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'''
Takes a TLE at a certain time epoch and then computes the state vectors and
hence orbital elements at every time epoch (at every second) for the next 8
hours.
'''
import sys
import os.path
sys.path.append(os.path.abspath(os.path.join(os.path.dirname(__file__), os.path.pardir)))
import numpy as np
import math
from kep_determination.gibbsMethod import *
pi = np.pi
meu = 398600.4418
two_pi = 2*pi;
min_per_day = 1440
ae = 1
tothrd = 2.0/3.0
XJ3 = -2.53881e-6
e6a = 1.0E-6
xkmper = 6378.135
ge = 398600.8 # Earth gravitational constant
CK2 = 1.0826158e-3/2.0
CK4 = -3.0*-1.65597e-6/8.0
class Error(Exception):
'''Base class for the exceptions.'''
pass
class FlagCheckError(Error):
'''Raised when compute_necessary_xxx() function is not called.'''
def __init__(self):
print("Error: Call compute_necessary_kep() or compute_necessary_tle() function of the class SGP4\n\
before calling propagate().\n\n\
Function Declaration:\n\n\
compute_necessary_kep(list, float)\n\
Parameter 1:List of keplerian elements (semi-major axis, inclination, ascension,\n\
eccentricity, perigee, anomaly)\n\
Parameter 2:bstar drag term\n\
Returns: NIL\n\n\
compute_necessary_tle(str, str)\n\
Parameter 1: First line of the TLE\n\
Parameter 2: Second line of the TLE\n\
Returns: NIL\n")
class SGP4(object):
def __init__(self):
'''Initializes flag variable to check for FlagCheckError (custom exception).'''
self.flag = 0
def compute_necessary_kep(self, kep, b_star=0.21109E-4):
'''
Initializes the necessary class variables using keplerian elements which
are needed in the computation of the propagation model.
Args:
kep (list): kep elements in order [axis, inclination, ascension, eccentricity, perigee, anomaly]
b_star (float): bstar drag term
Returns:
NIL
'''
self.flag = 1
self.xincl = float(kep[1]) * (pi/180) # in degree
self.xnodeo = float(kep[2]) * (pi/180)
self.eo = float(kep[3])
self.omegao = float(kep[4]) * (pi/180)
self.xmo = float(kep[5]) * (pi/180)
t = 2*pi*math.sqrt(kep[0]**3/meu)
n = 1/t
n = n*86400 # 86400 seconds in a day
self.xno = n*two_pi/min_per_day
self.bstar = b_star
# print(self.xmo,self.xnodeo,self.omegao,self.xincl,self.eo,self.xno,self.bstar)
def compute_necessary_tle(self, line1, line2):
'''
Initializes the necessary class variables using TLE which are needed in
the computation of the propagation model.
Args:
line1 (str): line 1 of the TLE
line2 (str): line 2 of the TLE
Returns:
NIL
'''
self.flag = 1
self.xmo = float(''.join(line2[43:51])) * (pi/180)
self.xnodeo = float(''.join(line2[17:25])) * (pi/180)
self.omegao = float(''.join(line2[34:42])) * (pi/180)
self.xincl = float(''.join(line2[8:16])) * (pi/180)
self.eo = float('0.'+str(''.join(line2[26:33])))
self.xno = float(''.join(line2[52:63]))*two_pi/min_per_day
self.bstar = int(''.join(line1[53:59]))*(1e-5)*(10**int(''.join(line1[59:61])))
# print(self.xmo,self.xnodeo,self.omegao,self.xincl,self.eo,self.xno,self.bstar)
def propagate(self, t1, t2):
'''
Invokes the function to compute state vectors and organises the final result.
The function first checks if compute_necessary_xxx() is called or not if
not then a custom exception is raised stating that call this function
first. Then it computes the state vector for the next 8 hours (28800
seconds in 8 hours) at every time epoch (28800 time epcohs) using the
sgp4 propagation model. The values of state vector is formatted upto
five decimal points and then all the state vectors got appended in a
list which stores the final output.
Args:
t1 (int): start time epoch
t2 (int): end time epoch
Returns:
numpy.ndarray: vector containing all state vectors
'''
try:
if(self.flag == 0):
raise FlagCheckError
except FlagCheckError:
sys.exit()
i = t1
size = t2-t1+1
final = np.zeros((size,6))
# gibbs = Gibbs()
while(i <= t2):
tsince = i
pos, vel = self.propagation_model(tsince)
data = [pos[0], pos[1], pos[2], vel[0], vel[1], vel[2]]
data = [float("{0:.5f}".format(i)) for i in data]
# ele = gibbs.orbital_elements(pos, vel)
# print(str(tsince) + " - " + str(ele))
# print(str(tsince) + " - " + str(pos) + " " + str(vel))
final[i,:] = data
i = i + 1
# del(gibbs)
return final
def propagation_model(self, tsince):
'''
From the time epoch and information from TLE, applies SGP4 on it.
The function applies the Simplified General Perturbations algorithm
SGP4 on the information extracted from the TLE at the given time epoch
'tsince' and computes the state vector from it.
Args:
tsince (int): time epoch
Returns:
tuple: position and velocity vector
'''
# Constants
s = ae + 78 / xkmper
qo = ae + 120 / xkmper
xke = math.sqrt((3600 * ge)/(xkmper**3))
qoms2t = ((qo-s)**2)**2
temp2 = xke/self.xno
a1 = temp2**tothrd
cosio = math.cos(self.xincl)
theta2 = cosio**2
x3thm1 = 3*theta2-1
eosq = self.eo**2
betao2 = 1-eosq
betao = math.sqrt(betao2)
del1 = (1.5*CK2*x3thm1)/((a1**2)*betao*betao2)
ao = a1*(1-del1*((1.0/3.0)+del1*(1+(134.0/81.0)*del1)))
delo = 1.5*CK2*x3thm1/((ao**2)*betao*betao2)
xnodp = (self.xno)/(1+delo)
aodp = ao/(1-delo)
# Initialization
isimp = 0
if((aodp*(1-self.eo)/ae) < (220.0/xkmper+ae)):
isimp = 1
s4 = s
qoms24 = qoms2t
perigee = (aodp*(1-self.eo)-ae)*xkmper
if(perigee < 156):
s4 = perigee - 78
if(perigee <= 98):
s4 = 20
qoms24 = ((120-s4)*ae/xkmper)**4
s4 = s4/xkmper+ae
pinvsq = 1/((aodp**2)*(betao2**2))
tsi = 1/(aodp-s4)
eta = aodp*(self.eo)*tsi
etasq = eta**2
eeta = (self.eo)*eta
psisq = abs(1-etasq)
coef = qoms24*(tsi**4)
coef1 = coef/(psisq**3.5)
c2 = coef1*xnodp*(aodp*(1+1.5*etasq+eeta*(4+etasq))+0.75*CK2*tsi/psisq*x3thm1*(8+3*etasq*(8+etasq)))
c1 = self.bstar*c2
sinio = math.sin(self.xincl)
a3ovk2 = -XJ3/CK2*(ae**3)
c3 = coef*tsi*a3ovk2*xnodp*ae*sinio/self.eo
x1mth2 = 1-theta2
c4 = 2*xnodp*coef1*aodp*betao2*(eta*(2.0+0.5*etasq)+(self.eo)*(0.5+2*etasq)-2*CK2*tsi/(aodp*psisq)*(-3*x3thm1*(1-2*eeta+etasq*(1.5-0.5*eeta))+0.75*x1mth2*(2*etasq-eeta*(1+etasq))*math.cos(2*self.omegao)))
c5 = 2*coef1*aodp*betao2*(1+2.75*(etasq+eeta)+eeta*etasq)
theta4 = theta2**2
temp1 = 3*CK2*pinvsq*xnodp
temp2 = temp1*CK2*pinvsq
temp3 = 1.25*CK4*(pinvsq**2)*xnodp
xmdot = xnodp+0.5*temp1*betao*x3thm1+0.0625*temp2*betao*(13-78*theta2+137*theta4)
x1m5th = 1-5*theta2
omgdot = -0.5*temp1*x1m5th+0.0625*temp2*(7-114*theta2+395*theta4)+temp3*(3-36*theta2+49*theta4)
xhdot1 = -temp1*cosio
xnodot = xhdot1+(0.5*temp2*(4-19*theta2)+2*temp3*(3-7*theta2))*cosio
omgcof = self.bstar*c3*math.cos(self.omegao)
xmcof = -(2/3)*coef*(self.bstar)*ae/eeta
xnodcf = 3.5*betao2*xhdot1*c1
t2cof = 1.5*c1
xlcof = 0.125*a3ovk2*sinio*(3+5*cosio)/(1+cosio)
aycof = 0.25*a3ovk2*sinio
delmo = (1+eta*math.cos(self.xmo))**3
sinmo = math.sin(self.xmo)
x7thm1 = 7*theta2-1
if(isimp == 0):
c1sq = c1**2
d2 = 4*aodp*tsi*c1sq
temp = d2*tsi*c1/3
d3 = (17*aodp+s4)*temp
d4 = 0.5*temp*aodp*tsi*(221*aodp+31*4)*c1
t3cof = d2+2*c1sq
t4cof = 0.25*(3*d3+c1*(12*d2+10*c1sq))
t5cof = 0.2*(3*d4+12*c1*d3+6*(d2**2)+15*c1sq*(2*d2+c1sq))
xmdf = self.xmo+xmdot*tsince
omgadf = self.omegao+omgdot*tsince
xnoddf = self.xnodeo+xnodot*tsince
omega = omgadf
xmp = xmdf
tsq = tsince**2
xnode = xnoddf+xnodcf*tsq
tempa = 1 - c1*tsince
tempe = self.bstar*c4*tsince
templ = t2cof*tsq
if(isimp == 0):
delomg = omgcof*tsince
delm = xmcof*(((1+eta*math.cos(xmdf))**3)-delmo)
temp = delomg+delm
xmp = xmdf+temp
omega = omgadf-temp
tcube = tsq*tsince
tfour = tsince*tcube
tempa = tempa-d2*tsq-d3*tcube-d4*tfour
tempe = tempe+self.bstar*c5*(math.sin(xmp)-sinmo)
templ = templ+t3cof*tcube+tfour*(t4cof+tsince*t5cof)
a = aodp*(tempa**2)
e = self.eo-tempe
xl = xmp+omega+xnode+xnodp*templ
beta = math.sqrt(1-e**2)
xn = xke/(a**1.5)
axn = e*math.cos(omega)
temp = 1/(a*(beta**2))
xll = temp*xlcof*axn
aynl = temp*aycof
xlt = xl+xll
ayn = e*math.sin(omega)+aynl
diff = xlt - xnode
capu = diff - math.floor(diff/two_pi) * two_pi
if(capu < 0):
capu = capu + two_pi
temp2 = capu
i = 1
while(1):
sinepw = math.sin(temp2)
cosepw = math.cos(temp2)
temp3 = axn*sinepw
temp4 = ayn*cosepw
temp5 = axn*cosepw
temp6 = ayn*sinepw
epw = (capu-temp4+temp3-temp2)/(1-temp5-temp6)+temp2
temp7 = temp2
temp2 = epw
i = i + 1
if((i>10) | (abs(epw-temp7)<=e6a)):
break
ecose = temp5+temp6
esine = temp3-temp4
elsq = axn**2 + ayn**2
temp = 1-elsq
pl = a*temp
r = a*(1-ecose)
temp1 = 1/r
rdot = xke*math.sqrt(a)*esine*temp1
rfdot = xke*math.sqrt(pl)*temp1
temp2 = a*temp1
betal = math.sqrt(temp)
temp3 = 1/(1+betal)
cosu = temp2*(cosepw-axn+ayn*esine*temp3)
sinu = temp2*(sinepw-ayn-axn*esine*temp3)
u = math.atan2(sinu, cosu)
if(u < 0):
u = u + two_pi
sin2u = 2*sinu*cosu
cos2u = 2*(cosu**2)-1
temp = 1/pl
temp1 = CK2*temp
temp2 = temp1*temp
rk = r*(1-1.5*temp2*betal*x3thm1)+0.5*temp1*x1mth2*cos2u
uk = u-0.25*temp2*x7thm1*sin2u
xnodek = xnode+1.5*temp2*cosio*sin2u
xinck = self.xincl+1.5*temp2*cosio*sinio*cos2u
rdotk = rdot-xn*temp1*x1mth2*sin2u
rfdotk = rfdot+xn*temp1*(x1mth2*cos2u+1.5*x3thm1)
MV = [-math.sin(xnodek)*math.cos(xinck), math.cos(xnodek)*math.cos(xinck), math.sin(xinck)]
NV = [math.cos(xnodek), math.sin(xnodek), 0]
UV = [0, 0, 0]
VV = [0, 0, 0]
for i in range(3):
UV[i] = MV[i]*math.sin(uk) + NV[i]*math.cos(uk)
VV[i] = MV[i]*math.cos(uk) - NV[i]*math.sin(uk)
pos = [0, 0, 0]
vel = [0, 0, 0]
for i in range(3):
pos[i] = rk*UV[i]*xkmper
vel[i] = (rdotk*UV[i] + rfdotk*VV[i])*xkmper/60
return pos, vel
@classmethod
def recover_tle(self, pos, vel):
"""
Recovers TLE back from state vector.
First of all, only necessary information (which are inclination, right
ascension of the ascending node, eccentricity, argument of perigee, mean
anomaly, mean motion and bstar) that are needed in the computation of
SGP4 propagation model are recovered. It is using a general format of
TLE. State vectors are used to find orbital elements which are then
inserted into the TLE format at their respective positions. Mean motion
and bstar is calculated separately as it is not a part of orbital elements.
Format of TLE: x denotes that there is a digit, c denotes a character value,
underscore(_) denotes a plus/minus(+/-) sign value and period(.) denotes
a decimal point.
Args:
pos (list): position vector
vel (list): velocity vector
Returns:
list: line1 and line2 of TLE
"""
# TLE format
line1 = "1 xxxxxc xxxxxccc xxxxx.xxxxxxxx _.xxxxxxxx _xxxxx_x _xxxxx_x x xxxxx"
line2 = "2 xxxxx xxx.xxxx xxx.xxxx xxxxxxx xxx.xxxx xxx.xxxx xx.xxxxxxxxxxxxxx"
# line 1
# line1 = list(line1)
# line1 = "".join(line1)
# line 2
line2 = list(line2)
gibbs = Gibbs()
ele = gibbs.orbital_elements(pos, vel)
del(gibbs)
# inclination
inc = float("{0:.4f}".format(ele[1]))
if(inc < 10.0):
inc = str(" ") + str(inc)
elif(inc < 100.0):
inc = str(" ") + str(inc)
line2[8:16] = str(inc)
# right ascension of ascending node
asc = float("{0:.4f}".format(ele[2]))
if(asc < 10.0):
asc = str(" ") + str(asc)
elif(asc < 100.0):
asc = str(" ") + str(asc)
line2[17:25] = str(asc)
# eccentricity
e = list("{0:.7f}".format(ele[3]))
e = str("".join(e[2:]))
line2[26:33] = e
# argument of perigee
per = float("{0:.4f}".format(ele[4]))
if(per < 10.0):
per = str(" ") + str(per)
elif(per < 100.0):
per = str(" ") + str(per)
line2[34:42] = str(per)
# mean anomaly
anom = float("{0:.4f}".format(ele[5]))
if(anom < 10.0):
anom = str(" ") + str(anom)
elif(anom < 100.0):
anom = str(" ") + str(anom)
line2[43:51] = str(anom)
# mean motion (revolution per day)
t = 2*pi*math.sqrt(ele[0]**3/meu)
n = 1/t
n = n*86400 # 86400 seconds in a day
n = float("{0:.8f}".format(n))
if(n < 10.0):
n = str(" ") + str(n)
line2[52:63] = str(n)
line2 = "".join(line2)
tle = [line1, line2]
return tle
# if __name__ == "__main__":
# line1 = "1 88888U 80275.98708465 .00073094 13844-3 66816-4 0 8"
# line2 = "2 88888 72.8435 115.9689 0086731 52.6988 110.5714 16.05824518 105"
#
# # using compute_necessary_tle()
# obj = SGP4()
# obj.compute_necessary_tle(line1,line2)
# state_vec = obj.propagate(0, 28800)
#
# # using compute_necessary_kep()
# ele = [6641.785974865588, 72.8538850731544, 115.96228572568285, \
# 0.009668565050958889, 59.42251148052069, 104.89188402366825]
# obj.compute_necessary_kep(ele)
# state_vec = obj.propagate(0, 28800)
#
# # Recover TLE from state vector
# pos = [state_vec[0][0], state_vec[0][1], state_vec[0][2]]
# vel = [state_vec[0][3], state_vec[0][4], state_vec[0][5]]
# tle = obj.recover_tle(pos, vel)
#
# del(obj)
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