Table of contents
CSPICE_GETELM parses the "lines" of a two-line element set, returning the
elements in units suitable for use in SPICE software.
Given:
frstyr the first year possible for two-line elements.
[1,1] = size(frstyr); int32 = class(frstyr)
Since two-line elements allow only two digits for the year,
some conventions must be followed concerning which century
the two digits refer to. `frstyr' is the year of the earliest
representable elements. The two-digit year is mapped to the
year in the interval from `frstyr' to frstyr + 99 that has
the same last two digits as the two digit year in the element
set. For example if `frstyr' is set to 1960 then the two
digit years are mapped as shown in the table below:
Two-line Maps to
element year
00 2000
01 2001
02 2002
. .
. .
. .
58 2058
59 2059
-------------------
60 1960
61 1961
62 1962
. .
. .
. .
99 1999
Note that if Space Command should decide to represent
years in 21st century as 100 + the last two digits
of the year (for example: 2015 is represented as 115)
instead of simply dropping the first two digits of
the year, this routine will correctly map the year
as long as you set `frstyr' to some value between 1900
and 1999.
lines a pair of lines of text that comprise a Space command
"two-line element" set.
[2,c1] = size(lines); char = class(lines)
or
[2,1] = size(lines); cell = class(lines)
These text lines should be the same as they are presented
in the two-line element files available from Space Command
(formerly NORAD). See -Particulars for a detailed description
of the format.
the call:
[epoch, elems] = cspice_getelm( frstyr, lines )
returns:
epoch the epoch of the two-line elements supplied via the input
array `lines'.
[1,1] = size(epoch); double = class(epoch)
`epoch' is returned in TDB seconds past J2000.
elems an array containing the elements from the two-line set
supplied via the array `lines'.
[10,1] = size(elems); double = class(elems)
The elements are in units suitable for use by the SPICE
routines EV2LIN and cspice_spkw10.
Also note that the elements XNDD6O and BSTAR
incorporate the exponential factor present in the
input two-line elements in `lines'. (See -Particulars
below).
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.
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 that you have collected the two-line element data
for a spacecraft with NORAD ID 18123. The following example
code demonstrates how you could go about creating a type 10
SPK segment.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: getelm_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 getelm_ex1()
%
% Local parameters.
%
SPK10 = 'getelm_ex1.bsp';
%
% The SPK type 10 segment will contain 18 two-line
% elements sets for the `norad' spacecraft 18123 with
% respect to the Earth (ID 399) in the J2000 reference
% frame.
%
% As stated in the naif_ids required reading, for Earth
% orbiting spacecraft lacking a DSN identification code,
% the NAIF ID is derived from the tracking ID assigned to
% it by `norad' via:
%
% NAIF ID = -100000 - norad ID code
%
TLESSZ = 9;
BODY = -118123;
CENTER = 399;
FRMNAM = 'J2000';
%
% Local variables.
%
consts = zeros( 8,1 );
elems = zeros( 10*TLESSZ,1 );
epochs = zeros( TLESSZ,1 );
%
% These are the variables that will hold the constants
% required by SPK type 10. 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 sets.
%
tle = [ '1 18123U 87 53 A 87324.61041692 -.00000023 ' ...
'00000-0 -75103-5 0 00675',
'2 18123 98.8296 152.0074 0014950 168.7820 ' ...
'191.3688 14.12912554 21686',
'1 18123U 87 53 A 87326.73487726 .00000045 ' ...
'00000-0 28709-4 0 00684',
'2 18123 98.8335 154.1103 0015643 163.5445 ' ...
'196.6235 14.12912902 21988',
'1 18123U 87 53 A 87331.40868801 .00000104 ' ...
'00000-0 60183-4 0 00690',
'2 18123 98.8311 158.7160 0015481 149.9848 ' ...
'210.2220 14.12914624 22644',
'1 18123U 87 53 A 87334.24129978 .00000086 ' ...
'00000-0 51111-4 0 00702',
'2 18123 98.8296 161.5054 0015372 142.4159 ' ...
'217.8089 14.12914879 23045',
'1 18123U 87 53 A 87336.93227900 -.00000107 ' ...
'00000-0 -52860-4 0 00713',
'2 18123 98.8317 164.1627 0014570 135.9191 ' ...
'224.2321 14.12910572 23425',
'1 18123U 87 53 A 87337.28635487 .00000173 ' ...
'00000-0 10226-3 0 00726',
'2 18123 98.8284 164.5113 0015289 133.5979 ' ...
'226.6438 14.12916140 23475',
'1 18123U 87 53 A 87339.05673569 .00000079 ' ...
'00000-0 47069-4 0 00738',
'2 18123 98.8288 166.2585 0015281 127.9985 ' ...
'232.2567 14.12916010 24908',
'1 18123U 87 53 A 87345.43010859 .00000022 ' ...
'00000-0 16481-4 0 00758',
'2 18123 98.8241 172.5226 0015362 109.1515 ' ...
'251.1323 14.12915487 24626',
'1 18123U 87 53 A 87349.04167543 .00000042 ' ...
'00000-0 27370-4 0 00764',
'2 18123 98.8301 176.1010 0015565 100.0881 ' ...
'260.2047 14.12916361 25138' ];
%
% Load the PCK file that provides the geophysical
% constants required for the evaluation of the two-line
% elements sets. Load also an LSK, as it is required by
% cspice_getelm to perform time conversions. Use a metakernel for
% convenience.
%
cspice_furnsh( 'getelm_ex1.tm' );
%
% Retrieve the data from the kernel, and place it on
% the `consts' array.
%
for i=1:8
[consts(i)] = cspice_bodvcd( CENTER, noadpn(i), 1 );
end
%
% Convert the Two Line Elements lines to the
% element sets.
%
j = 0;
for i=1:TLESSZ
[tmpEpochs, tmpElems] = cspice_getelm( 1950, ...
tle(1+2*(i-1):i*2,:) );
epochs(i) = tmpEpochs;
elems(1+j*10:10+j*10) = tmpElems;
j = j + 1;
end
%
% Define the beginning and end of the segment to be
% -/+ 12 hours from the first and last epochs,
% respectively.
%
first = epochs(1) - 0.5 * cspice_spd;
last = epochs(TLESSZ-1) + 0.5 * cspice_spd;
%
% `ncomch' is the number of characters to reserve for the
% kernel's comment area. This example doesn't write
% comments, so set to zero.
%
ncomch = 0;
%
% Internal file name and segment ID.
%
ifname = 'Test for type 10 SPK internal file name';
segid = 'SPK type 10 test segment';
%
% Open a new SPK file.
%
[handle] = cspice_spkopn( SPK10, ifname, ncomch );
%
% Now add the segment.
%
cspice_spkw10( handle, BODY, CENTER, FRMNAM, first, last, ...
segid, consts, TLESSZ, elems, epochs );
%
% Close the SPK file.
%
cspice_spkcls( handle );
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program is executed, no output is presented on
screen. After run completion, a new SPK type 10 exists in
the output directory.
2) 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_evsgp4 to propagate a state to an
epoch of interest.
Use the meta-kernel from the previous example to load the
required SPICE kernels.
Example code begins here.
function getelm_ex2()
%
% 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 PCK file that provides the geophysical
% constants required for the evaluation of the two-line
% elements sets. Load also an LSK, as it is required by
% cspice_getelm to perform time conversions. Use a metakernel for
% convenience.
%
cspice_furnsh( 'getelm_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 parses a Space Command Two-line element set and
returns the orbital elements properly scaled and in units
suitable for use by other SPICE software. Input elements
are provided in two-lines in accordance with the format
required by the two-line element sets available from Space
Command (formerly NORAD). See [1] and [2] for details.
Each of these lines is 69 characters long. The following table
defines each of the individual fields for lines 1 and 2.
Line Column Type Description
---- ------ ---- ------------------------------------------
1 01 N Line number of Element Data (always 1)
1 03-07 N Satellite number (NORAD catalog number)
1 08 A Classification (U:Unclassified; S:Secret)
1 10-11 N International designator (last two digits
of launch year).
1 12-14 N International designator (launch number of
the year).
1 15-17 A International designator (piece of the
launch)
1 19-20 N Epoch year (last two digits of year).
1 21-32 N Epoch (day of the year and portion of the
day)
1 34-43 N NDT20: first time derivative of Mean
Motion
1 45-52 N NDD60: Second time derivative of Mean
Motion (decimal point assumed)
1 54-61 N BSTAR drag term (decimal point assumed)
1 63 N Ephemeris type
1 65-68 N Element number
1 69 N Checksum.
2 01 N Line number of Element Data (always 2)
2 03-07 N Satellite number (must be the same as in
line 1)
2 09-16 N INCL: Inclination, in degrees
2 18-25 N NODE0: Right Ascension of the Ascending
Node, in degrees
2 27-33 N ECC: Eccentricity (decimal point assumed)
2 35-42 N OMEGA: Argument of Perigee, in degrees
2 44-51 N M0: Mean Anomaly, in degrees
2 53-63 N N0: Mean Motion (revolutions per day)
2 64-68 N Revolution number at epoch
2 69 N Checksum
The column type A indicates "characters A-Z", the type N means
"numeric."
Column refers to the substring within the line, e.g.
1 22076U 92052A 97173.53461370 -.00000038 00000-0 10000-3 0 594
2 22076 66.0378 163.4372 0008359 278.7732 81.2337 12.80930736227550
^
123456789012345678901234567890123456789012345678901234567890123456789
1 2 3 4 5 6
In this example, the satellite number (column 03-07) is 22076.
The "raw" elements used by this routine in the first lines are
described in detail below as in several instances exponents and
decimal points are implied. Note that the input units are
degrees, degrees/day**n and revolutions/day.
The epoch (column 19-32; line 1) has a format NNNNN.NNNNNNNN,
where:
Fraction
DOY of day
--- --------
NNNNN.NNNNNNNN
--
Year
An epoch of 00001.00000000 corresponds to 00:00:00 UTC on
2000 January 01.
The first derivative of Mean Motion (column 34-43, line 1), has
a format +.NNNNNNNN, where the first character could be either
a plus sign, a minus sign or a space.
The second derivative of Mean Motion (column 45-52, line 1) and
the BSTAR drag term (see [1] for details -- column 54-61, line
1) have a format +NNNNN-N, where the first character could be
either a plus sign, a minus sign or a space, the decimal point
is assumed, and the exponent is marked by the sign (+/-) at
character 6 (column 51 and 60 for the second derivative and
BSTAR drag term respectively).
The "raw" elements in the second line consists primarily of
mean elements calculated using the sgp4/sdp4 orbital model (See
[1]). The Inclination, the Right Ascension of the Ascending
Node, the Argument of Perigee and the Mean Anomaly have units
of degrees and can range from 0 up to 360 degrees, except for
the Inclination that ranges from 0 to 180 degrees. The
Eccentricity value is provided with an assumed leading decimal
point. For example, a value of 9790714 corresponds to an
eccentricity of 0.9790714. The Mean motion is measured in
revolutions per day and its format is NN.NNNNNNN.
This routine extracts these values, "inserts" the implied
decimal points and exponents and then converts the inputs
to units of radians, radians/minute, radians/minute**2, and
radians/minute**3
1) If an error occurs while trying to parse the two-line element
set, the error SPICE(BADTLE) is signaled by a routine in the
call tree of this routine and a description of the detected
issue in the "two-line element" set is reported on the long
error message.
2) If any of the input arguments, `frstyr' or `lines', is
undefined, an error is signaled by the Matlab error handling
system.
3) If any of the input arguments, `frstyr' or `lines', is not of
the expected type, or it does not have the expected dimensions
and size, an error is signaled by the Mice interface.
You must have loaded a SPICE leapseconds kernel into the
kernel pool prior to calling this routine.
1) The format of the two-line elements suffer from a "millennium"
problem --- only two digits are used for the year of the
elements. It is not clear how Space Command will deal with
this problem. NAIF hopes that by adjusting the input `frstyr'
you should be able to use this routine well into the 21st
century.
The approach taken to mapping the two-digit year to the
full year is given by the code below. Here, YR is the
integer obtained by parsing the two-digit year from the first
line of the elements.
begyr = (frstyr/100)*100;
year = begyr + yr;
if ( year < frstyr )
year = year + 100;
end
This mapping will be changed if future two-line element
representations make this method of computing the full year
inaccurate.
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] "SDC/SCC Two Card Element Set - Transmission Format,"
ADCOM/DO Form 12.
[3] F. Hoots, "Spacetrack Report #6: Models for Propagation of
Space Command Element Sets," U.S. Air Force Aerospace
Defense Command, Colorado Springs, CO, 1986.
[4] 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.
[5] 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, 06-NOV-2021 (MCS)
Parse two-line elements
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