Table of contents
CSPICE_EVSGP4 evaluates NORAD two-line element data for earth orbiting
spacecraft. This evaluator uses algorithms as described
in Vallado 2006 [4].
Given:
et the epoch in seconds past ephemeris epoch J2000 at which a
state should be produced from the input elements.
[1,1] = size(et); double = class(et)
geophs a collection of 8 geophysical constants needed for computing
a state.
[8,1] = size(geophs); double = class(geophs)
The order of these constants must be:
geophs(1) = j2 gravitational harmonic for Earth.
geophs(2) = j3 gravitational harmonic for Earth.
geophs(3) = j4 gravitational harmonic for Earth.
These first three constants are dimensionless.
geophs(4) = KE: Square root of the GM for Earth where
GM is expressed in Earth radii cubed per
minutes squared.
geophs(5) = QO: High altitude bound for atmospheric
model in km.
geophs(6) = SO: Low altitude bound for atmospheric
model in km.
geophs(7) = RE: Equatorial radius of the earth in km.
geophs(8) = AE: Distance units/earth radius
(normally 1)
Below are currently recommended values for these
items:
J2 = 1.082616e-3
J3 = -2.53881e-6
J4 = -1.65597e-6
The next item is the square root of GM for the Earth
given in units of earth-radii**1.5/Minute
KE = 7.43669161e-2
The next two items define the top and bottom of the
atmospheric drag model used by the type 10 ephemeris
type. Don't adjust these unless you understand the full
implications of such changes.
QO = 120.0e0
SO = 78.0e0
The ER value is the equatorial radius in km of the Earth
as used by NORAD.
ER = 6378.135e0
The value of AE is the number of distance units per
Earth radii used by the NORAD state propagation
software. The value should be 1 unless you've got a very
good understanding of the NORAD routine SGP4 and the
affect of changing this value.
AE = 1.0e0
elems an array containing two-line element data as prescribed
below.
[10,1] = size(elems); double = class(elems)
The elements NDD6O and BSTAR must already be scaled by the
proper exponent stored in the two line elements set.
Moreover, the various items must be converted to the units
shown here.
elems( 1 ) = NDT20 in radians/minute**2
elems( 2 ) = NDD60 in radians/minute**3
elems( 3 ) = BSTAR
elems( 4 ) = INCL in radians
elems( 5 ) = NODE0 in radians
elems( 6 ) = ECC
elems( 7 ) = OMEGA in radians
elems( 8 ) = M0 in radians
elems( 9 ) = N0 in radians/minute
elems( 10 ) = `epoch' of the elements in seconds
past ephemeris epoch J2000.
the call:
[state] = cspice_evsgp4( et, geophs, elems )
returns:
state the state produced by evaluating the input elements at the
input epoch `et'.
[6,1] = size(state); double = class(state)
Units are km and km/sec relative to the TEME reference
frame.
None.
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
1) Suppose you have a set of two-line elements for the LUME-1
cubesat. This example shows how you can use this routine
together with the routine cspice_getelm to propagate a state to an
epoch of interest.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: evsgp4_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
--------- ------------------------------------
naif0012.tls Leapseconds
geophysical.ker geophysical constants for evaluation
of two-line element sets.
The geophysical.ker is a PCK file that is provided with the
Mice toolkit under the "/data" directory.
\begindata
KERNELS_TO_LOAD = ( 'naif0012.tls',
'geophysical.ker' )
\begintext
End of meta-kernel
Example code begins here.
function evsgp4_ex1()
%
% Local parameters.
%
TIMSTR = '2020-05-26 02:25:00';
%
% The LUME-1 cubesat is an Earth orbiting object; set
% the center ID to the Earth ID.
%
CENTER = 399;
%
% Local variables.
%
geophs = zeros(8,1);
%
% These are the variables that will hold the constants
% required by cspice_evsgp4. These constants are available
% from the loaded PCK file, which provides the actual
% values and units as used by NORAD propagation model.
%
% Constant Meaning
% -------- ------------------------------------------
% J2 J2 gravitational harmonic for Earth.
% J3 J3 gravitational harmonic for Earth.
% J4 J4 gravitational harmonic for Earth.
% KE Square root of the GM for Earth.
% QO High altitude bound for atmospheric model.
% SO Low altitude bound for atmospheric model.
% ER Equatorial radius of the Earth.
% AE Distance units/earth radius.
%
noadpn = {'J2','J3','J4','KE','QO','SO','ER','AE'};
%
% Define the Two-Line Element set for LUME-1.
%
tle = [ '1 43908U 18111AJ 20146.60805006 .00000806' ...
' 00000-0 34965-4 0 9999',
'2 43908 97.2676 47.2136 0020001 220.6050 ' ...
'139.3698 15.24999521 78544' ];
%
% Load the MK file that includes the PCK file that provides
% the geophysical constants required for the evaluation of
% the two-line elements sets and the LSK, as it is required
% by cspice_getelm to perform time conversions.
%
cspice_furnsh( 'evsgp4_ex1.tm' );
%
% Retrieve the data from the kernel, and place it on
% the `geophs' array.
%
for i=1:8
[geophs(i)] = cspice_bodvcd( CENTER, noadpn(i), 1 );
end
%
% Convert the Two Line Elements lines to the element sets.
% Set the lower bound for the years to be the beginning
% of the space age.
%
[epoch, elems] = cspice_getelm( 1957, tle );
%
% Now propagate the state using cspice_evsgp4 to the epoch
% of interest.
%
[et] = cspice_str2et( TIMSTR );
[state] = cspice_evsgp4( et, geophs, elems );
%
% Display the results.
%
fprintf( 'Epoch : %s\n', TIMSTR )
fprintf( 'Position: %15.8f %15.8f %15.8f\n', ...
state(1), state(2), state(3) )
fprintf( 'Velocity: %15.8f %15.8f %15.8f\n', ...
state(4), state(5), state(6) )
%
% 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 PC/Linux/Matlab9.x/32-bit
platform, the output was:
Epoch : 2020-05-26 02:25:00
Position: -4644.60403398 -5038.95025539 -337.27141116
Velocity: -0.45719025 0.92884817 -7.55917355
This routine evaluates any NORAD two-line element sets for
near-earth orbiting satellites using the algorithms described in
Vallado 2006 [4].
1) No checks are made on the reasonableness of the inputs.
2) If a problem occurs when evaluating the elements, an
error is signaled by a routine in the call tree of this
routine.
3) If any of the input arguments, `et', `geophs' or `elems', is
undefined, an error is signaled by the Matlab error handling
system.
4) If any of the input arguments, `et', `geophs' or `elems', 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
[1] F. Hoots and R. Roehrich, "Spacetrack Report #3: Models for
Propagation of the NORAD Element Sets," U.S. Air Force
Aerospace Defense Command, Colorado Springs, CO, 1980.
[2] F. Hoots, "Spacetrack Report #6: Models for Propagation of
Space Command Element Sets," U.S. Air Force Aerospace
Defense Command, Colorado Springs, CO, 1986.
[3] F. Hoots, P. Schumacher and R. Glover, "History of Analytical
Orbit Modeling in the U. S. Space Surveillance System,"
Journal of Guidance, Control, and Dynamics. 27(2):174-185,
2004.
[4] D. Vallado, P. Crawford, R. Hujsak and T. Kelso, "Revisiting
Spacetrack Report #3," paper AIAA 2006-6753 presented at the
AIAA/AAS Astrodynamics Specialist Conference, Keystone, CO.,
August 21-24, 2006.
M. Costa Sitja (JPL)
-Mice Version 1.0.0, 02-NOV-2021 (MCS)
Evaluate NORAD two-line element data using SGP4.
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