def f(tau):
series_pt1 = 1-(tau**2)/(2*r2_mag**3) + \
(tau**3)*od.dot(r2, r2_dot)/(2*r2_mag**5)
coeff = (tau**4) / (24 * r2_mag**3)
disgusting = 3*(od.dot(r2_dot, r2_dot)/(r2_mag)**2) - 1/(r2_mag**3) - \
15*(od.dot(r2, r2_dot)/(r2_mag**2))**2 + 1/(r2_mag**3)
return series_pt1 + coeff * disgusting
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 orbitalElements(r, rDot):
rMag = odlib.mag(r)
vSqr = odlib.dot(rDot, rDot)
a = 1 / (2 / rMag - vSqr)
h = odlib.cross(r, rDot)
hMag = odlib.mag(h)
e = sqrt(1 - hMag**2 / a)
i = acos(h[2] / hMag)
cosOmega = -h[1] / (hMag * sin(i))
sinOmega = h[0] / (hMag * sin(i))
omega = odlib.sinCosToAngle(sinOmega, cosOmega)
sinNu = (a * (1 - e**2) / hMag * (odlib.dot(r, rDot) / rMag)) / e
cosNu = (a * (1 - e**2) / rMag - 1) / e
nu = odlib.sinCosToAngle(sinNu, cosNu)
cosU = (r[0] * cosOmega + r[1] * sinOmega) / rMag
sinU = r[2] / (rMag * sin(i))
u = odlib.sinCosToAngle(sinU, cosU)
lowerOmega = u - nu
E = acos((1 - rMag / a) / e)
M = E - e * sin(E)
return [a, e, i, omega, lowerOmega, M]
def g(tau):
return tau - (tau**3) / (6 * r2_mag**3) + (tau**4) * (od.dot(
r2, r2_dot)) / (4 * r2_mag**5)
DEC[i] = od.DMStoDeg(DEC[i]) * pi / 180
rho_hat1 = [cos(RA[0]) * cos(DEC[0]),
sin(RA[0]) * cos(DEC[0]),
sin(DEC[0])] # calculating rho from RA and Dec
rho_hat2 = [cos(RA[1]) * cos(DEC[1]), sin(RA[1]) * cos(DEC[1]), sin(DEC[1])]
rho_hat3 = [cos(RA[2]) * cos(DEC[2]), sin(RA[2]) * cos(DEC[2]), sin(DEC[2])]
T0 = k * (t3 - t1)
T1 = k * (t1 - t2)
T3 = k * (t3 - t2)
a1 = T3 / T0
a2 = -1
a3 = -T1 / T0
a = [a1, a2, a3]
D0 = od.dot(rho_hat1, od.cross(rho_hat2, rho_hat3))
D = np.ones((3, 3))
rho = np.ones(3)
rho_hat = np.array([rho_hat1, rho_hat2, rho_hat3])
r2 = [0, 0, 0]
r2_dot = [0, 0, 0] # set values for while loop to carry over
r2_old = [1, 1, 1]
r2_dot_old = [1, 1, 1]
# setting up while loop
def bool_comp(vec1, vec2):
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
def orbit_ele(x_pos1, y_pos1, z_pos1, x_pos2, y_pos2, z_pos2, J1, J2):
k = 0.01720209847
r_dot = [(x_pos2 - x_pos1) / (k * (J2 - J1)),
(y_pos2 - y_pos1) / (k * (J2 - J1)),
(z_pos2 - z_pos1) / (k * (J2 - J1))]
r = [x_pos1, y_pos1, z_pos1]
r_mag = od.mag(r)
h = od.cross(r, r_dot)
h_x = h[0]
h_y = h[1]
h_z = h[2]
h_mag = od.mag(h)
v2 = od.dot(r_dot, r_dot)
a = 1 / ((2 / r_mag) - v2)
ecc = (1 - (h_mag)**2 / a)**.5
inc = acos(h_z / h_mag)
cO = -h_y / (h_mag * sin(inc)) # cos of Omega
sO = h_x / (h_mag * sin(inc)) # sin of Omega
Ome = od.rads(sO, cO)
cU = (x_pos1 * cO + y_pos1 * sO) / r_mag # cos of U
sU = z_pos1 / (r_mag * sin(inc)) # sin of U
U = od.rads(sU, cU)
cV = (1 / ecc) * ((a * (1 - ecc**2)) / r_mag - 1) # cos of V
sV = (1 / ecc) * (((a * (1 - ecc**2)) / h_mag) *
(od.dot(r, r_dot)) / r_mag)
V = od.rads(sV, cV)
w = U - V
E = acos((1 / ecc) * (1 - r_mag / a))
M = E - ecc * sin(E)
inc = inc * 180 / pi
U = U * 180 / pi
V = V * 180 / pi
Ome = Ome * 180 / pi
w = w * 180 / pi
if w < 0:
w = 360 + w
E = E * 180 / pi
M = M * 180 / pi
experi = [a, ecc, inc, Ome, V, w, M]
expect = [
1.056800057682216, 3.442331106521022 * 10**-1, 2.515525601713781 * 10,
236.2379793903064, 1.589559274581728 * 10**2, 255.5046093427637,
1.404194621765141 * 10**2
]
per_error = []
for i in range(len(experi)):
per_error.append(abs(experi[i] - expect[i]) / expect[i] * 100)
print('Semi-major axis: ', a, ', Expected: ', expect[0], ', % error: ',
per_error[0])
print('Eccentricity: ', ecc, ', Expected: ', expect[1], ', % error: ',
per_error[1])
print('Inclination (degrees): ', inc, ', Expected: ', expect[2],
', % error: ', per_error[2])
print('Longitude of the Ascending Node (degrees): ', Ome, ', Expected: ',
expect[3], ', % error: ', per_error[3])
print('True Anomoly (degrees): ', V, ', Expected: ', expect[4],
', % error: ', per_error[4])
print('Argument of Perihelion, (degrees): ', w, ', Expected: ', expect[5],
', % error: ', per_error[5])
print('Mean Anomaly (degrees): ', M, ', Expected: ', expect[6],
', % error: ', per_error[6])