def __calc_equatorialCoordinates(self):
''' calculates position in equatorial coords from ecliptic '''
import math
Jcty = self._TSMgr.time_get_julianCenturiesJ2000()
Lam_deg = self._moonCoordinates["ecl_Lon"] # Lambda
Bet_deg = self._moonCoordinates["ecl_Lat"] # Beta
Eps_deg = MH.eps_deg(Jcty) # Epsilon
sinLam = MH.sin_deg(Lam_deg)
cosLam = MH.cos_deg(Lam_deg)
sinBet = MH.sin_deg(Bet_deg)
cosBet = MH.cos_deg(Bet_deg)
sinEps = MH.sin_deg(Eps_deg)
cosEps = MH.cos_deg(Eps_deg)
# [o. Montenbruck] "Grundlagen der Ephemeridenrechnung" S.14
# cos(del)*cos(alp) = cos(bet)*cos(lam)
# cos(del)*sin(alp) = cos(eps)*cos(bet)*sin(lam) - sin(eps)*sin(bet)
# sin(del) = sin(eps)*cos(bet)*sin(lam) + cos(eps)*sin(bet)
Del_rad = math.asin( sinEps*cosBet*sinLam + cosEps*sinBet )
Del_deg = math.degrees(Del_rad)
cosDel = math.cos(Del_rad)
cosAlp = (cosBet*cosLam) / cosDel
sinAlp = (cosEps*cosBet*sinLam - sinEps*sinBet) / cosDel
Alp_deg = MH.atan2_deg(sinAlp,cosAlp)%360
self._moonCoordinates["equa_Lon"] = Alp_deg # Alpha / RA
self._moonCoordinates["equa_Lat"] = Del_deg # Delta / DE
def _calc_ECI(self):
''' calc position in ECI reference from time:LMST and pos:LLA'''
self._df_clear("time") # clear dirty flags
self._df_clear("pos")
a = wgs72_complete["radiusearthkm"]
e2 = wgs72_complete["e^2"]
phi = self._geo_lat
lambd = self.sidereal_get_LMST()
h = self._geo_alti / 1000 # m to km
sin_phi = math_helper.sin_deg(phi)
cos_phi = math_helper.cos_deg(phi)
sin_lambd = math_helper.sin_deg(lambd)
cos_lambd = math_helper.cos_deg(lambd)
# [Günter Seeber, "Satellite Geodesy", 2nd edition] page 24
# N is the radius of curvature in the prime vertical:
# N = a / sqrt( 1 - (e^2)*(sin(lat)^2) )
# EQUATION (2.36)
N = a / math.sqrt(1 - e2 * (sin_phi**2))
# EQUATION (2.35)
self._eci_x = (N + h) * cos_phi * cos_lambd
self._eci_y = (N + h) * cos_phi * sin_lambd
self._eci_z = ((1 - e2) * N + h) * sin_phi
def calcMoonCoords_1stSolution(self):
# self.__meanArgs_checkDF()
self.calcMoonMeanArgumentsFromDate()
L0 = self._moonMeanArguments['L0']
l = self._moonMeanArguments['l']
l_ = self._moonMeanArguments['l_']
F = self._moonMeanArguments['F']
D = self._moonMeanArguments['D']
# print('L0 ',L0)
# print('l ',l)
# print('l_ ',l_)
# print('F ',F)
# print('D ',D)
term = [None]*13
term[0] = (
22640 * MH.sin_deg(l) +
769 * MH.sin_deg(2*l) +
36 * MH.sin_deg(3*l) ) #grosse ungleicheit
term[1] = -4586 * MH.sin_deg(l-2*D) #evektion
term[2] = 2370 * MH.sin_deg(2*D) #variation
term[3] = -668 * MH.sin_deg(l_) #jaehrliche ungleichheit
term[4] = -412 * MH.sin_deg(2*F) #differenz in bahnlaenge und ekliptikaler laenge
term[5] = -212 * MH.sin_deg(2*l-2*D)
term[6] = -206 * MH.sin_deg(l+l_-2*D)
term[7] = 192 * MH.sin_deg(l+2*D)
term[8] = -165 * MH.sin_deg(l_-2*D)
term[9] = 148 * MH.sin_deg(l-l_)
term[10] = -125 * MH.sin_deg(D) #paralaktiche gleichung
term[11] = -110 * MH.sin_deg(l+l_)
term[12] = -55 * MH.sin_deg(2*F-2*D)
ecl_Laenge = L0 + sum(term)/3600
self._moonCoordinates["ecl_Lon"] = ecl_Laenge %360
# Reset des "term" Arrays
term = [None]*8
term[0] = 18520* MH.sin_deg( F + ecl_Laenge - L0 +
0.114*MH.sin_deg(2*F) +0.15*MH.sin_deg(l_) )
term[1] = -526 * MH.sin_deg( F - 2*D )
term[2] = 44 * MH.sin_deg( l + F - 2*D )
term[3] = -31 * MH.sin_deg( -l + F - 2*D )
term[4] = -25 * MH.sin_deg( -2*l + F )
term[5] = -23 * MH.sin_deg( l_ + F - 2*D )
term[6] = 21 * MH.sin_deg( -l + F )
term[7] = 11 * MH.sin_deg( -l_ + F - 2*D )
self._moonCoordinates["ecl_Lat"] = sum(term)/3600
# ergebnis ist im ekliptischen koordsys
# wird benötigt im äquatorialen koordsys
self.__calc_equatorialCoordinates()