/usr/lib/python2.7/dist-packages/sgp4/ext.py is in python-sgp4 1.4-1.
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"""Utility routines from "sgp4ext.cpp"."""
from math import (acos, asinh, atan2, copysign, cos, fabs, fmod,
pi, sin, sinh, sqrt, tan)
undefined = None
"""
/* -----------------------------------------------------------------------------
*
* function mag
*
* this procedure finds the magnitude of a vector. the tolerance is set to
* 0.000001, thus the 1.0e-12 for the squared test of underflows.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec - vector
*
* outputs :
* vec - answer stored in fourth component
*
* locals :
* none.
*
* coupling :
* none.
* --------------------------------------------------------------------------- */
"""
def mag(x):
return sqrt(x[0]*x[0] + x[1]*x[1] + x[2]*x[2]);
"""
/* -----------------------------------------------------------------------------
*
* procedure cross
*
* this procedure crosses two vectors.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec1 - vector number 1
* vec2 - vector number 2
*
* outputs :
* outvec - vector result of a x b
*
* locals :
* none.
*
* coupling :
* mag magnitude of a vector
---------------------------------------------------------------------------- */
"""
def cross(vec1, vec2, outvec):
outvec[0]= vec1[1]*vec2[2] - vec1[2]*vec2[1];
outvec[1]= vec1[2]*vec2[0] - vec1[0]*vec2[2];
outvec[2]= vec1[0]*vec2[1] - vec1[1]*vec2[0];
"""
/* -----------------------------------------------------------------------------
*
* function dot
*
* this function finds the dot product of two vectors.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec1 - vector number 1
* vec2 - vector number 2
*
* outputs :
* dot - result
*
* locals :
* none.
*
* coupling :
* none.
*
* --------------------------------------------------------------------------- */
"""
def dot(x, y):
return (x[0]*y[0] + x[1]*y[1] + x[2]*y[2]);
"""
/* -----------------------------------------------------------------------------
*
* procedure angle
*
* this procedure calculates the angle between two vectors. the output is
* set to 999999.1 to indicate an undefined value. be sure to check for
* this at the output phase.
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* vec1 - vector number 1
* vec2 - vector number 2
*
* outputs :
* theta - angle between the two vectors -pi to pi
*
* locals :
* temp - temporary real variable
*
* coupling :
* dot dot product of two vectors
* --------------------------------------------------------------------------- */
"""
def angle(vec1, vec2):
small = 0.00000001;
undefined = 999999.1;
magv1 = mag(vec1);
magv2 = mag(vec2);
if magv1*magv2 > small*small:
temp= dot(vec1,vec2) / (magv1*magv2);
if fabs(temp) > 1.0:
temp = copysign(1.0, temp)
return acos( temp );
else:
return undefined;
"""
/* -----------------------------------------------------------------------------
*
* function newtonnu
*
* this function solves keplers equation when the true anomaly is known.
* the mean and eccentric, parabolic, or hyperbolic anomaly is also found.
* the parabolic limit at 168° is arbitrary. the hyperbolic anomaly is also
* limited. the hyperbolic sine is used because it's not double valued.
*
* author : david vallado 719-573-2600 27 may 2002
*
* revisions
* vallado - fix small 24 sep 2002
*
* inputs description range / units
* ecc - eccentricity 0.0 to
* nu - true anomaly -2pi to 2pi rad
*
* outputs :
* e0 - eccentric anomaly 0.0 to 2pi rad 153.02 °
* m - mean anomaly 0.0 to 2pi rad 151.7425 °
*
* locals :
* e1 - eccentric anomaly, next value rad
* sine - sine of e
* cose - cosine of e
* ktr - index
*
* coupling :
* asinh - arc hyperbolic sine
*
* references :
* vallado 2007, 85, alg 5
* --------------------------------------------------------------------------- */
"""
def newtonnu(ecc, nu):
# --------------------- implementation ---------------------
e0= 999999.9;
m = 999999.9;
small = 0.00000001;
# --------------------------- circular ------------------------
if fabs(ecc) < small:
m = nu;
e0= nu;
else:
# ---------------------- elliptical -----------------------
if ecc < 1.0-small:
sine= ( sqrt( 1.0 -ecc*ecc ) * sin(nu) ) / ( 1.0 +ecc*cos(nu) );
cose= ( ecc + cos(nu) ) / ( 1.0 + ecc*cos(nu) );
e0 = atan2( sine,cose );
m = e0 - ecc*sin(e0);
else:
# -------------------- hyperbolic --------------------
if ecc > 1.0 + small:
if ecc > 1.0 and fabs(nu)+0.00001 < pi-acos(1.0 /ecc):
sine= ( sqrt( ecc*ecc-1.0 ) * sin(nu) ) / ( 1.0 + ecc*cos(nu) );
e0 = asinh( sine );
m = ecc*sinh(e0) - e0;
else:
# ----------------- parabolic ---------------------
if fabs(nu) < 168.0*pi/180.0:
e0= tan( nu*0.5 );
m = e0 + (e0*e0*e0)/3.0;
if ecc < 1.0:
m = fmod( m,2.0 *pi );
if m < 0.0:
m = m + 2.0 *pi;
e0 = fmod( e0,2.0 *pi );
return e0, m
"""
/* -----------------------------------------------------------------------------
*
* function rv2coe
*
* this function finds the classical orbital elements given the geocentric
* equatorial position and velocity vectors.
*
* author : david vallado 719-573-2600 21 jun 2002
*
* revisions
* vallado - fix special cases 5 sep 2002
* vallado - delete extra check in inclination code 16 oct 2002
* vallado - add constant file use 29 jun 2003
* vallado - add mu 2 apr 2007
*
* inputs description range / units
* r - ijk position vector km
* v - ijk velocity vector km / s
* mu - gravitational parameter km3 / s2
*
* outputs :
* p - semilatus rectum km
* a - semimajor axis km
* ecc - eccentricity
* incl - inclination 0.0 to pi rad
* omega - longitude of ascending node 0.0 to 2pi rad
* argp - argument of perigee 0.0 to 2pi rad
* nu - true anomaly 0.0 to 2pi rad
* m - mean anomaly 0.0 to 2pi rad
* arglat - argument of latitude (ci) 0.0 to 2pi rad
* truelon - true longitude (ce) 0.0 to 2pi rad
* lonper - longitude of periapsis (ee) 0.0 to 2pi rad
*
* locals :
* hbar - angular momentum h vector km2 / s
* ebar - eccentricity e vector
* nbar - line of nodes n vector
* c1 - v**2 - u/r
* rdotv - r dot v
* hk - hk unit vector
* sme - specfic mechanical energy km2 / s2
* i - index
* e - eccentric, parabolic,
* hyperbolic anomaly rad
* temp - temporary variable
* typeorbit - type of orbit ee, ei, ce, ci
*
* coupling :
* mag - magnitude of a vector
* cross - cross product of two vectors
* angle - find the angle between two vectors
* newtonnu - find the mean anomaly
*
* references :
* vallado 2007, 126, alg 9, ex 2-5
* --------------------------------------------------------------------------- */
"""
def rv2coe(r, v, mu):
hbar = [None, None, None]
nbar = [None, None, None]
ebar = [None, None, None]
typeorbit = [None, None, None];
twopi = 2.0 * pi;
halfpi = 0.5 * pi;
small = 0.00000001;
undefined = 999999.1;
infinite = 999999.9;
# ------------------------- implementation -----------------
magr = mag( r );
magv = mag( v );
# ------------------ find h n and e vectors ----------------
cross( r,v, hbar );
magh = mag( hbar );
if magh > small:
nbar[0]= -hbar[1];
nbar[1]= hbar[0];
nbar[2]= 0.0;
magn = mag( nbar );
c1 = magv*magv - mu /magr;
rdotv = dot( r,v );
for i in range(0, 3):
ebar[i]= (c1*r[i] - rdotv*v[i])/mu;
ecc = mag( ebar );
# ------------ find a e and semi-latus rectum ----------
sme= ( magv*magv*0.5 ) - ( mu /magr );
if fabs( sme ) > small:
a= -mu / (2.0 *sme);
else:
a= infinite;
p = magh*magh/mu;
# ----------------- find inclination -------------------
hk= hbar[2]/magh;
incl= acos( hk );
# -------- determine type of orbit for later use --------
# ------ elliptical, parabolic, hyperbolic inclined -------
typeorbit = 'ei'
if ecc < small:
# ---------------- circular equatorial ---------------
if incl < small or fabs(incl-pi) < small:
typeorbit = 'ce'
else:
# -------------- circular inclined ---------------
typeorbit = 'ci'
else:
# - elliptical, parabolic, hyperbolic equatorial --
if incl < small or fabs(incl-pi) < small:
typeorbit = 'ee'
# ---------- find longitude of ascending node ------------
if magn > small:
temp= nbar[0] / magn;
if fabs(temp) > 1.0:
temp = copysign(1.0, temp)
omega= acos( temp );
if nbar[1] < 0.0:
omega= twopi - omega;
else:
omega= undefined;
# ---------------- find argument of perigee ---------------
if typeorbit == 'ei':
argp = angle( nbar,ebar);
if ebar[2] < 0.0:
argp= twopi - argp;
else:
argp= undefined;
# ------------ find true anomaly at epoch -------------
if typeorbit[0] == 'e':
nu = angle( ebar,r);
if rdotv < 0.0:
nu= twopi - nu;
else:
nu= undefined;
# ---- find argument of latitude - circular inclined -----
if typeorbit == 'ci':
arglat = angle( nbar,r );
if r[2] < 0.0:
arglat= twopi - arglat;
m = arglat;
else:
arglat= undefined;
# -- find longitude of perigee - elliptical equatorial ----
if ecc > small and typeorbit == 'ee':
temp= ebar[0]/ecc;
if fabs(temp) > 1.0:
temp = copysign(1.0, temp)
lonper= acos( temp );
if ebar[1] < 0.0:
lonper= twopi - lonper;
if incl > halfpi:
lonper= twopi - lonper;
else:
lonper= undefined;
# -------- find true longitude - circular equatorial ------
if magr > small and typeorbit == 'ce':
temp= r[0]/magr;
if fabs(temp) > 1.0:
temp = copysign(1.0, temp)
truelon= acos( temp );
if r[1] < 0.0:
truelon= twopi - truelon;
if incl > halfpi:
truelon= twopi - truelon;
m = truelon;
else:
truelon= undefined;
# ------------ find mean anomaly for all orbits -----------
if typeorbit[0] == 'e':
e, m = newtonnu(ecc, nu);
else:
p = undefined;
a = undefined;
ecc = undefined;
incl = undefined;
omega= undefined;
argp = undefined;
nu = undefined;
m = undefined;
arglat = undefined;
truelon= undefined;
lonper = undefined;
return p, a, ecc, incl, omega, argp, nu, m, arglat, truelon, lonper
"""
/* -----------------------------------------------------------------------------
*
* procedure jday
*
* this procedure finds the julian date given the year, month, day, and time.
* the julian date is defined by each elapsed day since noon, jan 1, 4713 bc.
*
* algorithm : calculate the answer in one step for efficiency
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* year - year 1900 .. 2100
* mon - month 1 .. 12
* day - day 1 .. 28,29,30,31
* hr - universal time hour 0 .. 23
* min - universal time min 0 .. 59
* sec - universal time sec 0.0 .. 59.999
*
* outputs :
* jd - julian date days from 4713 bc
*
* locals :
* none.
*
* coupling :
* none.
*
* references :
* vallado 2007, 189, alg 14, ex 3-14
*
* --------------------------------------------------------------------------- */
"""
def jday(year, mon, day, hr, minute, sec):
return (367.0 * year -
7.0 * (year + ((mon + 9.0) // 12.0)) * 0.25 // 1.0 +
275.0 * mon // 9.0 +
day + 1721013.5 +
((sec / 60.0 + minute) / 60.0 + hr) / 24.0 # ut in days
# - 0.5*sgn(100.0*year + mon - 190002.5) + 0.5;
)
"""
/* -----------------------------------------------------------------------------
*
* procedure days2mdhms
*
* this procedure converts the day of the year, days, to the equivalent month
* day, hour, minute and second.
*
* algorithm : set up array for the number of days per month
* find leap year - use 1900 because 2000 is a leap year
* loop through a temp value while the value is < the days
* perform int conversions to the correct day and month
* convert remainder into h m s using type conversions
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* year - year 1900 .. 2100
* days - julian day of the year 0.0 .. 366.0
*
* outputs :
* mon - month 1 .. 12
* day - day 1 .. 28,29,30,31
* hr - hour 0 .. 23
* min - minute 0 .. 59
* sec - second 0.0 .. 59.999
*
* locals :
* dayofyr - day of year
* temp - temporary extended values
* inttemp - temporary int value
* i - index
* lmonth[12] - int array containing the number of days per month
*
* coupling :
* none.
* --------------------------------------------------------------------------- */
"""
def days2mdhms(year, days):
lmonth = (31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31);
dayofyr = int(days // 1.0);
# ----------------- find month and day of month ----------------
if (year % 4) == 0:
lmonth = (31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31);
i = 1;
inttemp = 0;
while dayofyr > inttemp + lmonth[i-1] and i < 12:
inttemp = inttemp + lmonth[i-1];
i += 1;
mon = i;
day = dayofyr - inttemp;
# ----------------- find hours minutes and seconds -------------
temp = (days - dayofyr) * 24.0;
hr = int(temp // 1.0);
temp = (temp - hr) * 60.0;
minute = int(temp // 1.0);
sec = (temp - minute) * 60.0;
return mon, day, hr, minute, sec
"""
/* -----------------------------------------------------------------------------
*
* procedure invjday
*
* this procedure finds the year, month, day, hour, minute and second
* given the julian date. tu can be ut1, tdt, tdb, etc.
*
* algorithm : set up starting values
* find leap year - use 1900 because 2000 is a leap year
* find the elapsed days through the year in a loop
* call routine to find each individual value
*
* author : david vallado 719-573-2600 1 mar 2001
*
* inputs description range / units
* jd - julian date days from 4713 bc
*
* outputs :
* year - year 1900 .. 2100
* mon - month 1 .. 12
* day - day 1 .. 28,29,30,31
* hr - hour 0 .. 23
* min - minute 0 .. 59
* sec - second 0.0 .. 59.999
*
* locals :
* days - day of year plus fractional
* portion of a day days
* tu - julian centuries from 0 h
* jan 0, 1900
* temp - temporary double values
* leapyrs - number of leap years from 1900
*
* coupling :
* days2mdhms - finds month, day, hour, minute and second given days and year
*
* references :
* vallado 2007, 208, alg 22, ex 3-13
* --------------------------------------------------------------------------- */
"""
def invjday(jd):
# --------------- find year and days of the year ---------------
temp = jd - 2415019.5;
tu = temp / 365.25;
year = 1900 + int(tu // 1.0);
leapyrs = int(((year - 1901) * 0.25) // 1.0);
# optional nudge by 8.64x10-7 sec to get even outputs
days = temp - ((year - 1900) * 365.0 + leapyrs) + 0.00000000001;
# ------------ check for case of beginning of a year -----------
if (days < 1.0):
year = year - 1;
leapyrs = int(((year - 1901) * 0.25) // 1.0);
days = temp - ((year - 1900) * 365.0 + leapyrs);
# ----------------- find remaing data -------------------------
mon, day, hr, minute, sec = days2mdhms(year, days);
sec = sec - 0.00000086400;
return year, mon, day, hr, minute, sec
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