PDS_VERSION_ID = PDS3
RECORD_TYPE = STREAM
RECORD_BYTES = 70
FILE_RECORDS = 85384
^TEXT = "SH_101.TXT"
DATA_SET_ID = "NEAR-A-NLR-5-EROS/SHAPE/GRAVITY-V1.0"
PRODUCT_ID = "NAV-SHAPE-MODEL-TEXT"
PRODUCT_NAME = "NAV SHAPE MODEL, TEXT FORMAT"
PRODUCT_CREATION_TIME = 2001-09-01
TARGET_NAME = EROS
INSTRUMENT_HOST_NAME = "NEAR EARTH ASTEROID RENDEZVOUS"
INSTRUMENT_NAME = "NEAR LASER RANGEFINDER"
START_TIME = 2000-04-30
STOP_TIME = 2000-08-27
SPACECRAFT_CLOCK_START_COUNT = "UNK"
SPACECRAFT_CLOCK_STOP_COUNT = "UNK"
OBJECT = TEXT
PUBLICATION_DATE = 2000-10-09
NOTE = "This file contains a shape model for
the asteroid Eros derived from NEAR Laser Rangefinder observations.
The NLR measurements were made over the period 30 April 2000 to
27 August 2000 from orbits of 35 and 50 km. It is presented in the
in-house format used by the NAV team, as described below.
The shape model includes both a triangular plate model and a set
of spherical harmonics. The plate model is comprised of two lists:
a list of (x,y,z) vertex positions relative to the center of the
model; and a list of the triples of vertices defining each of the
triangular plates.
The spherical harmonics are provided as a set of coefficients
with corresponding values for volume, center-of-gravity offset
and the inertia tensor. The coefficients are the normalized
(Cnm,Snm) coefficients of the standard spherical harmonic expansion
of Lengendre polynomials and related functions. For a complete
discussion of the derivations of the gravitational potential and
related shape model, see Miller, et al. (2002) and Kaula (1966).
The gravity model obtained by integrating this shape model is
provided as a separate companion file ('gr_101.txt') to this
file.
The shape model files and descriptive information regarding the file
formats and contents were kindly supplied by J.K. Miller of the NEAR
navigation team, in response to user requests made at the NEAR
PDS archive review.
REFERENCES
Kaula, W.M., 1966. Theory of Satellite Geodesy, Blaisdell, Waltham, MA.
Miller, J.K., A.S. Konopliv, P.G. Antreasian, J.J. Bordi, S. Chesley,
C.E. Helfrich, W.M. Owen, D.J. Scheeres, T.C.Wang, B.G. Williams
and D.K. Yoemans, 2002. Determination of Shape, Gravity and Rotational
State of Asteroid 433 Eros, Icarus, in press.
File Format
===========
The file is formatted as a set of tables with 1-4 numbers in each row.
The first two tables define the vertices and triangular facets of the
shape model. The values in each row are as follows:
Row 1 Column 1 Number of vertices, following
Column 2 -blank-
Column 3 -blank-
Column 4 -blank-
Row 2-28325 Column 1 Vertex number
Column 2 X position, in km
Column 3 Y position, in km
Column 4 Z position, in km
Row 28326 Column 1 Number of facets, following
Column 2 -blank-
Column 3 -blank-
Column 4 -blank-
Row 28327-84970 Column 1 Facet number
Column 2 First vertex number, from above
Column 3 Second vertex number
Column 4 Third vertex number
The remaining 3-column table provides the parameters and spherical
harmonic coefficients, as follows:
Row 84971 Column 1 Degree (NDEGREE) of the solution
Column 2 Normalization flag ('1')
Column 3 Internal processing flag ('1')
Row 84972 Column 1 Volume in km^3
Column 2 -blank-
Column 3 -blank-
The next row provides the offset from the center of the shape model to
the true center of gravity:
Row 84973 Column 1 Xcg in km
Column 2 Ycg in km
Column 3 Zcg in km
The next two records contain the coefficients for the inertia tensor.
Note that this is a symmetric matrix, so only the unique elements are
specified here:
Row 84974 Column 1 Ixx in km^2
Column 2 Iyy in km^2
Column 3 Izz in km^2
Row 84975 Column 1 Ixy in km^2
Column 2 Ixz in km^2
Column 3 Iyz in km^2
The subsequent records contain the shape model harmonic coefficients
Cij and Sij. All the Si0 are = 0, and are thus omitted from this file.
The remaining coefficients are stored three to a record, in this
logical sequence:
C00
C10 C11 S11
C20 C21 C22 S21 S22
C30 C31 C32 C33 S31 S32 S33
etc.
which becomes this physical sequence:
Row 84976: C00 C10 C11
Row 84977: S11 C20 C21
Row 84978: C22 S21 S22
Row 84979: C30 C31 C32
Row 84980: C33 S31 S32
etc.
The total number of coefficients stored is (NDEGREE+1)^2.
The last record in the file contains only a single entry in the first
column.
"
END_OBJECT = TEXT
END