  0.000298 degrees/cty^2 (estimated with MOI)
         Declination     =   42.232386 degrees (estimated)
         Dec rate        = -0.052184 degrees/cty (estimated with MOI)
         Dec acceleration=  0.0001118 degrees/cty (estimated with MOI)
         Prime Meridian  = 284.6430975804534 degrees (estimated)
         Rotation rate   = 1617.33312922 degrees/day (estimated)
   The pole location and rotation rate are estimated jointly with the
   gravity field. The motion of the pole in inertial space is given 
   by the modeled precession and nutation for a Vesta with polar moment 
   of inertia (MOI) C = 0.4208 (estimated). The prime meridian epoch value
   is estimated with the Claudia landmark longitude fixed to zero.
   The uncertainties of the pole and rotation rate for
   this solution are
         Right ascension = 0.00031 degrees
         Declination     = 0.000068 degrees
         Rotation rate   = 0.00000013 degrees/day

Observations for the gravity field consist of Doppler and
range measurements from Deep Space Network (DSN) tracking.

The count time for the Doppler observations is 60 seconds.
The typical accuracy for the Doppler is 0.02 mm/s for the
60 second sample time. The range accuracy is about 2 meters
and is limited by the station calibration accuracy. The actual
rms scatter is less than 0.3 meters in spacecraft position.

This product is a set of two ASCII tables: a header table and 
a coefficients table with 252 coefficients and a GM value.
Definitions of the tables follow.  

The VESTA26J gravity model is delivered as a Spherical Harmonics
Gravity ASCII Data Record (SHADR) and is produced by the JPL 
Dawn Gravity Science Team (Ryan Park and Alex Konopliv).

More details about VESTA26J can be found in:

Park, R.S., A.I. Ermakov, A.S. Konopliv, A.T. Vaughan,
N. Rambaux, B.G., Bills, J.C. Castillo-Rogez, R.R. Fu,
S A. Jacobson, S.T. Stewart, and M.J. Toplis,
“A small core in Vesta inferred from Dawn’s observations,”
Nature Astronomy, 2025. https://doi.org/10.1038/s41550-025-02533-7



SHBDR Files Descriptions
------------------------


# SHBDR Header Table Description

The SHBDR Header includes                     
descriptive information about the spherical harmonic   
coefficients which follow in SHBDR_COEFFICIENTS_TABLE. 
The header consists of a single record of nine data    
columns requiring 56 bytes.  The Header is followed by 
a pad of binary integer zeroes to ensure alignment     
with RECORD_BYTES.


# SHBDR Names Table

The SHBDR Names Table
contains names for the solution parameters (including
gravity field coefficients) which will follow in
SHBDR_COEFFICIENTS_TABLE.  The order of the names
in SHBDR_NAMES_TABLE corresponds identically to the
order of the parameters in SHBDR_COEFFICIENTS_TABLE.
Each coefficient  name is of the form  Cij  or  Sij
where  i  is the degree of the coefficient and  j  is
the order of the coefficient.  Both indices are three-
digit zero-filled right-justified ASCII character strings
(for example,  C010005  for the 10th degree 5th order C
coefficient, or  S002001  for the 2nd degree 1st order
S  coefficient).  The eighth byte in the table is an
ASCII blank used to ensure that the row length
is equal to RECORD_BYTES.  Names of other solution
parameters are limited to 8 ASCII characters; if less
than 8, they will be left-justified and padded with
ASCII blanks.  The Names Table itself will be padded
with ASCII blanks, if necessary, so that its length is
an integral multiple of RECORD_BYTES.


# SHBDR Coefficients Table

The SHBDR Coefficients Table
contains the coefficients and other solution parameters
for the spherical harmonic model.  The order of the
coefficients in this table corresponds exactly to the
order of the coefficient and parameter names in
SHBDR_NAMES_TABLE.  The SHBDR Coefficients Table will be
padded with double precision DATA_TYPE zeroes so that
its total length is an integral multiple of RECORD_BYTES.


# SHBDR Covariance Table

The SHBDR Covariance Table
contains the covariances for the spherical harmonic model
coefficients and other solution parameters.  The order of
the covariances in this table is defined as columnwise
vector storage of the upper triangular matrix formed by
the product of the SHBDR Names Table with its transpose.
For example, if the Names Table has four entries  A, B,
C, and D,  then the covariances are given by the column
vectors in the upper triangular matrix of

        | A | [ A B C D ] = | AA AB AC AD |
        | B |               | BA BB BC BD |
        | C |               | CA CB CC CD |
        | D |               | DA DB DC DD |

That is, the covariance table will list (in this order)
AA, AB, BB, AC, BC, CC, AD, BD, CD, and DD.
The SHBDR Covariance Table will be padded with double
precision DATA_TYPE zeroes so that its total length is
an integral multiple of RECORD_BYTES.



# JGDWN_VES20H_SHB Description

This file contains the covariance and related data for the JPL Dawn
Vesta gravity soluttion VESTA20H, a 20th degree and order spherical
harmonic model and covariance.

For a description of the solution and spherical harmonic coefficents,
see the ascii pds label file for the VESTA20H spherical harmonic
gravity coefficients in DATA/SHADR/JGDWN_VES20H_SHA.LBL

VESTA20H is a 20th degree and order model obtained from radiometric
tracking (Doppler and range data) and optical landmarks of the
Dawn spacecraft in orbit about Vesta. The gravity model includes
data from the Approach phase to the end of the HAMO-2 orbit.
The data span is July 13, 2011 to July 25, 2012. Optical landmark
tracking is included for the Survey, HAMO and LAMO phases.
Optical tracking is yet to be included for HAMO-2.

Some details describing this model are:
   The spherical harmonic coefficients are fully normalized.
   The associated GM = 17.2882449693 km^3/s^2
   The reference radius = 265.0 km
   The Vesta-fixed reference frame prime meridian and pole
      location in IAU coordinates is given by
         Right ascension = 309.05870 degrees (estimated)
         RA rate         = -0.207 degrees/cty (fixed)
         Declination     =   42.23190 degrees (estimated)
         Dec rate        = -0.048 degrees/cty (fixed)
         Prime Meridian  = 284.59521 degrees (fixed)
         Rotation rate   = 1617.3331279 degrees/day (estimated)
   The pole location and rotation rate are estimated jointly with the
   gravity field. The motion of the pole in inertial space is given
   by the modeled precession and nutation for a homogeneous Vesta and
   is not estimated. The prime meridian epoch value is chosen
   to match the Vesta LAMO shape model from Bob Gaskell on
   June 1, 2012 (Claudia is rotated to 146 deg E). This shape model
   includes images from the HAMO-2 phase and fills the previous gap
   in the shape model of the northern polar region.
   The uncertainties of the pole and rotation rate (5x formal) for
   this solution are
         Right ascension = 0.000043 degrees
         Declination     = 0.000031 degrees
         Rotation rate   = 0.00000087 degrees/day

The reference for this gravity field is Konopliv et al.,
The Vesta gravity field, spin pole and rotation, landmark
positions, and ephemeris from the Dawn tracking and optical data,
Icarus, 2013, http://dx.doi.org/10.1016/j.icarus.2013.09.005.
(Konopliv et al., 2014).

The original published gravity field is in the Claudia coordinate
system with the prime meridian location defined by the Claudia crater.
To be consistent with IAU standards, this version of the VESTA20H
gravity field has been rotated by 210 degrees to be similar to the
Claudia double-prime coordinate system. The difference between the
Claudia coordinate system and Claudia double-prime coordinate system is
documented in the document collection, VESTA_COORDINATES_131018.PDF. 
Note that because the pole and spin rate are jointly estimated with 
the gravity field, the coordinate system used in this map differs 
slightly from the official Claudia double-prime coordinate system. 
For details about the gravity coordinate frame, see the details above.

The formal error covariance of VESTA20H is delivered in the Spherical
Harmonics Gravity Binary Data Record (SHBDR) and is produced by the
Dawn Gravity Science Team at JPL.



# JGDWN_VES26J_SHB Description

This file contains the covariance and related data for the JPL Dawn
Vesta gravity solution VESTA26J, a 26th degree and order spherical
harmonic model and covariance.

VESTA26J is a 26th degree and order model obtained from radiometric
tracking (Doppler and range data) and optical landmarks of the
Dawn spacecraft in orbit about Vesta. The gravity model includes
data from the Approach phase to the end of the HAMO-2 orbit.
The data span is July 23, 2011 to July 25, 2012. Optical landmark
tracking is included for the Survey, HAMO, HAMO-2 and LAMO phases.

Some details describing this model are:
   The spherical harmonic coefficients are fully normalized.
   The associated GM = 17.2882844211 km^3/s^2
   The reference radius = 265.0 km
   The Vesta-fixed reference frame prime meridian and pole 
      location in IAU coordinates is given by 
         Right ascension = 309.06110 degrees (estimated)
         RA rate         = -0.225213 degrees/cty (estimated with MOI)
         RA acceleration =  0.000298 degrees/cty^2 (estimated with MOI)
         Declination     =   42.232386 degrees (estimated)
         Dec rate        = -0.052184 degrees/cty (estimated with MOI)
         Dec acceleration=  0.0001118 degrees/cty (estimated with MOI)
         Prime Meridian  = 284.6430975804534 degrees (estimated)
         Rotation rate   = 1617.33312922 degrees/day (estimated)
   The pole location and rotation rate are estimated jointly with the
   gravity field. The motion of the pole in inertial space is given 
   by the modeled precession and nutation for a Vesta with polar moment 
   of inertia (MOI) C = 0.4208 (estimated). The prime meridian epoch value
   is estimated with the Claudia landmark longitude fixed to zero.
   The uncertainties of the pole and rotation rate for
   this solution are
         Right ascension = 0.00031 degrees
         Declination     = 0.000068 degrees
         Rotation rate   = 0.00000013 degrees/day

Observations for the gravity field consist of Doppler and
range measurements from Deep Space Network (DSN) tracking.

The count time for the Doppler observations is 60 seconds.
The typical accuracy for the Doppler is 0.02 mm/s for the
60 second sample time. The range accuracy is about 2 meters
and is limited by the station calibration accuracy. The actual
rms scatter is less than 0.3 meters in spacecraft position. 

The VESTA26J gravity model is delivered as a Spherical Harmonics
Gravity Binary Data Record (SHBDR) and is produced by the JPL 
Dawn Gravity Science Team (Ryan Park and Alex Konopliv)."

More details about VESTA26J can be found in:

Park, R.S., A.I. Ermakov, A.S. Konopliv, A.T. Vaughan,
N. Rambaux, B.G., Bills, J.C. Castillo-Rogez, R.R. Fu,
S A. Jacobson, S.T. Stewart, and M.J. Toplis,
"A small core in Vesta inferred from Dawn's observations,"
Nature Astronomy, 2025. https://doi.org/10.1038/s41550-025-02533-7



Map Projection Descriptions
---------------------------


Note on value-added metadata: The PDS4 map products use updated projection 
values for upperleft_corner_x, upperleft_corner_y, pixel_resolution_x, and 
pixel_resolution_y. These values are based on proper cartographic parameters 
for equirectangular (simple cylindrical) projection. These values were 
provided by Trent Hare (PDS Imaging Node) and are documented in the figure 
equirectangular_map_projection_PDS4.pdf in the document collection; they 
supersede the values in the original PDS3 labels.


# Description of the Digital Map of the Radial Gravity

This file contains a digital map of the radial gravity derived from
the JPL VESTA20H model of the Vesta gravity field.  Each point gives the
Vesta gravity radial acceleration in milligals on a 290-km x 265-km
ellipsoid of revolution, which is the surface closest to Vesta that has
minimal convergence errors for the spherical harmonic expansion.
The JGDWN_VES20H_ACCEL gravity acceleration is computed from the full
VESTA20H solution (from degree 2 up to degree 20) using the prime
meridian given by W=284.59521 degrees.

Because gravity will not converge on the geoid, gravity anomaly cannot be
computed. Instead, the map is provided as radial acceleration on an
ellipsoid, which is computed using the radial component of the spherical
harmonic gravity potential. The JGDWN_VES20H_ACCEL_0020 gravity acceleration
is computed from the full VESTA20H solution (from degree 2 up to degree 20),
but without the J2 coefficient. The centrifugal acceleration due to the
rotation of Vesta is not included in this map.

The reference for this gravity field is Konopliv et al.,
The Vesta gravity field, spin pole and rotation, landmark
positions, and ephemeris from the Dawn tracking and optical data,
Icarus, 2013, http://dx.doi.org/10.1016/j.icarus.2013.09.005.
(Konopliv et al., 2014).

The original published gravity field is in the Claudia coordinate
system with the prime meridian location defined by the Claudia crater.
To be consistent with IAU standards, this version of the VESTA20H
gravity field has been rotated by 210 degrees to be similar to the
Claudia double-prime coordinate system. The difference between the
Claudia coordinate system and Claudia double-prime coordinate system is
documented in the document collection, VESTA_COORDINATES_131018.PDF. 
Note that because the pole and spin rate are jointly estimated with the 
gravity field, the coordinate system used in this map differs slightly 
from the official Claudia double-prime coordinate system. For details 
about the gravity coordinate frame, see JGDWN_VES20H_SHA File Description.

The map is delivered as a Radio Science Digital Map (RSDMAP) product. Each
pixel represents the radial acceleration on a simple cylindrical projection.
Latitude and longitude are gridded and intersect one another at right angles.
The map has 181 lines with 360 samples per line. For example, the first 8
bytes (PC_REAL) represent the first pixel at -180 degrees longitude and
+90 degrees latitude. The last 8 bytes represent the last pixel at
+179 degrees longitude and -90 degrees latitude.

The map is produced at JPL by the Dawn Radio Science Team (Alex Konopliv,
Ryan Park, Sami Asmar).



# Description of the Digital Map of the Radial Gravity Error

This file contains a digital map of the radial gravity error derived from
from the JPL VESTA20H covariance of the Vesta gravity field.  Each point
gives the Vesta gravity radial acceleration error in milligals on a
290-km x 265-km ellipsoid of revolution, which is the surface closest to
Vesta that has minimal convergence errors for the spherical harmonic
expansion. The JGDWN_VES20H_ACCERR gravity acceleration error is computed
from the full VESTA20H covariance (from degree 2 up to degree 20) using
the prime meridian given by W=284.59521 degrees.

The corresponding map of radial gravity acceleration is JGDWN_VES20H_ACCEL.

The reference for this gravity field is Konopliv et al.,
The Vesta gravity field, spin pole and rotation, landmark
positions, and ephemeris from the Dawn tracking and optical data,
Icarus, 2013, http://dx.doi.org/10.1016/j.icarus.2013.09.005.
(Konopliv et al., 2014).

The original published gravity field is in the Claudia coordinate
system with the prime meridian location defined by the Claudia crater.
To be consistent with IAU standards, this version of the VESTA20H
gravity field has been rotated by 210 degrees to be similar to the
Claudia double-prime coordinate system. The difference between the
Claudia coordinate system and Claudia double-prime coordinate system is
documented in the document collection, VESTA_COORDINATES_131018.PDF. 
Note that because the pole and spin rate are jointly estimated with the 
gravity field, the coordinate system used in this map differs slightly 
from the official Claudia double-prime coordinate system. For details 
about the gravity coordinate frame, see JGDWN_VES20H_SHA File Description.

The map is delivered as a Radio Science Digital Map (RSDMAP) product. Each
pixel represents the error in radial acceleration on a simple cylindrical
projection. Latitude and longitude are gridded and intersect one another at
right angles. The map has 181 lines with 360 samples per line. For example,
the first 8 bytes (PC_REAL) represent the first pixel at -180 degrees
longitude and +90 degrees latitude. The last 8 bytes represent the last
pixel at +179 degrees longitude and -90 degrees latitude.

The map is produced at JPL by the Dawn Radio Science Team (Alex Konopliv,
Ryan Park, Sami Asmar).



#  Description of the Digital Map of the Bouguer

This file contains a digital map of the Bouguer gravity derived from
the JPL VESTA20H model of the Vesta gravity field.  Each point gives the
Vesta gravity radial acceleration minus the gravity derived from
integration of Vesta shape assuming uniform density in milligals on a
290.0-km x 265.0-km ellipsoid of revolution, which is the surface closest
to Vesta that has minimal convergence errors for the spherical harmonic
expansion. The JGDWN_VES20H_BOU gravity acceleration is computed from
the truncated VESTA20H solution (from degree 2 up to degree 15).

Please note thtat the Bouguer anomaly map is computed up to degree 15,
for detailed information see Section 4, Figure 5 of the below
publication (Konopliv et al., 2014). At degree 15, the Bouguer spectrum
and sigma curve of the gravity field become close for the Bouguer
anomaly to be applicable.

The reference for this gravity field is Konopliv et al.,
The Vesta gravity field, spin pole and rotation, landmark
positions, and ephemeris from the Dawn tracking and optical data,
Icarus, 2013, http://dx.doi.org/10.1016/j.icarus.2013.09.005.
(Konopliv et al., 2014).

The original published gravity field is in the Claudia coordinate
system with the prime meridian location defined by the Claudia crater.
To be consistent with IAU standards, this version of the VESTA20H
gravity field has been rotated by 210 degrees to be similar to the
Claudia double-prime coordinate system. The difference between the
Claudia coordinate system and Claudia double-prime coordinate system is
documented in the document collection, VESTA_COORDINATES_131018.PDF. 
Note that because the pole and spin rate are jointly estimated with the 
gravity field, the coordinate system used in this map differs slightly 
from the official Claudia double-prime coordinate system. For details 
about the gravity coordinate frame, see JGDWN_VES20H_SHA File Description.

The map is delivered as a Radio Science Digital Map (RSDMAP) product. Each
pixel represents the Bouguer gravity on a simple cylindrical projection.
Latitude and longitude are gridded and intersect one another at right angles.
The map has 181 lines with 360 samples per line. For example, the first 8
bytes (PC_REAL) represent the first pixel at -180 degrees longitude and
+90 degrees latitude. The last 8 bytes represent the last pixel at
+179 degrees longitude and -90 degrees latitude.

The map is produced at JPL by the Dawn Radio Science Team (Alex Konopliv,
Ryan Park, Sami Asmar).



# Description of the Digital Map of the Vesta GEOID

This file contains a digital map of the Vesta geoid derived from
the JPL VESTA20H spherical harmonic model of the Vesta gravity field.
Each point is the Vesta geoid height in meters above a reference
ellipsoid (semi-major-axis = 281.0 km, GM = 17.2882449693 km**3/s**2,
flattening = 0.195729537, and rotation rate = 0.00032671051138233364
rad/s). The prime meridian is given by W=284.59521 degrees.

** IMPORTANT NOTE **
The JGDWN_VES20H_GEOID is computed from the VESTA20H
solution (from degree 2 up to degree 20). Note that the geoid is *not
valid* for all points on the surface due to divergence of the spherical
harmonics. The valid region is roughly between +- 60 degrees latitude.

The reference for this gravity field is Konopliv et al.,
The Vesta gravity field, spin pole and rotation, landmark
positions, and ephemeris from the Dawn tracking and optical data,
Icarus, 2013, http://dx.doi.org/10.1016/j.icarus.2013.09.005.
(Konopliv et al., 2014).

The original published gravity field is in the Claudia coordinate
system with the prime meridian location defined by the Claudia crater.
To be consistent with IAU standards, this version of the VESTA20H
gravity field has been rotated by 210 degrees to be similar to the
Claudia double-prime coordinate system. The difference between the
Claudia coordinate system and Claudia double-prime coordinate system is
documented in the document collection, VESTA_COORDINATES_131018.PDF. 
Note that because the pole and spin rate are jointly estimated with the 
gravity field, the coordinate system used in this map differs slightly 
from the official Claudia double-prime coordinate system. For details 
about the gravity coordinate frame, see JGDWN_VES20H_SHA File Description.

The map is delivered as a Radio Science Digital Map (RSDMAP) product. Each
pixel represents the geoid height  on a simple cylindrical projection.
Latitude and longitude are gridded and intersect one another at right angles.
The map has 181 lines with 360 samples per line. For example, the first 8
bytes (PC_REAL) represent the first pixel at -180 degrees longitude and
+90 degrees latitude. The last 8 bytes represent the last pixel at
+179 degrees longitude and -90 degrees latitude.

The map is produced by Dawn Gravity Team (Alex Konopliv, Ryan Park,
Sami Asmar) at JPL."



# Description of the Digital Map of the Vesta GEOID Error

This file contains a digital map of the Vesta geoid error derived
from the JPL VESTA20H spherical harmonic covariance of the Vesta
gravity field. Each point is the Vesta geoid height error in meters
above a reference ellipsoid (semi-major-axis = 281.0 km,
GM = 17.2882449693 km**3/s**2, flattening = 0.195729537, and
rotation rate = 0.00032671051138233364 rad/s).

The prime meridian is given by W=284.59521 degrees.
The JGDWN_VES20H_GEOIDERR is computed from the VESTA20H
covariance (from degree 2 up to degree 20). Note that the geoid is not
valid for all points on the surface due to divergence of the spherical
harmonics. The valid region is roughly between +- 60 degrees latitude.

** IMPORTANT NOTE **
The corresponding map of geoid height is JGDWN_VES20H_GEOID. Note that
the geoid is *not  valid* for all points on the surface due to divergence
of the spherical harmonics. The valid region is roughly between +- 60
degrees latitude.

The reference for this gravity field is Konopliv et al.,
The Vesta gravity field, spin pole and rotation, landmark
positions, and ephemeris from the Dawn tracking and optical data,
Icarus, 2013, http://dx.doi.org/10.1016/j.icarus.2013.09.005.
(Konopliv et al., 2014).

The original published gravity field is in the Claudia coordinate
system with the prime meridian location defined by the Claudia crater.
To be consistent with IAU standards, this version of the VESTA20H
gravity field has been rotated by 210 degrees to be similar to the
Claudia double-prime coordinate system. The difference between the
Claudia coordinate system and Claudia double-prime coordinate system is
documented in the document collection, VESTA_COORDINATES_131018.PDF. 
Note that because the pole and spin rate are jointly estimated with the 
gravity field, the coordinate system used in this map differs slightly 
from the official Claudia double-prime coordinate system. For details 
about the gravity coordinate frame, see JGDWN_VES20H_SHA File Description.

The map is delivered as a Radio Science Digital Map (RSDMAP) product. Each
pixel represents the error in geoid height on a simple cylindrical projection.
Latitude and longitude are gridded and intersect one another at right angles.
The map has 181 lines with 360 samples per line. For example, the first 8
bytes (PC_REAL) represent the first pixel at -180 degrees longitude and
+90 degrees latitude. The last 8 bytes represent the last pixel at
+179 degrees longitude and -90 degrees latitude.

The map is produced by Dawn Gravity Team (Alex Konopliv, Ryan Park,
Sami Asmar) at JPL.



Coordinate System
=================

Dawn Gravity SDP files use a Vesta centered body-fixed coordinate system
similar to the IAU coordinate system. The values differ slightly
because the the orientation of Vesta is estimated in the orbit
determination process.

See labels of specific gravity products for details.

Software
========

None.

CONFIDENCE LEVEL NOTE
=====================

Overview
========

Data in this collection have been reduced as part of mission data
analysis activities of the Dawn Gravity Team.

Review
======

This archival collection was reviewed by the Dawn Gravity
Team prior to submission to the Planetary Data System (PDS).
Bundle design, documentation, and sample products have passed
a PDS peer review.

Data Coverage and Quality
=========================

This collection contains gravity models and maps generated from Dawn
data collected between July 2011 and July 2012.

JGDWN_VES20H_SHA.TAB is an ASCII file of coefficients and related data
for a 20th degree and order Vesta gravity field produced at the
Jet Propulsion Laboratory. The name of this gravity model is
VESTA20H. The model used is described in the file's
detached label.

JGDWN_VES20H_ACCEL_0020.IMG is a digital map of the Vesta radial
acceleration due to gravity with the J2 coefficient removed. The radial
accelerations are computed with the VESTA20H field described in the
JGDWN_VES20H_SHA.TAB file. This Vesta gravity field was produced at
the Jet Propulsion Laboratory.  The model used is described in the
file's detached label.
