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sgp4.m
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% -----------------------------------------------------------------------------
%
% procedure sgp4
%
% this procedure is the sgp4 prediction model from space command. this is an
% updated and combined version of sgp4 and sdp4, which were originally
% published separately in spacetrack report #3. this version follows the
% methodology from the aiaa paper (2006) describing the history and
% development of the code.
%
% Author:
% Jeff Beck
% current :
% 7 may 08 david vallado
% update small eccentricity check
% changes :
% 16 nov 07 david vallado
% misc fixes for better compliance
% 1.0 (aug 7, 2006) - update for paper dav
% original comments from Vallado C++ version:
% author : david vallado 719-573-2600 28 jun 2005
%
% inputs :
% satrec - initialised structure from sgp4init() call.
% tsince - time eince epoch (minutes)
%
% outputs :
% r - position vector km
% v - velocity km/sec
% return code - non-zero on error.
% 1 - mean elements, ecc >= 1.0 or ecc < -0.001 or a < 0.95 er
% 2 - mean motion less than 0.0
% 3 - pert elements, ecc < 0.0 or ecc > 1.0
% 4 - semi-latus rectum < 0.0
% 5 - epoch elements are sub-orbital
% 6 - satellite has decayed
%
% locals :
% am -
% axnl, aynl -
% betal -
% COSIM , SINIM , COSOMM , SINOMM , Cnod , Snod , Cos2u ,
% Sin2u , Coseo1 , Sineo1 , Cosi , Sini , Cosip , Sinip ,
% Cosisq , Cossu , Sinsu , Cosu , Sinu
% Delm -
% Delomg -
% Dndt -
% Eccm -
% EMSQ -
% Ecose -
% El2 -
% Eo1 -
% Eccp -
% Esine -
% Argpm -
% Argpp -
% Omgadf -
% Pl -
% R -
% RTEMSQ -
% Rdotl -
% Rl -
% Rvdot -
% Rvdotl -
% Su -
% T2 , T3 , T4 , Tc
% Tem5, Temp , Temp1 , Temp2 , Tempa , Tempe , Templ
% U , Ux , Uy , Uz , Vx , Vy , Vz
% inclm - inclination
% mm - mean anomaly
% nm - mean motion
% nodem - longi of ascending node
% xinc -
% xincp -
% xl -
% xlm -
% mp -
% xmdf -
% xmx -
% xmy -
% nodedf -
% xnode -
% nodep -
% np -
%
% coupling :
% getgravconst
% dpper
% dspace
%
% references :
% hoots, roehrich, norad spacetrack report #3 1980
% hoots, norad spacetrack report #6 1986
% hoots, schumacher and glover 2004
% vallado, crawford, hujsak, kelso 2006
% ----------------------------------------------------------------------------*/
function [satrec, r, v] = sgp4(satrec,tsince);
% /* ------------------ set mathematical constants --------------- */
twopi = 2.0 * pi;
x2o3 = 2.0 / 3.0;
% sgp4fix divisor for divide by zero check on inclination
% the old check used 1.0 + cos(pi-1.0e-9), but then compared it to
% 1.5 e-12, so the threshold was changed to 1.5e-12 for consistancy
temp4 = 1.5e-12;
% // sgp4fix identify constants and allow alternate values
global tumin mu radiusearthkm xke j2 j3 j4 j3oj2
vkmpersec = radiusearthkm * xke/60.0;
% /* --------------------- clear sgp4 error flag ----------------- */
satrec.t = tsince;
satrec.error = 0;
mrt = 0.0;
% /* ------- update for secular gravity and atmospheric drag ----- */
xmdf = satrec.mo + satrec.mdot * satrec.t;
argpdf = satrec.argpo + satrec.argpdot * satrec.t;
nodedf = satrec.nodeo + satrec.nodedot * satrec.t;
argpm = argpdf;
mm = xmdf;
t2 = satrec.t * satrec.t;
nodem = nodedf + satrec.nodecf * t2;
tempa = 1.0 - satrec.cc1 * satrec.t;
tempe = satrec.bstar * satrec.cc4 * satrec.t;
templ = satrec.t2cof * t2;
if (satrec.isimp ~= 1)
delomg = satrec.omgcof * satrec.t;
delm = satrec.xmcof *...
((1.0 + satrec.eta * cos(xmdf))^3 -...
satrec.delmo);
temp = delomg + delm;
mm = xmdf + temp;
argpm = argpdf - temp;
t3 = t2 * satrec.t;
t4 = t3 * satrec.t;
tempa = tempa - satrec.d2 * t2 - satrec.d3 * t3 -...
satrec.d4 * t4;
tempe = tempe + satrec.bstar * satrec.cc5 * (sin(mm) -...
satrec.sinmao);
templ = templ + satrec.t3cof * t3 + t4 * (satrec.t4cof +...
satrec.t * satrec.t5cof);
end
nm = satrec.no;
em = satrec.ecco;
inclm = satrec.inclo;
if (satrec.method == 'd')
tc = satrec.t;
[satrec.atime,em,argpm,inclm,satrec.xli,mm,...
satrec.xni,nodem,dndt,nm] = dspace(...
satrec.d2201,satrec.d2211,satrec.d3210,...
satrec.d3222,satrec.d4410,satrec.d4422,...
satrec.d5220,satrec.d5232,satrec.d5421,...
satrec.d5433,satrec.dedt,satrec.del1,...
satrec.del2,satrec.del3,satrec.didt,...
satrec.dmdt,satrec.dnodt,satrec.domdt,...
satrec.irez,satrec.argpo,satrec.argpdot,satrec.t,...
tc,satrec.gsto,satrec.xfact,satrec.xlamo,satrec.no,...
satrec.atime,em,argpm,inclm,satrec.xli,mm,...
satrec.xni,nodem,nm);
end % // if method = d
if (nm <= 0.0)
% fprintf(1,'# error nm %f\n', nm);
satrec.error = 2;
end
am = (xke / nm)^x2o3 * tempa * tempa;
nm = xke / am^1.5;
em = em - tempe;
% // fix tolerance for error recognition
if ((em >= 1.0) || (em < -0.001) || (am < 0.95))
% fprintf(1,'# error em %f\n', em);
satrec.error = 1;
end
% sgp4fix change test condition for eccentricity
if (em < 1.0e-6)
em = 1.0e-6;
end
mm = mm + satrec.no * templ;
xlm = mm + argpm + nodem;
emsq = em * em;
temp = 1.0 - emsq;
nodem = rem(nodem, twopi);
argpm = rem(argpm, twopi);
xlm = rem(xlm, twopi);
mm = rem(xlm - argpm - nodem, twopi);
% /* ----------------- compute extra mean quantities ------------- */
sinim = sin(inclm);
cosim = cos(inclm);
% /* -------------------- add lunar-solar periodics -------------- */
ep = em;
xincp = inclm;
argpp = argpm;
nodep = nodem;
mp = mm;
sinip = sinim;
cosip = cosim;
if (satrec.method == 'd')
[ep,xincp,nodep,argpp,mp] = dpper(...
satrec.e3,satrec.ee2,satrec.peo,...
satrec.pgho,satrec.pho,satrec.pinco,...
satrec.plo,satrec.se2,satrec.se3,...
satrec.sgh2,satrec.sgh3,satrec.sgh4,...
satrec.sh2,satrec.sh3,satrec.si2,...
satrec.si3,satrec.sl2,satrec.sl3,...
satrec.sl4,satrec.t,satrec.xgh2,...
satrec.xgh3,satrec.xgh4,satrec.xh2,...
satrec.xh3,satrec.xi2,satrec.xi3,...
satrec.xl2,satrec.xl3,satrec.xl4,...
satrec.zmol,satrec.zmos,satrec.inclo,...
satrec.init,ep,xincp,nodep,argpp,mp);
if (xincp < 0.0)
xincp = -xincp;
nodep = nodep + pi;
argpp = argpp - pi;
end
if ((ep < 0.0 ) || ( ep > 1.0))
% fprintf(1,'# error ep %f\n', ep);
satrec.error = 3;
end
end % // if method = d
% /* -------------------- long period periodics ------------------ */
if (satrec.method == 'd')
sinip = sin(xincp);
cosip = cos(xincp);
satrec.aycof = -0.5*j3oj2*sinip;
% // sgp4fix for divide by zero with xinco = 180 deg
if (abs(cosip+1.0) > 1.5e-12)
satrec.xlcof = -0.25 * j3oj2 * sinip * (3.0 + 5.0 * cosip) /...
(1.0+cosip);
else
satrec.xlcof = -0.25 * j3oj2 * sinip * (3.0 + 5.0 * cosip) /...
temp4;
end;
end
axnl = ep * cos(argpp);
temp = 1.0 / (am * (1.0 - ep * ep));
aynl = ep* sin(argpp) + temp * satrec.aycof;
xl = mp + argpp + nodep + temp * satrec.xlcof * axnl;
% /* --------------------- solve kepler's equation --------------- */
u = rem(xl - nodep, twopi);
eo1 = u;
tem5 = 9999.9;
ktr = 1;
% // sgp4fix for kepler iteration
% // the following iteration needs better limits on corrections
while (( abs(tem5) >= 1.0e-12) && (ktr <= 10) )
sineo1 = sin(eo1);
coseo1 = cos(eo1);
tem5 = 1.0 - coseo1 * axnl - sineo1 * aynl;
tem5 = (u - aynl * coseo1 + axnl * sineo1 - eo1) / tem5;
if(abs(tem5) >= 0.95)
if tem5 > 0.0
tem5 = 0.95;
else
tem5 = -0.95;
end
end
eo1 = eo1 + tem5;
ktr = ktr + 1;
end
% /* ------------- short period preliminary quantities ----------- */
ecose = axnl*coseo1 + aynl*sineo1;
esine = axnl*sineo1 - aynl*coseo1;
el2 = axnl*axnl + aynl*aynl;
pl = am*(1.0-el2);
if (pl < 0.0)
% fprintf(1,'# error pl %f\n', pl);
satrec.error = 4;
r = [0;0;0];
v = [0;0;0];
else
rl = am * (1.0 - ecose);
rdotl = sqrt(am) * esine/rl;
rvdotl = sqrt(pl) / rl;
betal = sqrt(1.0 - el2);
temp = esine / (1.0 + betal);
sinu = am / rl * (sineo1 - aynl - axnl * temp);
cosu = am / rl * (coseo1 - axnl + aynl * temp);
su = atan2(sinu, cosu);
sin2u = (cosu + cosu) * sinu;
cos2u = 1.0 - 2.0 * sinu * sinu;
temp = 1.0 / pl;
temp1 = 0.5 * j2 * temp;
temp2 = temp1 * temp;
% /* -------------- update for short period periodics ------------ */
if (satrec.method == 'd')
cosisq = cosip * cosip;
satrec.con41 = 3.0*cosisq - 1.0;
satrec.x1mth2 = 1.0 - cosisq;
satrec.x7thm1 = 7.0*cosisq - 1.0;
end
mrt = rl * (1.0 - 1.5 * temp2 * betal * satrec.con41) +...
0.5 * temp1 * satrec.x1mth2 * cos2u;
su = su - 0.25 * temp2 * satrec.x7thm1 * sin2u;
xnode = nodep + 1.5 * temp2 * cosip * sin2u;
xinc = xincp + 1.5 * temp2 * cosip * sinip * cos2u;
mvt = rdotl - nm * temp1 * satrec.x1mth2 * sin2u / xke;
rvdot = rvdotl + nm * temp1 * (satrec.x1mth2 * cos2u +...
1.5 * satrec.con41) / xke;
% /* --------------------- orientation vectors ------------------- */
sinsu = sin(su);
cossu = cos(su);
snod = sin(xnode);
cnod = cos(xnode);
sini = sin(xinc);
cosi = cos(xinc);
xmx = -snod * cosi;
xmy = cnod * cosi;
ux = xmx * sinsu + cnod * cossu;
uy = xmy * sinsu + snod * cossu;
uz = sini * sinsu;
vx = xmx * cossu - cnod * sinsu;
vy = xmy * cossu - snod * sinsu;
vz = sini * cossu;
% /* --------- position and velocity (in km and km/sec) ---------- */
r(1) = (mrt * ux)* radiusearthkm;
r(2) = (mrt * uy)* radiusearthkm;
r(3) = (mrt * uz)* radiusearthkm;
v(1) = (mvt * ux + rvdot * vx) * vkmpersec;
v(2) = (mvt * uy + rvdot * vy) * vkmpersec;
v(3) = (mvt * uz + rvdot * vz) * vkmpersec;
end % // if pl > 0
% // sgp4fix for decaying satellites
if (mrt < 1.0)
% printf("# decay condition %11.6f \n",mrt);
satrec.error = 6;
end
global idebug dbgfile
if idebug
debug7;
end
return;