def test_geo_cases_numerical(ecc_0, ecc_f):
a = 42164 # km
inc_0 = 0.0 # rad, baseline
inc_f = (20.0 * u.deg).to(u.rad).value # rad
argp = 0.0 # rad, the method is efficient for 0 and 180
f = 2.4e-7 # km / s2
# Retrieve r and v from initial orbit
s0 = Orbit.from_classical(
Earth,
a * u.km,
ecc_0 * u.one,
inc_0 * u.deg,
0 * u.deg,
argp * u.deg,
0 * u.deg,
)
a_d, _, _, t_f = change_inc_ecc(s0, ecc_f, inc_f, f)
# Propagate orbit
def f_geo(t0, u_, k):
du_kep = func_twobody(t0, u_, k)
ax, ay, az = a_d(t0, u_, k)
du_ad = np.array([0, 0, 0, ax, ay, az])
return du_kep + du_ad
sf = s0.propagate(t_f * u.s, method=cowell, f=f_geo, rtol=1e-8)
assert_allclose(sf.ecc.value, ecc_f, rtol=1e-2, atol=1e-2)
assert_allclose(sf.inc.to(u.rad).value, inc_f, rtol=1e-1)
def test_geo_cases_beta_dnd_delta_v(ecc_0, inc_f, expected_beta,
expected_delta_V):
a = 42164 # km
ecc_f = 0.0
inc_0 = 0.0 # rad, baseline
argp = 0.0 # rad, the method is efficient for 0 and 180
f = 2.4e-7 # km / s2, unused
inc_f = np.radians(inc_f)
expected_beta = np.radians(expected_beta)
s0 = Orbit.from_classical(
Earth,
a * u.km,
ecc_0 * u.one,
inc_0 * u.deg,
0 * u.deg,
argp * u.deg,
0 * u.deg,
)
_, delta_V, beta, _ = change_inc_ecc(s0, ecc_f, inc_f, f)
assert_allclose(delta_V, expected_delta_V, rtol=1e-2)
assert_allclose(beta, expected_beta, rtol=1e-2)
def test_geo_cases_numerical(ecc_0, ecc_f):
a = 42164 # km
inc_0 = 0.0 # rad, baseline
inc_f = (20.0 * u.deg).to(u.rad).value # rad
argp = 0.0 # rad, the method is efficient for 0 and 180
f = 2.4e-7 # km / s2
k = Earth.k.to(u.km**3 / u.s**2).value
# Retrieve r and v from initial orbit
s0 = Orbit.from_classical(Earth, a * u.km, ecc_0 * u.one, inc_0 * u.deg,
0 * u.deg, argp * u.deg, 0 * u.deg)
a_d, _, _, t_f = change_inc_ecc(s0, ecc_f, inc_f, f)
# Propagate orbit
sf = s0.propagate(t_f * u.s, method=cowell, ad=a_d, rtol=1e-8)
assert_allclose(sf.ecc.value, ecc_f, rtol=1e-2, atol=1e-2)
assert_allclose(sf.inc.to(u.rad).value, inc_f, rtol=1e-1)
def test_geo_cases_beta_dnd_delta_v(ecc_0, inc_f, expected_beta, expected_delta_V):
a = 42164 # km
ecc_f = 0.0
inc_0 = 0.0 # rad, baseline
argp = 0.0 # rad, the method is efficient for 0 and 180
f = 2.4e-7 # km / s2, unused
inc_f = np.radians(inc_f)
expected_beta = np.radians(expected_beta)
s0 = Orbit.from_classical(
Earth,
a * u.km, ecc_0 * u.one, inc_0 * u.deg,
0 * u.deg, argp * u.deg, 0 * u.deg
)
_, delta_V, beta, _ = change_inc_ecc(s0, ecc_f, inc_f, f)
assert_allclose(delta_V, expected_delta_V, rtol=1e-2)
assert_allclose(beta, expected_beta, rtol=1e-2)
def test_geo_cases_numerical(ecc_0, ecc_f):
a = 42164 # km
inc_0 = 0.0 # rad, baseline
inc_f = (20.0 * u.deg).to(u.rad).value # rad
argp = 0.0 # rad, the method is efficient for 0 and 180
f = 2.4e-7 # km / s2
# Retrieve r and v from initial orbit
s0 = Orbit.from_classical(
Earth,
a * u.km, ecc_0 * u.one, inc_0 * u.deg,
0 * u.deg, argp * u.deg, 0 * u.deg
)
a_d, _, _, t_f = change_inc_ecc(s0, ecc_f, inc_f, f)
# Propagate orbit
sf = s0.propagate(t_f * u.s, method=cowell, ad=a_d, rtol=1e-8)
assert_allclose(sf.ecc.value, ecc_f, rtol=1e-2, atol=1e-2)
assert_allclose(sf.inc.to(u.rad).value, inc_f, rtol=1e-1)
argp = 0.0 # rad, the method is efficient for 0 and 180
f = 2.4e-6 # km / s2
k = Earth.k.to(u.km**3 / u.s**2).value
s0 = Orbit.from_classical(
Earth,
a * u.km,
ecc_0 * u.one,
inc_0 * u.deg,
0 * u.deg,
argp * u.deg,
0 * u.deg,
epoch=Time(0, format="jd", scale="tdb"),
)
a_d, _, _, t_f = change_inc_ecc(s0, ecc_f, inc_f, f)
tofs = TimeDelta(np.linspace(0, t_f * u.s, num=1000))
rr2 = propagate(s0, tofs, method=cowell, rtol=1e-6, ad=a_d)
# In[12]:
frame = OrbitPlotter3D()
frame.set_attractor(Earth)
frame.plot_trajectory(rr2, label="orbit with artificial thrust")
# ### Combining multiple perturbations
#
# It might be of interest to determine what effect multiple perturbations have on a single object. In order to add multiple perturbations we can create a custom function that adds them up: