dnearp_c |

Table of contents## Procedurednearp_c ( Derivative of near point ) void dnearp_c ( ConstSpiceDouble state [6], SpiceDouble a, SpiceDouble b, SpiceDouble c, SpiceDouble dnear [6], SpiceDouble dalt [2], SpiceBoolean * found ) ## AbstractCompute the state (position and velocity) of an ellipsoid surface point nearest to the position component of a specified state. ## Required_ReadingNone. ## KeywordsDERIVATIVE ELLIPSOID GEOMETRY ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- state I State of an object in body-fixed coordinates. a I Length of semi-axis parallel to X-axis. b I Length of semi-axis parallel to Y-axis. c I Length on semi-axis parallel to Z-axis. dnear O State of the nearest point on the ellipsoid. dalt O Altitude and derivative of altitude. found O Flag that indicates whether `dnear' is degenerate. ## Detailed_Inputstate is a 6-vector giving the position and velocity of some object in the body-fixed coordinates of the ellipsoid. In body-fixed coordinates, the semi-axes of the ellipsoid are aligned with the x, y, and z-axes of the coordinate system. a is the length of the semi-axis of the ellipsoid that is parallel to the X-axis of the body-fixed coordinate system. b is the length of the semi-axis of the ellipsoid that is parallel to the Y-axis of the body-fixed coordinate system. c is the length of the semi-axis of the ellipsoid that is parallel to the Z-axis of the body-fixed coordinate system. ## Detailed_Outputdnear is 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'. While the position component of `dnear' is always meaningful, the velocity component of `dnear' will be meaningless if `found' if SPICEFALSE (See the discussion of the meaning of `found' below.) dalt is an array of two double precision numbers. 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 SPICETRUE (See the discussion of the meaning of `found' below.) found is a logical flag indicating whether or not the velocity portion of `dnear' is meaningful. If the velocity portion of `dnear' is meaningful `found' will be returned with a value of SPICETRUE. Under very rare circumstance the velocity of the near point is undefined. Under these circumstances `found' will be returned with the value SPICEFALSE. `found' can be SPICEFALSE 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. ## ParametersNone. ## Exceptions1) 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'). ## FilesNone. ## ParticularsIf 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. ## ExamplesThe numerical results shown for these examples may differ across platforms. The results depend on the SPICE kernels used as input, the compiler and supporting libraries, 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. /. Program dnearp_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local parameters ./ #define BODYNM "MARS" #define META "dnearp_ex1.tm" /. Local variables ./ SpiceDouble a; SpiceDouble b; SpiceDouble c; SpiceDouble dalt [2]; SpiceDouble dnear [6]; SpiceDouble et; SpiceDouble lt; SpiceDouble radii [3]; SpiceDouble state [6]; SpiceDouble gtvel [3]; SpiceInt dim; SpiceBoolean found; /. Load kernel files via the meta-kernel. ./ furnsh_c ( META ); /. Convert the TDB input time string to seconds past J2000, TDB. ./ str2et_c ( "2007 SEP 30 00:00:00 TDB", &et ); /. First get the axes of the body. ./ bodvrd_c ( BODYNM, "RADII", 3, &dim, radii ); vupack_c ( radii, &a, &b, &c ); /. 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. ./ spkezr_c ( "MRO", et, "IAU_MARS", "NONE", BODYNM, state, < ); ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionJ. Diaz del Rio (ODC Space) ## Version-CSPICE Version 1.0.0, 01-NOV-2021 (JDR) ## Index_EntriesVelocity 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 |

Fri Dec 31 18:41:04 2021