Table of contents
CSPICE_DNEARP computes the state (position and velocity) of an ellipsoid
surface point nearest to the position component of a specified state.
Given:
state a 6-vector giving the position and velocity of some object in
the body-fixed coordinates of the ellipsoid.
[6,1] = size(state); double = class(state)
In body-fixed coordinates, the semi-axes of the ellipsoid
are aligned with the X, Y, and Z-axes of the coordinate
system.
a the length of the semi-axis of the ellipsoid that is parallel
to the X-axis of the body-fixed coordinate system.
[1,1] = size(a); double = class(a)
b the length of the semi-axis of the ellipsoid that is parallel
to the Y-axis of the body-fixed coordinate system.
[1,1] = size(b); double = class(b)
c the length of the semi-axis of the ellipsoid that is parallel
to the Z-axis of the body-fixed coordinate system.
[1,1] = size(c); double = class(c)
the call:
[dnear, dalt, found] = cspice_dnearp( state, a, b, c )
returns:
dnear the 6-vector giving the position and velocity in body-fixed
coordinates of the point on the ellipsoid, closest to the
object whose position and velocity are represented by
`state'.
[6,1] = size(dnear); double = class(dnear)
While the position component of `dnear' is always
meaningful, the velocity component of `dnear' will be
meaningless if `found' if false (See the discussion of
the meaning of `found' below.)
dalt an array of two double precision numbers.
[2,1] = size(dalt); double = class(dalt)
The first gives the altitude of `state' with respect to the
ellipsoid. The second gives the rate of change of the
altitude.
Note that the rate of change of altitude is meaningful if
and only if `found' is true (See the discussion of the
meaning of `found' below.)
found a logical flag indicating whether or not the velocity portion
of `dnear' is meaningful.
[1,1] = size(found); logical = class(found)
If the velocity portion of `dnear' is meaningful `found'
will be returned with a value of true. Under very rare
circumstance the velocity of the near point is undefined.
Under these circumstances `found' will be returned with the
value false.
`found' can be false only for states whose position
components are inside the ellipsoid and then only at
points on a special surface contained inside the
ellipsoid called the focal set of the ellipsoid.
A point in the interior is on this special surface only
if there are two or more points on the ellipsoid that are
closest to it. The origin is such a point and the only
such point if the ellipsoid is a sphere. For
non-spheroidal ellipsoids the focal set contains small
portions of the planes of symmetry of the ellipsoid.
None.
Any numerical results shown for these examples may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
1) Suppose you wish to compute the velocity of the ground track
of a satellite as it passes over a location on Mars and that
the moment of passage has been previously determined. (We
assume that the spacecraft is close enough to the surface that
light time corrections do not matter.)
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File: dnearp_ex1.tm
This meta-kernel is intended to support operation of SPICE
example programs. The kernels shown here should not be
assumed to contain adequate or correct versions of data
required by SPICE-based user applications.
In order for an application to use this meta-kernel, the
kernels referenced here must be present in the user's
current working directory.
The names and contents of the kernels referenced
by this meta-kernel are as follows:
File name Contents
--------- --------
pck00010.tpc Planet orientation and
radii
naif0012.tls Leapseconds
de430.bsp Planetary ephemeris
mar097.bsp Mars satellite ephemeris
mro_psp4_ssd_mro95a.bsp MRO ephemeris
\begindata
KERNELS_TO_LOAD = ( 'pck00010.tpc',
'naif0012.tls',
'de430.bsp',
'mar097.bsp',
'mro_psp4_ssd_mro95a.bsp' )
\begintext
End of meta-kernel
Example code begins here.
function dnearp_ex1()
%
% Local parameters
%
BODYNM = 'MARS';
META = 'dnearp_ex1.tm';
%
% Load kernel files via the meta-kernel.
%
cspice_furnsh( META );
%
% Convert the TDB input time string to seconds past
% J2000, TDB.
%
[et] = cspice_str2et( '2007 SEP 30 00:00:00 TDB' );
%
% First get the axes of the body.
%
[radii] = cspice_bodvrd( BODYNM, 'RADII', 3 );
[a, b, c] = cspice_vupack( radii );
%
% Get the geometric state of the spacecraft with
% respect to BODYNM in the body-fixed reference frame
% at `et' and compute the state of the sub-spacecraft point.
%
[state, lt] = cspice_spkezr( 'MRO', et, 'IAU_MARS', ...
'NONE', BODYNM );
[dnear, dalt, found] = cspice_dnearp( state, a, b, c );
if ( found )
%
% `dnear' contains the state of the subspacecraft point.
%
gtvel = dnear(4:6);
fprintf( 'Ground-track velocity (km/s): %9.6f %9.6f %9.6f\n', ...
gtvel' )
fprintf( 'Ground-track speed (km/s): %9.6f\n', ...
cspice_vnorm( gtvel ) )
else
fprintf( 'DNEAR is degenerate.\n' )
end
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
Ground-track velocity (km/s): 0.505252 1.986553 -2.475506
Ground-track speed (km/s): 3.214001
2) Suppose you wish to compute the one-way doppler shift of a
radar mounted on board a spacecraft as it passes over some
region. Moreover, assume that for your purposes it is
sufficient to neglect effects of atmosphere, topography and
antenna pattern for the sake of this computation.
Use the meta-kernel from Example 1 above.
Example code begins here.
function dnearp_ex2()
%
% Local parameters
%
BODYNM = 'MARS';
META = 'dnearp_ex1.tm';
%
% Define the central frequency of the radar,
% in megahertz.
%
RCFRQ = 20.0;
%
% Load kernel files via the meta-kernel.
%
cspice_furnsh( META );
%
% Convert the TDB input time string to seconds past
% J2000, TDB.
%
[et] = cspice_str2et( '2007 SEP 30 00:00:00 TDB' );
%
% First get the axes of the body.
%
[radii] = cspice_bodvrd( BODYNM, 'RADII', 3 );
[a, b, c] = cspice_vupack( radii );
%
% Get the geometric state of the spacecraft with
% respect to BODYNM in the body-fixed reference frame
% at `et' and compute the state of the sub-spacecraft point.
%
[state, lt] = cspice_spkezr( 'MRO', et, 'IAU_MARS', ...
'NONE', BODYNM );
[dnear, dalt, found] = cspice_dnearp( state, a, b, c );
if ( found )
%
% The change in frequency is given by multiplying `shift'
% times the carrier frequency
%
shift = ( dalt(2) / cspice_clight );
fprintf( 'Central frequency (MHz): %19.16f\n', RCFRQ )
fprintf( 'Doppler shift (MHz): %19.16f\n', RCFRQ * shift )
else
fprintf( 'DNEAR is degenerate.\n' )
end
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
Central frequency (MHz): 20.0000000000000000
Doppler shift (MHz): -0.0000005500991159
If an object is moving relative to some triaxial body along a
trajectory c(t) then there is a companion trajectory n(t) that
gives the point on the ellipsoid that is closest to c(t) as a
function of `t'. The instantaneous position and velocity of c(t),
`state', are sufficient to compute the instantaneous position and
velocity of n(t), `dnear'.
This routine computes `dnear' from `state'. In addition it returns the
altitude and rate of change of altitude.
Note that this routine can compute `dnear' for `state' outside, on,
or inside the ellipsoid. However, the velocity of `dnear' and
derivative of altitude do not exist for a "small" set of `state'
in the interior of the ellipsoid. See the discussion of `found'
above for a description of this set of points.
1) If the axes are non-positive, an error is signaled by a
routine in the call tree of this routine.
2) If an object is passing through the interior of an ellipsoid
there are points at which there is more than 1 point on the
ellipsoid that is closest to the object. At these points the
velocity of the near point is undefined. (See the description
of the output variable `found').
3) If any of the input arguments, `state', `a', `b' or `c', is
undefined, an error is signaled by the Matlab error handling
system.
4) If any of the input arguments, `state', `a', `b' or `c', is
not of the expected type, or it does not have the expected
dimensions and size, an error is signaled by the Mice
interface.
None.
None.
MICE.REQ
None.
J. Diaz del Rio (ODC Space)
-Mice Version 1.0.0, 01-NOV-2021 (JDR)
Velocity of the nearest point on an ellipsoid
Rate of change of the altitude over an ellipsoid
Derivative of altitude over an ellipsoid
Velocity of a ground track
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