def kepler(argp, delta_t_sec, ecc, inc, p, raan, sma, ta):
# Initial mean anomaly
M_0 = ta_to_M(ta, ecc)
# Mean motion
n = sqrt(wgs84.mu / sma**3)
# Propagation
M = M_0 + n * delta_t_sec
# New true anomaly
ta = M_to_ta(M, ecc)
# Position and velocity vectors
position_eci, velocity_eci = coe2rv(MU_E, p, ecc, inc, raan, argp, ta)
return position_eci, velocity_eci
def test_true_to_mean(self):
# Data from Schlesinger & Udick, 1912
data = [
# ecc, M (deg), ta (deg)
(0.0, 0.0, 0.0),
(0.05, 10.0, 11.06),
(0.06, 30.0, 33.67),
(0.04, 120.0, 123.87),
(0.14, 65.0, 80.50),
(0.19, 21.0, 30.94),
(0.35, 65.0, 105.71),
(0.48, 180.0, 180.0),
(0.75, 125.0, 167.57)
]
for row in data:
ecc, expected_M, ta = row
M = angles.ta_to_M(radians(ta), ecc)
self.assertAlmostEqual(degrees(M), expected_M, places=1)
def pkepler(argp, delta_t_sec, ecc, inc, p, raan, sma, ta):
"""Perturbed Kepler problem (only J2)
Notes
-----
Based on algorithm 64 of Vallado 3rd edition
"""
# Mean motion
n = sqrt(MU_E / sma**3)
# Initial mean anomaly
M_0 = ta_to_M(ta, ecc)
# Update for perturbations
delta_raan = (-(3 * n * R_E_KM**2 * J2) / (2 * p**2) * cos(inc) *
delta_t_sec)
raan = raan + delta_raan
delta_argp = ((3 * n * R_E_KM**2 * J2) / (4 * p**2) *
(4 - 5 * sin(inc)**2) * delta_t_sec)
argp = argp + delta_argp
M0_dot = ((3 * n * R_E_KM**2 * J2) / (4 * p**2) * (2 - 3 * sin(inc)**2) *
sqrt(1 - ecc**2))
M_dot = n + M0_dot
# Propagation
M = M_0 + M_dot * delta_t_sec
# New true anomaly
ta = M_to_ta(M, ecc)
# Position and velocity vectors
position_eci, velocity_eci = coe2rv(MU_E, p, ecc, inc, raan, argp, ta)
return position_eci, velocity_eci