def getRhoHat(rah, ram, ras, dech, decm, decs):
raRad = odlib.degreesToRadians(odlib.HMStoDeg(rah, ram, ras))
decRad = odlib.degreesToRadians(odlib.DMStoDeg(dech, decm, decs))
rhox = cos(raRad) * cos(decRad)
rhoy = sin(raRad) * cos(decRad)
rhoz = sin(decRad)
return [rhox, rhoy, rhoz]
def getRhoHat(rah, ram, ras=0, dech=0, decm=0, decs=0):
# First two elements will be RA (hr) and DEC (deg) if radecAsDecimal
if radecAsDecimal:
raRad = odlib.degreesToRadians(rah * 15)
decRad = odlib.degreesToRadians(ram)
else:
raRad = odlib.degreesToRadians(odlib.HMStoDeg(rah, ram, ras))
decRad = odlib.degreesToRadians(odlib.DMStoDeg(dech, decm, decs))
rhox = cos(raRad) * cos(decRad)
rhoy = sin(raRad) * cos(decRad)
rhoz = sin(decRad)
return np.array([rhox, rhoy, rhoz])
import odlib
import numpy as np
from math import sin, cos, sqrt, pi, asin
a = 3.333373705525415
e = 0.6300217569592357
i = odlib.degreesToRadians(12.607673026103942)
omega = odlib.degreesToRadians(232.6027678824531)
w = odlib.degreesToRadians(50.817782977450406)
M2 = odlib.degreesToRadians(1.6803544595919)
t2 = 2458671.6550316783
# Change these for different dates
t = 2458671.6550316783
eclipticObliquity = 23.4367540863
R = np.array(
[-2.547806549329457E-01, 9.031163132855038E-01, 3.914640974482125E-01])
# Finds the value of E in the equation M = E + e * sin(E)
# Uses Newton's method
def newtonFindE(e, realM):
# An initial guess
E = realM
# 100 was chosen arbitrarily, but it works
for i in range(100):
M = E - e * sin(E)
derivM = 1 - e * cos(E)
E = E - (M - realM) / derivM
return E
def od(t1, t2, t3, ra1, dec1, ra2, dec2, ra3, dec3, R):
tau3 = odlib.timeToGaussian(t3, t2)
tau1 = odlib.timeToGaussian(t1, t2)
tau0 = tau3 - tau1
realR2Dot = (realR3 - realR1) / tau0
if radecAsDecimal:
rhoHat1 = getRhoHat(ra1, dec1)
rhoHat2 = getRhoHat(ra2, dec2)
rhoHat3 = getRhoHat(ra3, dec3)
else:
rhoHat1 = getRhoHat(*ra1, *dec1)
rhoHat2 = getRhoHat(*ra2, *dec2)
rhoHat3 = getRhoHat(*ra3, *dec3)
a = [tau3 / tau0, -1, -tau1 / tau0]
rhoHats = np.array([rhoHat1, rhoHat2, rhoHat3])
rho = rhoHats.copy()
D0 = odlib.tri_product(rhoHat1, rhoHat2, rhoHat3)
assert (D0 != 0)
D1 = odlib.tri_product(rhoHat3, R[0], rhoHat2)
D2 = odlib.tri_product(rhoHat3, R[1], rhoHat2)
D3 = odlib.tri_product(rhoHat3, R[2], rhoHat2)
rho[0] *= (a[0] * D1 + a[1] * D2 + a[2] * D3) / (a[0] * D0)
D1 = odlib.tri_product(rhoHat3, rhoHat1, R[0])
D2 = odlib.tri_product(rhoHat3, rhoHat1, R[1])
D3 = odlib.tri_product(rhoHat3, rhoHat1, R[2])
rho[1] *= (a[0] * D1 + a[1] * D2 + a[2] * D3) / (a[1] * D0)
D1 = odlib.tri_product(rhoHat1, rhoHat2, R[0])
D2 = odlib.tri_product(rhoHat1, rhoHat2, R[1])
D3 = odlib.tri_product(rhoHat1, rhoHat2, R[2])
rho[2] *= (a[0] * D1 + a[1] * D2 + a[2] * D3) / (a[2] * D0)
r = rho - R
r2Dot = (r[2] - r[0]) / tau0
tauAt1 = odlib.timeToGaussian(t1)
tauAt2 = odlib.timeToGaussian(t2)
tauAt3 = odlib.timeToGaussian(t3)
def f(tau, tau2, r2, r2Dot):
res = 1 - (tau - tau2)**2 / (2 * odlib.mag(r2)**3)
res += odlib.dot(r2, r2Dot) / (2 * odlib.mag(r2)**5) * (tau - tau2)**3
O4 = 3 * (odlib.dot(r2Dot, r2Dot) / odlib.mag(r2)**2 -
1 / odlib.mag(r2)**3)
O4 += -15 * (odlib.dot(r2, r2Dot) /
odlib.mag(r2)**2)**2 + 1 / odlib.mag(r2)**3
O4 *= ((tau - tau2)**4 / (24 * odlib.mag(r2)**3))
return res + O4
def g(tau, tau2, r2, r2Dot):
res = tau - tau2 - (tau - tau2)**3 / (6 * odlib.mag(r2)**3)
res += (odlib.dot(r2, r2Dot) *
(tau - tau2)**4) / (4 * odlib.mag(r2)**5)
return res
tiny = 1E-9
maxIterations = 200
iteration = 0
# Minus 100 so the loop doesn't exit immediately
r2Old = r[1] - 100
r2DotOld = r2Dot
while (np.any(abs(r[1] - r2Old) > tiny) or
np.any(abs(r2Dot - r2DotOld) > tiny)) and iteration < maxIterations:
r2Old = r[1].copy()
r2DotOld = r2Dot.copy()
if useLightspeedCorrection:
# Lightspeed correction
correctedT1 = t1 - odlib.mag(rho[0]) / c
correctedT2 = t2 - odlib.mag(rho[1]) / c
correctedT3 = t3 - odlib.mag(rho[2]) / c
tauAt1 = odlib.timeToGaussian(correctedT1)
tauAt2 = odlib.timeToGaussian(correctedT2)
tauAt3 = odlib.timeToGaussian(correctedT3)
rho = rhoHats.copy()
D0 = odlib.tri_product(rhoHat1, rhoHat2, rhoHat3)
assert (D0 != 0)
D1 = odlib.tri_product(rhoHat3, R[0], rhoHat2)
D2 = odlib.tri_product(rhoHat3, R[1], rhoHat2)
D3 = odlib.tri_product(rhoHat3, R[2], rhoHat2)
rho[0] *= (a[0] * D1 + a[1] * D2 + a[2] * D3) / (a[0] * D0)
D1 = odlib.tri_product(rhoHat3, rhoHat1, R[0])
D2 = odlib.tri_product(rhoHat3, rhoHat1, R[1])
D3 = odlib.tri_product(rhoHat3, rhoHat1, R[2])
rho[1] *= (a[0] * D1 + a[1] * D2 + a[2] * D3) / (a[1] * D0)
D1 = odlib.tri_product(rhoHat1, rhoHat2, R[0])
D2 = odlib.tri_product(rhoHat1, rhoHat2, R[1])
D3 = odlib.tri_product(rhoHat1, rhoHat2, R[2])
rho[2] *= (a[0] * D1 + a[1] * D2 + a[2] * D3) / (a[2] * D0)
r = rho - R
f1 = f(tauAt1, tauAt2, r[1], r2Dot)
f3 = f(tauAt3, tauAt2, r[1], r2Dot)
g1 = g(tauAt1, tauAt2, r[1], r2Dot)
g3 = g(tauAt3, tauAt2, r[1], r2Dot)
a[0] = g3 / (f1 * g3 - f3 * g1)
a[2] = g1 / (f3 * g1 - f1 * g3)
r[1] = a[0] * r[0] + a[2] * r[2]
r2Dot = f3 / (g1 * f3 - g3 * f1) * r[0] + f1 / (g3 * f1 -
g1 * f3) * r[2]
iteration += 1
assert (iteration < maxIterations)
# print(r)
r[1] = odlib.rotateVector(r[1], 0,
odlib.degreesToRadians(eclipticObliquity), 0)
r2Dot = odlib.rotateVector(r2Dot, 0,
odlib.degreesToRadians(eclipticObliquity), 0)
elements = orbitalElements(r[1], r2Dot)
elements[2] = odlib.radiansToDegrees(elements[2])
elements[3] = odlib.radiansToDegrees(elements[3])
elements[4] = odlib.radiansToDegrees(elements[4])
elements[5] = odlib.radiansToDegrees(elements[5])
while elements[4] < 0:
elements[4] += 360
while elements[4] > 360:
elements[4] -= 360
return elements
D1 = odlib.tri_product(rhoHat1, rhoHat2, R[0])
D2 = odlib.tri_product(rhoHat1, rhoHat2, R[1])
D3 = odlib.tri_product(rhoHat1, rhoHat2, R[2])
rho[2] *= (a[0] * D1 + a[1] * D2 + a[2] * D3) / (a[2] * D0)
r = rho - R
f1 = f(tauAt1, tauAt2, r[1], r2Dot)
f3 = f(tauAt3, tauAt2, r[1], r2Dot)
g1 = g(tauAt1, tauAt2, r[1], r2Dot)
g3 = g(tauAt3, tauAt2, r[1], r2Dot)
a[0] = g3 / (f1 * g3 - f3 * g1)
a[2] = g1 / (f3 * g1 - f1 * g3)
r[1] = a[0] * r[0] + a[2] * r[2]
r2Dot = f3 / (g1 * f3 - g3 * f1) * r[0] + f1 / (g3 * f1 - g1 * f3) * r[2]
iteration += 1
assert(iteration < maxIterations)
r[1] = odlib.rotateVector(r[1], 0, odlib.degreesToRadians(23.4368815858), 0)
r2Dot = odlib.rotateVector(r2Dot, 0, odlib.degreesToRadians(23.4368815858), 0)
percentErrorR2 = abs(r[1] - realR2) / realR2 * 100
percentErrorR2Dot = abs(r2Dot - realR2Dot) / realR2Dot * 100
print('iterations', iteration)
print(f"Expected r: {realR2}\nCalulated r: {r[1]}")
print(f"Percent difference for each component: {percentErrorR2}\n")
print(f"Expected rdot: {realR2Dot}\nCalulated rdot: {r2Dot}")
print(f"Percent difference for each component: {percentErrorR2Dot}")
r = rho - R
f1 = f(tauAt1, tauAt2, r[1], r2Dot)
f3 = f(tauAt3, tauAt2, r[1], r2Dot)
g1 = g(tauAt1, tauAt2, r[1], r2Dot)
g3 = g(tauAt3, tauAt2, r[1], r2Dot)
a[0] = g3 / (f1 * g3 - f3 * g1)
a[2] = g1 / (f3 * g1 - f1 * g3)
r[1] = a[0] * r[0] + a[2] * r[2]
r2Dot = f3 / (g1 * f3 - g3 * f1) * r[0] + f1 / (g3 * f1 - g1 * f3) * r[2]
iteration += 1
assert(iteration < maxIterations)
print(r)
r[1] = odlib.rotateVector(r[1], 0, odlib.degreesToRadians(eclipticObliquity), 0)
r2Dot = odlib.rotateVector(r2Dot, 0, odlib.degreesToRadians(eclipticObliquity), 0)
print('r and r2Dot',r[1], np.array(r2Dot) * odlib.k)
elements = orbitalElements(r[1], r2Dot)
elements[2] = odlib.radiansToDegrees(elements[2])
elements[3] = odlib.radiansToDegrees(elements[3])
elements[4] = odlib.radiansToDegrees(elements[4])
elements[5] = odlib.radiansToDegrees(elements[5])
while elements[4] < 0:
elements[4] += 360
while elements[4] > 360:
elements[4] -= 360
# Moves M to a negative angle to make the percent error more fitting