CSPICE_DPGRDR computes the Jacobian matrix of the transformation
from rectangular to planetographic coordinates.
body name of the body with which the planetographic coordinate system
[1,m] = size(body); char = class(body)
`body' is used by this routine to look up from the
kernel pool the prime meridian rate coefficient giving
the body's spin sense.
x [1,n] = size(x); double = class(x)
y [1,n] = size(y); double = class(y)
z [1,n] = size(z); double = class(z)
the rectangular coordinates of the point at which the Jacobian of
the map from rectangular to planetographic coordinates is
re equatorial radius of a reference spheroid. This spheroid is a
volume of revolution: its horizontal cross sections are circular.
The shape of the spheroid is defined by an equatorial radius `re'
and a polar radius `rp'.
[1,1] = size(re); double = class(re)
f the flattening coefficient
[1,1] = size(f); double = class(f)
f = (re-rp) / re
where rp is the polar radius of the spheroid. (More importantly
rp = re*(1-f).)
jacobi = cspice_dpgrdr( body, x, y, z, re, f)
jacobi the matrix of partial derivatives of the conversion from
rectangular to planetographic coordinates. It has the form
If [1,1] = size(x) then [3,3] = size(jacobi).
If [1,n] = size(x) then [3,3,n] = size(jacobi).
double = class(jacobi)
| dlon/dx dlon/dy dlon/dz |
| dlat/dx dlat/dy dlat/dz |
| dalt/dx dalt/dy dalt/dz |
evaluated at the input values of 'x', 'y', and 'z'.
When performing vector calculations with velocities it is usually
most convenient to work in rectangular coordinates. However, once
the vector manipulations have been performed, it is often
desirable to convert the rectangular representations into
planetographic coordinates to gain insights about phenomena in
this coordinate frame.
To transform rectangular velocities to derivatives of coordinates
in a planetographic system, one uses the Jacobian of the
transformation between the two systems.
Given a state in rectangular coordinates
( x, y, z, dx, dy, dz )
the velocity in planetographic coordinates is given by the matrix
t | t
(dlon, dlat, dalt) = jacobi| * (dx, dy, dz)
This routine computes the matrix
|(x, y, z)
The planetographic definition of latitude is identical to the
planetodetic (also called "geodetic" in SPICE documentation)
definition. In the planetographic coordinate system, latitude is
defined using a reference spheroid. The spheroid is
characterized by an equatorial radius and a polar radius. For a
point P on the spheroid, latitude is defined as the angle between
the X-Y plane and the outward surface normal at P. For a point P
off the spheroid, latitude is defined as the latitude of the
nearest point to P on the spheroid. Note if P is an interior
point, for example, if P is at the center of the spheroid, there
may not be a unique nearest point to P.
In the planetographic coordinate system, longitude is defined
using the spin sense of the body. Longitude is positive to the
west if the spin is prograde and positive to the east if the spin
is retrograde. The spin sense is given by the sign of the first
degree term of the time-dependent polynomial for the body's prime
meridian Euler angle "W": the spin is retrograde if this term is
negative and prograde otherwise. For the sun, planets, most
natural satellites, and selected asteroids, the polynomial
expression for W may be found in a SPICE PCK kernel.
The earth, moon, and sun are exceptions: planetographic longitude
is measured positive east for these bodies.
If you wish to override the default sense of positive longitude
for a particular body, you can do so by defining the kernel
where <body ID> represents the NAIF ID code of the body. This
variable may be assigned either of the values
For example, you can have this routine treat the longitude
of the earth as increasing to the west using the kernel
BODY399_PGR_POSITIVE_LON = 'WEST'
Normally such assignments are made by placing them in a text
kernel and loading that kernel via cspice_furnsh.
The definition of this kernel variable controls the behavior of
the CSPICE planetographic routines
It does not affect the other CSPICE coordinate conversion
For important details concerning this module's function, please refer to
the CSPICE routine dpgrdr_c.
-Mice Version 1.0.0, 11-NOV-2013, EDW (JPL), SCK (JPL)
Jacobian of planetographic w.r.t. rectangular coordinates