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sgp_models.jl
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########################
# Two Line Element Set #
########################
@enum gravconsttype begin
wgs72old
wgs72
wgs84
end
# Constants of SGP Models
const twopi = 2.0 * pi
const xpdotp = 1440.0 / twopi
# const mu = 398600.5 # in km3 / s2
# const radiusearthkm = 6378.137 # km
# const xke = 60.0 / sqrt(radiusearthkm^3 / mu)
# const tumin = 1.0 / xke
# const j2 = 0.00108262998905
# const j3 = -0.00000253215306
# const j4 = -0.00000161098761
# const j3oj2 = j3 / j2
export TLE
"""
Structure for storing a NORAD Two-Line Element
Atributes:
- `line1::String` First line of Two-Line Element set including checksum
- `line2::String` Second line of Two-Line Element set including checksum
- `epoch::Epoch` Epoch of element set.
"""
mutable struct TLE
# String Representation
line1::String
line2::String
# Propagator settings
whichconst::gravconsttype
afspc_mode::Bool
init::Char
# Generic values
satnum::Int
classification::Char
intldesg::String
epochyr::Int
epoch::Epoch
elnum::Int
revnum::Int
method::Char
# SGP4 Propagator variables #
# Common
a::Float64
altp::Float64
alta::Float64
epochdays::Float64
jdsatepoch::Float64
nddot::Float64
ndot::Float64
bstar::Float64
rcse::Float64
inclo::Float64
nodeo::Float64
ecco::Float64
argpo::Float64
mo::Float64
no::Float64
# Near Earth
isimp::Int
aycof::Float64
con41::Float64
cc1::Float64
cc4::Float64
cc5::Float64
d2::Float64
d3::Float64
d4::Float64
delmo::Float64
eta::Float64
argpdot::Float64
omgcof::Float64
sinmao::Float64
t::Float64
t2cof::Float64
t3cof::Float64
t4cof::Float64
t5cof::Float64
x1mth2::Float64
x7thm1::Float64
mdot::Float64
nodedot::Float64
xlcof::Float64
xmcof::Float64
nodecf::Float64
# Deep Space
irez::Int
d2201::Float64
d2211::Float64
d3210::Float64
d3222::Float64
d4410::Float64
d4422::Float64
d5220::Float64
d5232::Float64
d5421::Float64
d5433::Float64
dedt::Float64
del1::Float64
del2::Float64
del3::Float64
didt::Float64
dmdt::Float64
dnodt::Float64
domdt::Float64
e3::Float64
ee2::Float64
peo::Float64
pgho::Float64
pho::Float64
pinco::Float64
plo::Float64
se2::Float64
se3::Float64
sgh2::Float64
sgh3::Float64
sgh4::Float64
sh2::Float64
sh3::Float64
si2::Float64
si3::Float64
sl2::Float64
sl3::Float64
sl4::Float64
gsto::Float64
xfact::Float64
xgh2::Float64
xgh3::Float64
xgh4::Float64
xh2::Float64
xh3::Float64
xi2::Float64
xi3::Float64
xl2::Float64
xl3::Float64
xl4::Float64
xlamo::Float64
zmol::Float64
zmos::Float64
atime::Float64
xli::Float64
xni::Float64
# Error Status Code
error::UInt8
end
function Base.show(io::IO, tle::TLE)
s = @sprintf "TLE(epoch: %s, line1: %s, line2: %s)" tle.epoch tle.line1 tle.line2
print(io, s)
end
##################
# SGP4 Internals #
##################
export tle_checksum
"""
Compute Two-Line Element checksum for a given line string.
Arguments:
- `line::String` Input line
Returns:
- `sum::Int`
"""
function tle_checksum(line::String)
sum = 0
for c in line
if c in "0123456789"
sum += parse(Int, c)
elseif c == '-'
sum += 1
end
end
return sum % 10
end
"""
Internal SGP method to convert year and days to month and hours, minutes,
seconds.
"""
function days2mdhms(year::Int, days::Real)
lmonth = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
dayofyr = floor(Int, days)
# ----------------- find month and day of month ---------------- */
if ( (year % 4) == 0 )
lmonth[1] = 29
end
i = 1
inttemp = 0
while ((dayofyr > inttemp + lmonth[i]) && (i < 12))
inttemp = inttemp + lmonth[i]
i = i + 1
end
mon = i
day = dayofyr - inttemp
# ----------------- find hours minutes and seconds ------------- */
temp = (days - dayofyr) * 24.0
hr = floor(Int, temp)
temp = (temp - hr) * 60.0
minute = floor(Int, temp)
sec = (temp - minute) * 60.0
return mon, day, hr, minute, sec
end
"""
Internal SGP method to convert year, month and hours, minutes, seconds to a
Julian Date.
"""
function jday(year::Int, mon::Int, day::Int, hr::Int, minute::Int, sec::Real)
jd = 367.0 * year -
floor((7 * (year + floor((mon + 9) / 12.0))) * 0.25) +
floor( 275 * mon / 9.0 ) +
day + 1721013.5 +
((sec / 60.0 + minute) / 60.0 + hr) / 24.0
return jd
end
"""
Function finds the Greenwich sidereal time consistent with SGP4 propagator
"""
function gstime(jdut1::Real)
tut1 = (jdut1 - 2451545.0) / 36525.0
temp = -6.2e-6* tut1 * tut1 * tut1 + 0.093104 * tut1 * tut1 +
(876600.0*3600 + 8640184.812866) * tut1 + 67310.54841 # sec
temp = (temp * DEG2RAD / 240.0) % 2*pi # 360/86400 = 1/240, to deg, to rad
# Check Quadrants
if (temp < 0.0)
temp += 2*pi
end
return temp
end
"""
/* -----------------------------------------------------------------------------
*
* function getgravconst
*
* this function gets constants for the propagator. note that mu is identified to
* facilitiate comparisons with newer models. the common useage is wgs72.
*
* author : david vallado 719-573-2600 21 jul 2006
*
* inputs :
* whichconst - which set of constants to use wgs72old, wgs72, wgs84
*
* outputs :
* tumin - minutes in one time unit
* mu - earth gravitational parameter
* radiusearthkm - radius of the earth in km
* xke - reciprocal of tumin
* j2, j3, j4 - un-normalized zonal harmonic values
* j3oj2 - j3 divided by j2
*
* locals :
*
* coupling :
* none
*
* references :
* norad spacetrack report #3
* vallado, crawford, hujsak, kelso 2006
--------------------------------------------------------------------------- */
"""
function getgravconst(whichconst::gravconsttype)
if whichconst == wgs72old::gravconsttype
# -- wgs-72 low precision str#3 constants --
mu = 398600.79964 # in km3 / s2
radiusearthkm = 6378.135 # km
xke = 0.0743669161
tumin = 1.0 / xke
j2 = 0.001082616
j3 = -0.00000253881
j4 = -0.00000165597
j3oj2 = j3 / j2
return tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2
elseif whichconst == wgs72::gravconsttype
# ------------ wgs-72 constants ------------
mu = 398600.8 # in km3 / s2
radiusearthkm = 6378.135 # km
xke = 60.0 / sqrt(radiusearthkm*radiusearthkm*radiusearthkm/mu)
tumin = 1.0 / xke
j2 = 0.001082616
j3 = -0.00000253881
j4 = -0.00000165597
j3oj2 = j3 / j2
return tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2
elseif whichconst == wgs84::gravconsttype
# ------------ wgs-84 constants ------------
mu = 398600.5 # in km3 / s2
radiusearthkm = 6378.137 # km
xke = 60.0 / sqrt(radiusearthkm*radiusearthkm*radiusearthkm/mu)
tumin = 1.0 / xke
j2 = 0.00108262998905
j3 = -0.00000253215306
j4 = -0.00000161098761
j3oj2 = j3 / j2
return tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2
else
@error ("Unknown gravity option $whichconst")
end
end
"""
/*-----------------------------------------------------------------------------
*
* procedure initl
*
* this procedure initializes the spg4 propagator. all the initialization is
* consolidated here instead of having multiple loops inside other routines.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* ecco - eccentricity 0.0 - 1.0
* epoch - epoch time in days from jan 0, 1950. 0 hr
* inclo - inclination of satellite
* no - mean motion of satellite
* satn - satellite number
*
* outputs :
* ainv - 1.0 / a
* ao - semi major axis
* con41 -
* con42 - 1.0 - 5.0 cos(i)
* cosio - cosine of inclination
* cosio2 - cosio squared
* eccsq - eccentricity squared
* method - flag for deep space 'd', 'n'
* omeosq - 1.0 - ecco * ecco
* posq - semi-parameter squared
* rp - radius of perigee
* rteosq - square root of (1.0 - ecco*ecco)
* sinio - sine of inclination
* gsto - gst at time of observation rad
* no - mean motion of satellite
*
* locals :
* ak -
* d1 -
* del -
* adel -
* po -
*
* coupling :
* getgravconst
* gstime - find greenwich sidereal time from the julian date
*
* 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 initl(satn::Int, whichconst::gravconsttype, ecco::Real, epoch::Real,
inclo::Real, no::Real, method::Char, afspc_mode::Bool)
# sgp4fix use old way of finding gst
# ----------------------- earth constants ----------------------
# sgp4fix identify constants and allow alternate values
tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 = getgravconst(whichconst)
x2o3 = 2.0 / 3.0
# ------------- calculate auxillary epoch quantities ----------
eccsq = ecco * ecco
omeosq = 1.0 - eccsq
rteosq = sqrt(omeosq)
cosio = cos(inclo)
cosio2 = cosio * cosio
# ------------------ un-kozai the mean motion -----------------
ak = (xke / no) ^ x2o3
d1 = 0.75 * j2 * (3.0 * cosio2 - 1.0) / (rteosq * omeosq)
del_ = d1 / (ak * ak)
adel = ak * (1.0 - del_ * del_ - del_ *
(1.0 / 3.0 + 134.0 * del_ * del_ / 81.0))
del_ = d1/(adel * adel)
no = no / (1.0 + del_)
ao = (xke / no) ^ x2o3
sinio = sin(inclo)
po = ao * omeosq
con42 = 1.0 - 5.0 * cosio2
con41 = -con42-cosio2-cosio2
ainv = 1.0 / ao
posq = po * po
rp = ao * (1.0 - ecco)
method = 'n'
# sgp4fix modern approach to finding sidereal time
if afspc_mode
# sgp4fix use old way of finding gst
# count integer number of days from 0 jan 1970
ts70 = epoch - 7305.0
ds70 = (ts70 + 1.0e-8) // 1.0
tfrac = ts70 - ds70
# find greenwich location at epoch
c1 = 1.72027916940703639e-2
thgr70= 1.7321343856509374
fk5r = 5.07551419432269442e-15
c1p2p = c1 + twopi
gsto = (thgr70 + c1*ds70 + c1p2p*tfrac + ts70*ts70*fk5r) % twopi
if gsto < 0.0
gsto = gsto + twopi
end
else
gsto = gstime(epoch + 2433281.5)
end
return (
no,
method,
ainv, ao, con41, con42, cosio,
cosio2,eccsq, omeosq, posq,
rp, rteosq,sinio , gsto,
)
end
"""
/*-----------------------------------------------------------------------------
*
* procedure dscom
*
* this procedure provides deep space common items used by both the secular
* and periodics subroutines. input is provided as shown. this routine
* used to be called dpper, but the functions inside weren't well organized.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* epoch -
* ep - eccentricity
* argpp - argument of perigee
* tc -
* inclp - inclination
* nodep - right ascension of ascending node
* np - mean motion
*
* outputs :
* sinim , cosim , sinomm , cosomm , snodm , cnodm
* day -
* e3 -
* ee2 -
* em - eccentricity
* emsq - eccentricity squared
* gam -
* peo -
* pgho -
* pho -
* pinco -
* plo -
* rtemsq -
* se2, se3 -
* sgh2, sgh3, sgh4 -
* sh2, sh3, si2, si3, sl2, sl3, sl4 -
* s1, s2, s3, s4, s5, s6, s7 -
* ss1, ss2, ss3, ss4, ss5, ss6, ss7, sz1, sz2, sz3 -
* sz11, sz12, sz13, sz21, sz22, sz23, sz31, sz32, sz33 -
* xgh2, xgh3, xgh4, xh2, xh3, xi2, xi3, xl2, xl3, xl4 -
* nm - mean motion
* z1, z2, z3, z11, z12, z13, z21, z22, z23, z31, z32, z33 -
* zmol -
* zmos -
*
* locals :
* a1, a2, a3, a4, a5, a6, a7, a8, a9, a10 -
* betasq -
* cc -
* ctem, stem -
* x1, x2, x3, x4, x5, x6, x7, x8 -
* xnodce -
* xnoi -
* zcosg , zsing , zcosgl , zsingl , zcosh , zsinh , zcoshl , zsinhl ,
* zcosi , zsini , zcosil , zsinil ,
* zx -
* zy -
*
* coupling :
* none.
*
* 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 dscom(epoch::Real, ep::Real, argpp::Real, tc::Real, inclp::Real,
nodep::Real, np::Real, e3::Real, ee2::Real, peo::Real, pgho::Real,
pho::Real, pinco::Real, plo::Real, se2::Real, se3::Real,
sgh2::Real, sgh3::Real, sgh4::Real, sh2::Real, sh3::Real,
si2::Real, si3::Real, sl2::Real, sl3::Real, sl4::Real,
xgh2::Real, xgh3::Real, xgh4::Real, xh2::Real,
xh3::Real, xi2::Real, xi3::Real, xl2::Real, xl3::Real,
xl4::Real, zmol::Real, zmos::Real,
)
# ------------------ initialize variables ----------------------
s1 = 0.0; s2 = 0.0; s3 = 0.0; s4 = 0.0; s5 = 0.0;
s6 = 0.0; s7 = 0.0; ss1 = 0.0; ss2 = 0.0; ss3 = 0.0;
ss4 = 0.0; ss5 = 0.0; ss6 = 0.0; ss7 = 0.0; sz1 = 0.0;
sz2 = 0.0; sz3 = 0.0; sz11 = 0.0; sz12 = 0.0; sz13 = 0.0;
sz21 = 0.0; sz22 = 0.0; sz23 = 0.0; sz31 = 0.0; sz32 = 0.0;
sz33 = 0.0; z1 = 0.0; z2 = 0.0; z3 = 0.0;
z11 = 0.0; z12 = 0.0; z13 = 0.0; z21 = 0.0; z22 = 0.0;
z23 = 0.0; z31 = 0.0; z32 = 0.0; z33 = 0.0;
# -------------------------- constants -------------------------
zes = 0.01675
zel = 0.05490
c1ss = 2.9864797e-6
c1l = 4.7968065e-7
zsinis = 0.39785416
zcosis = 0.91744867
zcosgs = 0.1945905
zsings = -0.98088458
# --------------------- local variables ------------------------
nm = np
em = ep
snodm = sin(nodep)
cnodm = cos(nodep)
sinomm = sin(argpp)
cosomm = cos(argpp)
sinim = sin(inclp)
cosim = cos(inclp)
emsq = em * em
betasq = 1.0 - emsq
rtemsq = sqrt(betasq)
# ----------------- initialize lunar solar terms ---------------
peo = 0.0
pinco = 0.0
plo = 0.0
pgho = 0.0
pho = 0.0
day = epoch + 18261.5 + tc / 1440.0
xnodce = (4.5236020 - 9.2422029e-4 * day) % twopi
stem = sin(xnodce)
ctem = cos(xnodce)
zcosil = 0.91375164 - 0.03568096 * ctem
zsinil = sqrt(1.0 - zcosil * zcosil)
zsinhl = 0.089683511 * stem / zsinil
zcoshl = sqrt(1.0 - zsinhl * zsinhl)
gam = 5.8351514 + 0.0019443680 * day
zx = 0.39785416 * stem / zsinil
zy = zcoshl * ctem + 0.91744867 * zsinhl * stem
zx = atan(zx, zy)
zx = gam + zx - xnodce
zcosgl = cos(zx)
zsingl = sin(zx)
# ------------------------- do solar terms ---------------------
zcosg = zcosgs
zsing = zsings
zcosi = zcosis
zsini = zsinis
zcosh = cnodm
zsinh = snodm
cc = c1ss
xnoi = 1.0 / nm
for lsflg in 1:2
a1 = zcosg * zcosh + zsing * zcosi * zsinh
a3 = -zsing * zcosh + zcosg * zcosi * zsinh
a7 = -zcosg * zsinh + zsing * zcosi * zcosh
a8 = zsing * zsini
a9 = zsing * zsinh + zcosg * zcosi * zcosh
a10 = zcosg * zsini
a2 = cosim * a7 + sinim * a8
a4 = cosim * a9 + sinim * a10
a5 = -sinim * a7 + cosim * a8
a6 = -sinim * a9 + cosim * a10
x1 = a1 * cosomm + a2 * sinomm
x2 = a3 * cosomm + a4 * sinomm
x3 = -a1 * sinomm + a2 * cosomm
x4 = -a3 * sinomm + a4 * cosomm
x5 = a5 * sinomm
x6 = a6 * sinomm
x7 = a5 * cosomm
x8 = a6 * cosomm
z31 = 12.0 * x1 * x1 - 3.0 * x3 * x3
z32 = 24.0 * x1 * x2 - 6.0 * x3 * x4
z33 = 12.0 * x2 * x2 - 3.0 * x4 * x4
z1 = 3.0 * (a1 * a1 + a2 * a2) + z31 * emsq
z2 = 6.0 * (a1 * a3 + a2 * a4) + z32 * emsq
z3 = 3.0 * (a3 * a3 + a4 * a4) + z33 * emsq
z11 = -6.0 * a1 * a5 + emsq * (-24.0 * x1 * x7-6.0 * x3 * x5)
z12 = -6.0 * (a1 * a6 + a3 * a5) + emsq *
(-24.0 * (x2 * x7 + x1 * x8) - 6.0 * (x3 * x6 + x4 * x5))
z13 = -6.0 * a3 * a6 + emsq * (-24.0 * x2 * x8 - 6.0 * x4 * x6)
z21 = 6.0 * a2 * a5 + emsq * (24.0 * x1 * x5 - 6.0 * x3 * x7)
z22 = 6.0 * (a4 * a5 + a2 * a6) + emsq *
(24.0 * (x2 * x5 + x1 * x6) - 6.0 * (x4 * x7 + x3 * x8))
z23 = 6.0 * a4 * a6 + emsq * (24.0 * x2 * x6 - 6.0 * x4 * x8)
z1 = z1 + z1 + betasq * z31
z2 = z2 + z2 + betasq * z32
z3 = z3 + z3 + betasq * z33
s3 = cc * xnoi
s2 = -0.5 * s3 / rtemsq
s4 = s3 * rtemsq
s1 = -15.0 * em * s4
s5 = x1 * x3 + x2 * x4
s6 = x2 * x3 + x1 * x4
s7 = x2 * x4 - x1 * x3
# ----------------------- do lunar terms -------------------
if lsflg == 1
ss1 = s1
ss2 = s2
ss3 = s3
ss4 = s4
ss5 = s5
ss6 = s6
ss7 = s7
sz1 = z1
sz2 = z2
sz3 = z3
sz11 = z11
sz12 = z12
sz13 = z13
sz21 = z21
sz22 = z22
sz23 = z23
sz31 = z31
sz32 = z32
sz33 = z33
zcosg = zcosgl
zsing = zsingl
zcosi = zcosil
zsini = zsinil
zcosh = zcoshl * cnodm + zsinhl * snodm
zsinh = snodm * zcoshl - cnodm * zsinhl
cc = c1l
end
end
zmol = (4.7199672 + 0.22997150 * day - gam) % twopi
zmos = (6.2565837 + 0.017201977 * day) % twopi
# ------------------------ do solar terms ----------------------
se2 = 2.0 * ss1 * ss6
se3 = 2.0 * ss1 * ss7
si2 = 2.0 * ss2 * sz12
si3 = 2.0 * ss2 * (sz13 - sz11)
sl2 = -2.0 * ss3 * sz2
sl3 = -2.0 * ss3 * (sz3 - sz1)
sl4 = -2.0 * ss3 * (-21.0 - 9.0 * emsq) * zes
sgh2 = 2.0 * ss4 * sz32
sgh3 = 2.0 * ss4 * (sz33 - sz31)
sgh4 = -18.0 * ss4 * zes
sh2 = -2.0 * ss2 * sz22
sh3 = -2.0 * ss2 * (sz23 - sz21)
# ------------------------ do lunar terms ----------------------
ee2 = 2.0 * s1 * s6
e3 = 2.0 * s1 * s7
xi2 = 2.0 * s2 * z12
xi3 = 2.0 * s2 * (z13 - z11)
xl2 = -2.0 * s3 * z2
xl3 = -2.0 * s3 * (z3 - z1)
xl4 = -2.0 * s3 * (-21.0 - 9.0 * emsq) * zel
xgh2 = 2.0 * s4 * z32
xgh3 = 2.0 * s4 * (z33 - z31)
xgh4 = -18.0 * s4 * zel
xh2 = -2.0 * s2 * z22
xh3 = -2.0 * s2 * (z23 - z21)
return (
snodm, cnodm, sinim, cosim, sinomm,
cosomm,day, e3, ee2, em,
emsq, gam, peo, pgho, pho,
pinco, plo, rtemsq, se2, se3,
sgh2, sgh3, sgh4, sh2, sh3,
si2, si3, sl2, sl3, sl4,
s1, s2, s3, s4, s5,
s6, s7, ss1, ss2, ss3,
ss4, ss5, ss6, ss7, sz1,
sz2, sz3, sz11, sz12, sz13,
sz21, sz22, sz23, sz31, sz32,
sz33, xgh2, xgh3, xgh4, xh2,
xh3, xi2, xi3, xl2, xl3,
xl4, nm, z1, z2, z3,
z11, z12, z13, z21, z22,
z23, z31, z32, z33, zmol,
zmos
)
end
"""
/* -----------------------------------------------------------------------------
*
* procedure dpper
*
* this procedure provides deep space long period periodic contributions
* to the mean elements. by design, these periodics are zero at epoch.
* this used to be dscom which included initialization, but it's really a
* recurring function.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* e3 -
* ee2 -
* peo -
* pgho -
* pho -
* pinco -
* plo -
* se2 , se3 , sgh2, sgh3, sgh4, sh2, sh3, si2, si3, sl2, sl3, sl4 -
* t -
* xh2, xh3, xi2, xi3, xl2, xl3, xl4 -
* zmol -
* zmos -
* ep - eccentricity 0.0 - 1.0
* inclo - inclination - needed for lyddane modification
* nodep - right ascension of ascending node
* argpp - argument of perigee
* mp - mean anomaly
*
* outputs :
* ep - eccentricity 0.0 - 1.0
* inclp - inclination
* nodep - right ascension of ascending node
* argpp - argument of perigee
* mp - mean anomaly
*
* locals :
* alfdp -
* betdp -
* cosip , sinip , cosop , sinop ,
* dalf -
* dbet -
* dls -
* f2, f3 -
* pe -
* pgh -
* ph -
* pinc -
* pl -
* sel , ses , sghl , sghs , shl , shs , sil , sinzf , sis ,
* sll , sls
* xls -
* xnoh -
* zf -
* zm -
*
* coupling :
* none.
*
* 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 dpper(tle::TLE, inclo::Real, init::Char,
ep::Real, inclp::Real, nodep::Real, argpp::Real, mp::Real, afspc_mode::Bool)
# Copy satellite attributes into local variables for convenience
# and symmetry in writing formulae.
e3 = tle.e3
ee2 = tle.ee2
peo = tle.peo
pgho = tle.pgho
pho = tle.pho
pinco = tle.pinco
plo = tle.plo
se2 = tle.se2
se3 = tle.se3
sgh2 = tle.sgh2
sgh3 = tle.sgh3
sgh4 = tle.sgh4
sh2 = tle.sh2
sh3 = tle.sh3
si2 = tle.si2
si3 = tle.si3
sl2 = tle.sl2
sl3 = tle.sl3
sl4 = tle.sl4
t = tle.t
xgh2 = tle.xgh2
xgh3 = tle.xgh3
xgh4 = tle.xgh4
xh2 = tle.xh2
xh3 = tle.xh3
xi2 = tle.xi2
xi3 = tle.xi3
xl2 = tle.xl2
xl3 = tle.xl3
xl4 = tle.xl4
zmol = tle.zmol
zmos = tle.zmos
# ---------------------- constants -----------------------------
zns = 1.19459e-5
zes = 0.01675
znl = 1.5835218e-4
zel = 0.05490
# --------------- calculate time varying periodics -----------
zm = zmos + zns * t
# be sure that the initial call has time set to zero
if init == 'y'
zm = zmos
end
zf = zm + 2.0 * zes * sin(zm)
sinzf = sin(zf)
f2 = 0.5 * sinzf * sinzf - 0.25
f3 = -0.5 * sinzf * cos(zf)
ses = se2* f2 + se3 * f3
sis = si2 * f2 + si3 * f3
sls = sl2 * f2 + sl3 * f3 + sl4 * sinzf
sghs = sgh2 * f2 + sgh3 * f3 + sgh4 * sinzf
shs = sh2 * f2 + sh3 * f3
zm = zmol + znl * t
if init == 'y'
zm = zmol
end
zf = zm + 2.0 * zel * sin(zm)
sinzf = sin(zf)
f2 = 0.5 * sinzf * sinzf - 0.25
f3 = -0.5 * sinzf * cos(zf)
sel = ee2 * f2 + e3 * f3
sil = xi2 * f2 + xi3 * f3
sll = xl2 * f2 + xl3 * f3 + xl4 * sinzf
sghl = xgh2 * f2 + xgh3 * f3 + xgh4 * sinzf
shll = xh2 * f2 + xh3 * f3
pe = ses + sel
pinc = sis + sil
pl = sls + sll
pgh = sghs + sghl
ph = shs + shll
if init == 'n'
pe = pe - peo;
pinc = pinc - pinco;
pl = pl - plo;
pgh = pgh - pgho;
ph = ph - pho;
inclp = inclp + pinc;
ep = ep + pe;
sinip = sin(inclp);
cosip = cos(inclp);
"""
/* ----------------- apply periodics directly ------------ */
// sgp4fix for lyddane choice
// strn3 used original inclination - this is technically feasible
// gsfc used perturbed inclination - also technically feasible
// probably best to readjust the 0.2 limit value and limit discontinuity
// 0.2 rad = 11.45916 deg
// use next line for original strn3 approach and original inclination
// if (inclo >= 0.2)
// use next line for gsfc version and perturbed inclination
"""
if inclp >= 0.2
ph /= sinip
pgh -= cosip * ph
argpp += pgh
nodep += ph
mp += pl
else
# ---- apply periodics with lyddane modification ----
sinop = sin(nodep);
cosop = cos(nodep);
alfdp = sinip * sinop;
betdp = sinip * cosop;
dalf = ph * cosop + pinc * cosip * sinop;
dbet = -ph * sinop + pinc * cosip * cosop;
alfdp = alfdp + dalf;
betdp = betdp + dbet;
nodep = nodep >= 0.0 ? nodep % twopi : -(-nodep % twopi)
# sgp4fix for afspc written intrinsic functions
# nodep used without a trigonometric function ahead
if nodep < 0.0 && afspc_mode
nodep = nodep + twopi
end
xls = mp + argpp + pl + pgh + (cosip - pinc * sinip) * nodep
xnoh = nodep;
nodep = atan(alfdp, betdp);
# sgp4fix for afspc written intrinsic functions
# nodep used without a trigonometric function ahead
if nodep < 0.0 && afspc_mode
nodep = nodep + twopi;
end
if abs(xnoh - nodep) > pi
if nodep < xnoh
nodep = nodep + twopi;
else
nodep = nodep - twopi;
end
mp += pl
argpp = xls - mp - cosip * nodep;
end
end
end
return ep, inclp, nodep, argpp, mp
end
"""
/*-----------------------------------------------------------------------------
*
* procedure dsinit
*
* this procedure provides deep space contributions to mean motion dot due
* to geopotential resonance with half day and one day orbits.
*
* author : david vallado 719-573-2600 28 jun 2005
*
* inputs :
* cosim, sinim-
* emsq - eccentricity squared
* argpo - argument of perigee
* s1, s2, s3, s4, s5 -
* ss1, ss2, ss3, ss4, ss5 -
* sz1, sz3, sz11, sz13, sz21, sz23, sz31, sz33 -
* t - time
* tc -
* gsto - greenwich sidereal time rad
* mo - mean anomaly
* mdot - mean anomaly dot (rate)
* no - mean motion
* nodeo - right ascension of ascending node
* nodedot - right ascension of ascending node dot (rate)
* xpidot -
* z1, z3, z11, z13, z21, z23, z31, z33 -
* eccm - eccentricity
* argpm - argument of perigee
* inclm - inclination
* mm - mean anomaly
* xn - mean motion
* nodem - right ascension of ascending node
*
* outputs :
* em - eccentricity
* argpm - argument of perigee
* inclm - inclination
* mm - mean anomaly
* nm - mean motion
* nodem - right ascension of ascending node
* irez - flag for resonance 0-none, 1-one day, 2-half day
* atime -
* d2201, d2211, d3210, d3222, d4410, d4422, d5220, d5232, d5421, d5433 -