def f(t0, u_, k):
du_kep = func_twobody(t0, u_, k)
ax, ay, az = J2_perturbation(
t0, u_, k, J2=Earth.J2.value, R=Earth.R.to(u.km).value
)
du_ad = np.array([0, 0, 0, ax, ay, az])
return du_kep + du_ad
def setup(self):
from poliastro.twobody import Orbit
self.a_ini = 8970.667 * u.km
self.ecc_ini = 0.25 * u.one
self.raan_ini = 1.047 * u.rad
self.nu_ini = 0.0 * u.rad
self.argp_ini = 1.0 * u.rad
self.inc_ini = 0.2618 * u.rad
self.k = Earth.k.to(u.km**3 / u.s**2).value
self.orbit = Orbit.from_classical(
Earth,
self.a_ini,
self.ecc_ini,
self.inc_ini,
self.raan_ini,
self.argp_ini,
self.nu_ini,
)
self.tof = [1.0] * u.min
self.a_J2J3 = lambda t0, u_, k_: J2_perturbation(
t0, u_, k_, J2=Earth.J2.value, R=Earth.R.to(
u.km).value) + J3_perturbation(
t0, u_, k_, J3=Earth.J3.value, R=Earth.R.to(u.km).value)
def f_combined(t0, u_, k):
du_kep = func_twobody(t0, u_, k)
ax, ay, az = J2_perturbation(
t0, u_, k, J2=Earth.J2.value, R=Earth.R.to_value(u.km)
) + J3_perturbation(t0, u_, k, J3=Earth.J3.value, R=Earth.R.to_value(u.km))
du_ad = np.array([0, 0, 0, ax, ay, az])
return du_kep + du_ad
def a_J2J3(t0, u_, k_):
j2 = J2_perturbation(t0,
u_,
k_,
J2=Earth.J2.value,
R=Earth.R.to(u.km).value)
j3 = J3_perturbation(t0,
u_,
k_,
J3=Earth.J3.value,
R=Earth.R.to(u.km).value)
return j2 + j3
def a_d(t0, state, k, perturbations: Dict):
"""
Custom perturbation function that is passed directly to poliastro to be executed in their code, hence the need for
summation() to be included within. Current structure allows user to pick and chose which perturbations they would
like to include, requiring that the desired perturbation objects are created, filled, and passed.
Note: To improve upon existing perturbation functions or to add more, everything must be self-contained within the
function.
:param t0: Required by poliastro
:param state: Required by poliastro
:param k: Required by poliastro (gravitational parameter-mu)
:param perturbations: Dictionary of perturbations desired by the user. Keys correspond to the perturbations Enum
class in Enum.py, while values correspond to objects in the dto.py class.
:return: Returns a force that describes the impact of all desired perturbations
"""
fun = []
if Perturbations.J2 in perturbations:
perturbation = perturbations.get(Perturbations.J2)
fun.append(J2_perturbation(t0, state, k, perturbation.J2, perturbation.R))
if Perturbations.Drag in perturbations:
perturbation = perturbations.get(Perturbations.Drag)
fun.append(atmospheric_drag(t0, state, k, perturbation.R, perturbation.C_D, perturbation.A, perturbation.m,
perturbation.H0, perturbation.rho0))
if Perturbations.J3 in perturbations:
perturbation = perturbations.get(Perturbations.J3)
fun.append(J3_perturbation(t0, state, k, perturbation.J3, perturbation.R))
if Perturbations.SRP in perturbations:
perturbation = perturbations.get(Perturbations.SRP)
fun.append(radiation_pressure(t0, state, k, perturbation.R, perturbation.C_R, perturbation.A, perturbation.m,
perturbation.Wdivc_s, perturbation.star))
if Perturbations.Moon in perturbations:
perturbation = perturbations.get(Perturbations.Moon)
fun.append(third_body(t0, state, k, perturbation.k_third, perturbation.third_body))
if Perturbations.Sun in perturbations:
perturbation = perturbations.get(Perturbations.Sun)
fun.append(third_body(t0, state, k, perturbation.k_third, perturbation.third_body))
def summation(arr):
if len(arr) == 0:
return np.zeros(3)
output = arr[0]
for i in range(1, len(arr)):
output += arr[i]
return output
return summation(fun)
def test_J3_propagation_Earth(test_params):
# Nai-ming Qi, Qilong Sun, Yong Yang, (2018) "Effect of J3 perturbation on satellite position in LEO",
# Aircraft Engineering and Aerospace Technology, Vol. 90 Issue: 1,
# pp.74-86, https://doi.org/10.1108/AEAT-03-2015-0092
a_ini = 8970.667 * u.km
ecc_ini = 0.25 * u.one
raan_ini = 1.047 * u.rad
nu_ini = 0.0 * u.rad
argp_ini = 1.0 * u.rad
inc_ini = test_params['inc']
k = Earth.k.to(u.km**3 / u.s**2).value
orbit = Orbit.from_classical(Earth, a_ini, ecc_ini, inc_ini, raan_ini, argp_ini, nu_ini)
tof = (10.0 * u.day).to(u.s).value
r_J2, v_J2 = cowell(orbit, np.linspace(0, tof, int(1e+3)), ad=J2_perturbation,
J2=Earth.J2.value, R=Earth.R.to(u.km).value, rtol=1e-8)
a_J2J3 = lambda t0, u_, k_: J2_perturbation(t0, u_, k_, J2=Earth.J2.value, R=Earth.R.to(u.km).value) + \
J3_perturbation(t0, u_, k_, J3=Earth.J3.value, R=Earth.R.to(u.km).value)
r_J3, v_J3 = cowell(orbit, np.linspace(0, tof, int(1e+3)), ad=a_J2J3, rtol=1e-8)
a_values_J2 = np.array([rv2coe(k, ri, vi)[0] / (1.0 - rv2coe(k, ri, vi)[1] ** 2) for ri, vi in zip(r_J2, v_J2)])
a_values_J3 = np.array([rv2coe(k, ri, vi)[0] / (1.0 - rv2coe(k, ri, vi)[1] ** 2) for ri, vi in zip(r_J3, v_J3)])
da_max = np.max(np.abs(a_values_J2 - a_values_J3))
ecc_values_J2 = np.array([rv2coe(k, ri, vi)[1] for ri, vi in zip(r_J2, v_J2)])
ecc_values_J3 = np.array([rv2coe(k, ri, vi)[1] for ri, vi in zip(r_J3, v_J3)])
decc_max = np.max(np.abs(ecc_values_J2 - ecc_values_J3))
inc_values_J2 = np.array([rv2coe(k, ri, vi)[2] for ri, vi in zip(r_J2, v_J2)])
inc_values_J3 = np.array([rv2coe(k, ri, vi)[2] for ri, vi in zip(r_J3, v_J3)])
dinc_max = np.max(np.abs(inc_values_J2 - inc_values_J3))
assert_quantity_allclose(dinc_max, test_params['dinc_max'], rtol=1e-1, atol=1e-7)
assert_quantity_allclose(decc_max, test_params['decc_max'], rtol=1e-1, atol=1e-7)
try:
assert_quantity_allclose(da_max * u.km, test_params['da_max'])
except AssertionError as exc:
pytest.xfail('this assertion disagrees with the paper')
def a_d_1(t0, state, k, J2, R, C_D, A, m, H0, rho0): # J2+atmospheric_drag
return (J2_perturbation(t0, state, k, J2, R) +
atmospheric_drag(t0, state, k, R, C_D, A, m, H0, rho0))
def J2_and_drag(t0, state, k, J2, R, C_D, A_over_m, H0, rho0):
return J2_perturbation(t0, state, k, J2, R) + atmospheric_drag_exponential(
t0, state, k, R, C_D, A_over_m, H0, rho0
)
def J23_perturbation(t0, state, k, J2, J3, R):
'''wrapper function that adds effects of J2 and J3 perturbations'''
a2 = J2_perturbation(t0, state, k, J2, R)
a3 = J3_perturbation(t0, state, k, J3, R)
return a2 + a3
def a_d_j2j3(t0, state, k, J2, J3, R):
return J2_perturbation(t0, state, k, J2, R) + J3_perturbation(
t0, state, k, J3, R)
