def test_true_to_eccentric_hyperbolic():
# Data from Curtis, H. (2013). *Orbital mechanics for engineering students*.
# Example 3.5
nu = 100 * u.deg
ecc = 2.7696 * u.one
expected_F = 2.2927 * u.rad
F = angles.nu_to_F(nu, ecc)
assert_quantity_allclose(F, expected_F, rtol=1e-4)
def test_true_to_eccentric_hyperbolic():
# Data from Curtis, H. (2013). *Orbital mechanics for engineering students*.
# Example 3.5
nu = 100 * u.deg
ecc = 2.7696 * u.one
expected_F = 2.2927 * u.rad
F = angles.nu_to_F(nu, ecc)
assert_quantity_allclose(F, expected_F, rtol=1e-4)
def test_true_to_mean_hyperbolic():
# Data from Curtis, H. (2013). "Orbital mechanics for engineering students".
# Example 3.5
nu = 100 * u.deg
ecc = 2.7696 * u.one
expected_M = 11.279 * u.rad
M = angles.F_to_M(angles.nu_to_F(nu, ecc), ecc)
assert_quantity_allclose(M, expected_M, rtol=1e-4)
def newton(func, x0, ecc, M, fprime=None, maxiter=50):
EFD = 1.0 * x0
delta = 1e-2
nu_prev = 1e+10
converged = False
# Newton-Rapheson method
with u.set_enabled_equivalencies(u.dimensionless_angles()):
for iter in range(maxiter):
if ecc < 1.0 - delta:
nu = E_to_nu(EFD, ecc)
E_plus = nu_to_E(nu + variation, ecc)
E_minus = nu_to_E(nu - variation, ecc)
M_actual = _kepler_equation(EFD, M, ecc, count=False)
M_plus = _kepler_equation(E_plus, M, ecc, count=False)
M_minus = _kepler_equation(E_minus, M, ecc, count=False)
elif ecc > 1.0 + delta:
nu = F_to_nu(EFD, ecc)
F_plus = nu_to_F(nu + variation, ecc)
F_minus = nu_to_F(nu - variation, ecc)
M_actual = _kepler_equation_hyper(EFD, M, ecc, count=False)
M_plus = _kepler_equation_hyper(F_plus, M, ecc, count=False)
M_minus = _kepler_equation_hyper(F_minus, M, ecc, count=False)
else:
nu = D_to_nu(EFD, ecc)
D_plus = nu_to_D(nu + variation, ecc)
D_minus = nu_to_D(nu - variation, ecc)
M_actual = _kepler_equation_parabolic(EFD, M, ecc, count=False)
M_plus = _kepler_equation_parabolic(D_plus, M, ecc, count=False)
M_minus = _kepler_equation_parabolic(D_minus, M, ecc, count=False)
converged = (np.abs(nu_prev - nu) < variation) and (M_actual * M_plus <= 0 or M_minus * M_actual <= 0)
nu_prev = nu
EFD_new = EFD - func(EFD, M, ecc) / fprime(EFD, M, ecc)
if converged:
return EFD_new
EFD = EFD_new
print(ecc, "fail")
return -1
def test_mean_to_true_hyperbolic_highecc(expected_nu, ecc):
M = angles.F_to_M(angles.nu_to_F(expected_nu, ecc), ecc)
nu = angles.F_to_nu(angles.M_to_F(M, ecc), ecc)
assert_quantity_allclose(nu, expected_nu, rtol=1e-4)
