def test_parabolic_elements_fail_early():
attractor = Earth
ecc = 1.0 * u.one
_d = 1.0 * u.AU # Unused distance
_a = 1.0 * u.deg # Unused angle
with pytest.raises(ValueError) as excinfo:
Orbit.from_classical(attractor, _d, ecc, _a, _a, _a, _a)
assert ("ValueError: For parabolic orbits use Orbit.parabolic instead" in excinfo.exconly())
def test_bad_inclination_raises_exception():
_d = 1.0 * u.AU # Unused distance
_ = 0.5 * u.one # Unused dimensionless value
_a = 1.0 * u.deg # Unused angle
bad_inc = 200 * u.deg
_body = Sun # Unused body
with pytest.raises(ValueError) as excinfo:
Orbit.from_classical(_body, _d, _, bad_inc, _a, _a, _a)
assert ("ValueError: Inclination must be between 0 and 180 degrees" in excinfo.exconly())
def test_parabolic_elements_fail_early():
attractor = Earth
ecc = 1.0 * u.one
_d = 1.0 * u.AU # Unused distance
_a = 1.0 * u.deg # Unused angle
with pytest.raises(ValueError) as excinfo:
Orbit.from_classical(attractor, _d, ecc, _a, _a, _a, _a)
assert ("ValueError: For parabolic orbits use Orbit.parabolic instead"
in excinfo.exconly())
def test_bad_hyperbolic_raises_exception():
bad_a = 1.0 * u.AU
ecc = 1.5 * u.one
_a = 1.0 * u.deg # Unused angle
_inc = 100 * u.deg # Unused inclination
_body = Sun # Unused body
with pytest.raises(ValueError) as excinfo:
Orbit.from_classical(_body, bad_a, ecc, _inc, _a, _a, _a)
assert ("Hyperbolic orbits have negative semimajor axis" in excinfo.exconly())
def test_state_raises_unitserror_if_elements_units_are_wrong():
_d = 1.0 * u.AU # Unused distance
_ = 0.5 * u.one # Unused dimensionless value
_a = 1.0 * u.deg # Unused angle
wrong_angle = 1.0 * u.AU
with pytest.raises(u.UnitsError) as excinfo:
Orbit.from_classical(Sun, _d, _, _a, _a, _a, wrong_angle)
assert ("UnitsError: Argument 'nu' to function 'from_classical' must be in units convertible to 'rad'."
in excinfo.exconly())
def test_state_raises_unitserror_if_elements_units_are_wrong():
_d = 1.0 * u.AU # Unused distance
_ = 0.5 * u.one # Unused dimensionless value
_a = 1.0 * u.deg # Unused angle
wrong_angle = 1.0 * u.AU
with pytest.raises(u.UnitsError) as excinfo:
Orbit.from_classical(Sun, _d, _, _a, _a, _a, wrong_angle)
assert (
"UnitsError: Argument 'nu' to function 'from_classical' must be in units convertible to 'rad'."
in excinfo.exconly())
def test_bad_inclination_raises_exception():
_d = 1.0 * u.AU # Unused distance
_ = 0.5 * u.one # Unused dimensionless value
_a = 1.0 * u.deg # Unused angle
_body = Sun # Unused body
bad_inc = 200 * u.deg
with pytest.raises(ValueError) as excinfo:
Orbit.from_classical(_body, _d, _, bad_inc, _a, _a, _a)
assert ("ValueError: Inclination must be between 0 and 180 degrees"
in excinfo.exconly())
def test_bad_hyperbolic_raises_exception():
bad_a = 1.0 * u.AU
ecc = 1.5 * u.one
_inc = 100 * u.deg # Unused inclination
_a = 1.0 * u.deg # Unused angle
_body = Sun # Unused body
with pytest.raises(ValueError) as excinfo:
Orbit.from_classical(_body, bad_a, ecc, _inc, _a, _a, _a)
assert "Hyperbolic orbits have negative semimajor axis" in excinfo.exconly(
)
def test_mean_motion(ecc):
_a = 0.0 * u.rad
tof = 1.0 * u.min
if ecc < 1.0:
orbit = Orbit.from_classical(Earth, 10000 * u.km, ecc * u.one, _a, _a, _a, 1.0 * u.rad)
else:
orbit = Orbit.from_classical(Earth, -10000 * u.km, ecc * u.one, _a, _a, _a, 1.0 * u.rad)
orbit_cowell = orbit.propagate(tof, method=cowell)
orbit_mean_motion = orbit.propagate(tof, method=mean_motion)
assert_quantity_allclose(orbit_cowell.r, orbit_mean_motion.r)
assert_quantity_allclose(orbit_cowell.v, orbit_mean_motion.v)
def test_mean_motion(ecc):
_a = 0.0 * u.rad
tof = 1.0 * u.min
if ecc < 1.0:
orbit = Orbit.from_classical(Earth, 10000 * u.km, ecc * u.one, _a, _a, _a, 1.0 * u.rad)
else:
orbit = Orbit.from_classical(Earth, -10000 * u.km, ecc * u.one, _a, _a, _a, 1.0 * u.rad)
orbit_cowell = orbit.propagate(tof, method=cowell)
orbit_mean_motion = orbit.propagate(tof, method=mean_motion)
assert_quantity_allclose(orbit_cowell.r, orbit_mean_motion.r)
assert_quantity_allclose(orbit_cowell.v, orbit_mean_motion.v)
def test_sso_disposal_numerical(ecc_0, ecc_f):
a_0 = Earth.R.to(u.km).value + 900 # km
f = 2.4e-7 # km / s2, assumed constant
k = Earth.k.decompose([u.km, u.s]).value
_, t_f = extra_quantities(k, a_0, ecc_0, ecc_f, f)
# Retrieve r and v from initial orbit
s0 = Orbit.from_classical(Earth, a_0 * u.km, ecc_0 * u.one, 0 * u.deg,
0 * u.deg, 0 * u.deg, 0 * u.deg)
r0, v0 = s0.rv()
optimal_accel = guidance_law(s0, ecc_f, f)
# Propagate orbit
r, v = cowell(k,
r0.to(u.km).value,
v0.to(u.km / u.s).value,
t_f,
ad=optimal_accel,
nsteps=1000000)
sf = Orbit.from_vectors(Earth, r * u.km, v * u.km / u.s,
s0.epoch + t_f * u.s)
assert_allclose(sf.ecc.value, ecc_f, rtol=1e-4, atol=1e-4)
def test_propagating_to_certain_nu_is_correct():
# take an elliptic orbit
a = 1.0 * u.AU
ecc = 1.0 / 3.0 * u.one
_a = 0.0 * u.rad
nu = 10 * u.deg
elliptic = Orbit.from_classical(Sun, a, ecc, _a, _a, _a, nu)
elliptic_at_perihelion = elliptic.propagate_to_anomaly(0.0 * u.rad)
r_per, _ = elliptic_at_perihelion.rv()
elliptic_at_aphelion = elliptic.propagate_to_anomaly(np.pi * u.rad)
r_ap, _ = elliptic_at_aphelion.rv()
assert_quantity_allclose(norm(r_per), a * (1.0 - ecc))
assert_quantity_allclose(norm(r_ap), a * (1.0 + ecc))
# TODO: Test specific values
assert elliptic_at_perihelion.epoch > elliptic.epoch
assert elliptic_at_aphelion.epoch > elliptic.epoch
# test 10 random true anomaly values
for _ in range(10):
nu = np.random.uniform(low=0.0, high=2 * np.pi)
elliptic = elliptic.propagate_to_anomaly(nu * u.rad)
r, _ = elliptic.rv()
assert_quantity_allclose(norm(r), a * (1.0 - ecc ** 2) / (1 + ecc * np.cos(nu)))
def test_soyuz_standard_gto_numerical():
# Data from Soyuz Users Manual, issue 2 revision 0
r_a = (Earth.R + 35950 * u.km).to(u.km).value
r_p = (Earth.R + 250 * u.km).to(u.km).value
a = (r_a + r_p) / 2 # km
ecc = r_a / a - 1
argp_0 = (178 * u.deg).to(u.rad).value # rad
argp_f = (178 * u.deg + 5 * u.deg).to(u.rad).value # rad
f = 2.4e-7 # km / s2
k = Earth.k.decompose([u.km, u.s]).value
optimal_accel = guidance_law(f)
_, t_f = extra_quantities(k, a, ecc, argp_0, argp_f, f)
# Retrieve r and v from initial orbit
s0 = Orbit.from_classical(Earth, a * u.km, (r_a / a - 1) * u.one,
6 * u.deg, 188.5 * u.deg, 178 * u.deg, 0 * u.deg)
r0, v0 = s0.rv()
# Propagate orbit
r, v = cowell(k,
r0.to(u.km).value,
v0.to(u.km / u.s).value,
t_f,
ad=optimal_accel,
nsteps=1000000)
sf = Orbit.from_vectors(Earth, r * u.km, v * u.km / u.s,
s0.epoch + t_f * u.s)
assert_allclose(sf.argp.to(u.rad).value, argp_f, rtol=1e-4)
def test_penumbra_event_crossing():
expected_penumbra_t = Time("2020-01-01 00:04:26.060",
scale="utc") # From Orekit.
attractor = Earth
tof = 2 * u.d
epoch = Time("2020-01-01", scale="utc")
orbit = Orbit.from_classical(
attractor=attractor,
a=6828137.0 * u.m,
ecc=0.0073 * u.one,
inc=87.0 * u.deg,
raan=20.0 * u.deg,
argp=10.0 * u.deg,
nu=0 * u.deg,
epoch=epoch,
)
penumbra_event = PenumbraEvent(orbit, terminal=True)
events = [penumbra_event]
rr, _ = cowell(
attractor.k,
orbit.r,
orbit.v,
[tof] * u.s,
events=events,
)
assert expected_penumbra_t.isclose(epoch + penumbra_event.last_t,
atol=1 * u.s)
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 * (u.km / u.s**2)
inc_f = np.radians(inc_f)
expected_beta = np.radians(expected_beta)
s0 = Orbit.from_classical(
attractor=Earth,
a=a * u.km,
ecc=ecc_0 * u.one,
inc=inc_0 * u.deg,
raan=0 * u.deg,
argp=argp * u.deg,
nu=0 * u.deg,
)
beta = beta_change_ecc_inc(ecc_0=ecc_0,
ecc_f=ecc_f,
inc_0=inc_0,
inc_f=inc_f,
argp=argp)
_, delta_V, _ = change_ecc_inc(ss_0=s0,
ecc_f=ecc_f,
inc_f=inc_f * u.rad,
f=f)
assert_allclose(delta_V.to_value(u.km / u.s), 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
inc_f = 20.0 * u.deg
argp = 0.0 # rad, the method is efficient for 0 and 180
f = 2.4e-7 * (u.km / u.s**2)
# Initial orbit
s0 = Orbit.from_classical(
attractor=Earth,
a=a * u.km,
ecc=ecc_0 * u.one,
inc=inc_0 * u.deg,
raan=0 * u.deg,
argp=argp * u.deg,
nu=0 * u.deg,
)
a_d, _, t_f = change_ecc_inc(ss_0=s0, ecc_f=ecc_f, inc_f=inc_f, 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, 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_value(u.rad), inc_f.to_value(u.rad), rtol=1e-1)
def test_solar_pressure():
# based on example 12.9 from Howard Curtis
solar_system_ephemeris.set('de432s')
j_date = 2438400.5 * u.day
tof = 600 * u.day
sun_r = build_ephem_interpolant(Sun, 365 * u.day, (j_date, j_date + tof), rtol=1e-2)
epoch = Time(j_date, format='jd', scale='tdb')
drag_force_orbit = [10085.44 * u.km, 0.025422 * u.one, 88.3924 * u.deg,
45.38124 * u.deg, 227.493 * u.deg, 343.4268 * u.deg]
initial = Orbit.from_classical(Earth, *drag_force_orbit, epoch=epoch)
# in Curtis, the mean distance to Sun is used. In order to validate against it, we have to do the same thing
sun_normalized = functools.partial(normalize_to_Curtis, sun_r=sun_r)
r, v = cowell(initial, np.linspace(0, (tof).to(u.s).value, 4000), rtol=1e-8, ad=radiation_pressure,
R=Earth.R.to(u.km).value, C_R=2.0, A=2e-4, m=100, Wdivc_s=Sun.Wdivc.value, star=sun_normalized)
delta_as, delta_eccs, delta_incs, delta_raans, delta_argps, delta_hs = [], [], [], [], [], []
for ri, vi in zip(r, v):
orbit_params = rv2coe(Earth.k.to(u.km**3 / u.s**2).value, ri, vi)
delta_eccs.append(orbit_params[1] - drag_force_orbit[1].value)
delta_incs.append((orbit_params[2] * u.rad).to(u.deg).value - drag_force_orbit[2].value)
delta_raans.append((orbit_params[3] * u.rad).to(u.deg).value - drag_force_orbit[3].value)
delta_argps.append((orbit_params[4] * u.rad).to(u.deg).value - drag_force_orbit[4].value)
# averaging over 5 last values in the way Curtis does
for check in solar_pressure_checks:
index = int(1.0 * check['t_days'] / tof.to(u.day).value * 4000)
delta_ecc, delta_inc, delta_raan, delta_argp = np.mean(delta_eccs[index - 5:index]), \
np.mean(delta_incs[index - 5:index]), np.mean(delta_raans[index - 5:index]), \
np.mean(delta_argps[index - 5:index])
assert_quantity_allclose([delta_ecc, delta_inc, delta_raan, delta_argp],
check['deltas_expected'], rtol=1e-1, atol=1e-4)
def test_sso_disposal_numerical(ecc_0, ecc_f):
a_0 = Earth.R.to(u.km).value + 900 # km
f = 2.4e-7 # km / s2, assumed constant
# Retrieve r and v from initial orbit
s0 = Orbit.from_classical(
attractor=Earth,
a=a_0 * u.km,
ecc=ecc_0 * u.one,
inc=0 * u.deg,
raan=0 * u.deg,
argp=0 * u.deg,
nu=0 * u.deg,
)
a_d, _, t_f = change_ecc_quasioptimal(s0, ecc_f, f)
# Propagate orbit
def f_ss0_disposal(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_ss0_disposal, rtol=1e-8)
assert_allclose(sf.ecc.value, ecc_f, rtol=1e-4, atol=1e-4)
def test_LOS_event():
t_los = 2327.165 * u.s
r2 = np.array([-500, 1500, 4012.09]) << u.km
v2 = np.array([5021.38, -2900.7, 1000.354]) << u.km / u.s
orbit = Orbit.from_vectors(Earth, r2, v2)
tofs = [100, 500, 1000, 2000] << u.s
# Propagate the secondary body to generate its position coordinates.
rr, vv = cowell(
Earth.k,
orbit.r,
orbit.v,
tofs,
)
pos_coords = rr # Trajectory of the secondary body.
orb = Orbit.from_classical(Earth, 16000 * u.km, 0.53 * u.one, 5 * u.deg,
5 * u.deg, 10 * u.deg, 30 * u.deg)
los_event = LosEvent(Earth, pos_coords, terminal=True)
events = [los_event]
tofs = [1, 5, 10, 100, 1000, 2000, 3000, 5000] << u.s
r, v = cowell(
Earth.k,
orb.r,
orb.v,
tofs,
events=events,
)
assert_quantity_allclose(los_event.last_t, t_los)
def test_3rd_body_Curtis(test_params):
# based on example 12.11 from Howard Curtis
body = test_params['body']
solar_system_ephemeris.set('de432s')
j_date = 2454283.0 * u.day
tof = (test_params['tof']).to(u.s).value
body_r = build_ephem_interpolant(body, test_params['period'], (j_date, j_date + test_params['tof']), rtol=1e-2)
epoch = Time(j_date, format='jd', scale='tdb')
initial = Orbit.from_classical(Earth, *test_params['orbit'], epoch=epoch)
r, v = cowell(initial, np.linspace(0, tof, 400), rtol=1e-10, ad=third_body,
k_third=body.k.to(u.km**3 / u.s**2).value, third_body=body_r)
incs, raans, argps = [], [], []
for ri, vi in zip(r, v):
angles = Angle(rv2coe(Earth.k.to(u.km**3 / u.s**2).value, ri, vi)[2:5] * u.rad) # inc, raan, argp
angles = angles.wrap_at(180 * u.deg)
incs.append(angles[0].value)
raans.append(angles[1].value)
argps.append(angles[2].value)
# averaging over 5 last values in the way Curtis does
inc_f, raan_f, argp_f = np.mean(incs[-5:]), np.mean(raans[-5:]), np.mean(argps[-5:])
assert_quantity_allclose([(raan_f * u.rad).to(u.deg) - test_params['orbit'][3],
(inc_f * u.rad).to(u.deg) - test_params['orbit'][2],
(argp_f * u.rad).to(u.deg) - test_params['orbit'][4]],
[test_params['raan'], test_params['inc'], test_params['argp']],
rtol=1e-1)
def test_umbra_event_crossing():
expected_umbra_t = Time("2020-01-01 00:04:51.328",
scale="utc") # From Orekit.
attractor = Earth
tof = 2 * u.d
epoch = Time("2020-01-01", scale="utc")
coe = (
6828137.0 * u.m,
0.0073 * u.one,
87.0 * u.deg,
20.0 * u.deg,
10.0 * u.deg,
0 * u.deg,
)
orbit = Orbit.from_classical(attractor, *coe, epoch=epoch)
umbra_event = UmbraEvent(orbit, terminal=True)
events = [umbra_event]
rr, _ = cowell(
attractor.k,
orbit.r,
orbit.v,
[tof] * u.s,
events=events,
)
assert expected_umbra_t.isclose(epoch + umbra_event.last_t, atol=1 * u.s)
def test_3rd_body_Curtis(test_params):
# based on example 12.11 from Howard Curtis
body = test_params['body']
with solar_system_ephemeris.set('builtin'):
j_date = 2454283.0 * u.day
tof = (test_params['tof']).to(u.s).value
body_r = build_ephem_interpolant(body, test_params['period'], (j_date, j_date + test_params['tof']), rtol=1e-2)
epoch = Time(j_date, format='jd', scale='tdb')
initial = Orbit.from_classical(Earth, *test_params['orbit'], epoch=epoch)
r, v = cowell(initial, np.linspace(0, tof, 400), rtol=1e-10, ad=third_body,
k_third=body.k.to(u.km**3 / u.s**2).value, third_body=body_r)
incs, raans, argps = [], [], []
for ri, vi in zip(r, v):
angles = Angle(rv2coe(Earth.k.to(u.km**3 / u.s**2).value, ri, vi)[2:5] * u.rad) # inc, raan, argp
angles = angles.wrap_at(180 * u.deg)
incs.append(angles[0].value)
raans.append(angles[1].value)
argps.append(angles[2].value)
# averaging over 5 last values in the way Curtis does
inc_f, raan_f, argp_f = np.mean(incs[-5:]), np.mean(raans[-5:]), np.mean(argps[-5:])
assert_quantity_allclose([(raan_f * u.rad).to(u.deg) - test_params['orbit'][3],
(inc_f * u.rad).to(u.deg) - test_params['orbit'][2],
(argp_f * u.rad).to(u.deg) - test_params['orbit'][4]],
[test_params['raan'], test_params['inc'], test_params['argp']],
rtol=1e-1)
def test_solar_pressure():
# based on example 12.9 from Howard Curtis
with solar_system_ephemeris.set('builtin'):
j_date = 2438400.5 * u.day
tof = 600 * u.day
sun_r = build_ephem_interpolant(Sun, 365 * u.day, (j_date, j_date + tof), rtol=1e-2)
epoch = Time(j_date, format='jd', scale='tdb')
drag_force_orbit = [10085.44 * u.km, 0.025422 * u.one, 88.3924 * u.deg,
45.38124 * u.deg, 227.493 * u.deg, 343.4268 * u.deg]
initial = Orbit.from_classical(Earth, *drag_force_orbit, epoch=epoch)
# in Curtis, the mean distance to Sun is used. In order to validate against it, we have to do the same thing
sun_normalized = functools.partial(normalize_to_Curtis, sun_r=sun_r)
r, v = cowell(initial, np.linspace(0, (tof).to(u.s).value, 4000), rtol=1e-8, ad=radiation_pressure,
R=Earth.R.to(u.km).value, C_R=2.0, A=2e-4, m=100, Wdivc_s=Sun.Wdivc.value, star=sun_normalized)
delta_eccs, delta_incs, delta_raans, delta_argps = [], [], [], []
for ri, vi in zip(r, v):
orbit_params = rv2coe(Earth.k.to(u.km**3 / u.s**2).value, ri, vi)
delta_eccs.append(orbit_params[1] - drag_force_orbit[1].value)
delta_incs.append((orbit_params[2] * u.rad).to(u.deg).value - drag_force_orbit[2].value)
delta_raans.append((orbit_params[3] * u.rad).to(u.deg).value - drag_force_orbit[3].value)
delta_argps.append((orbit_params[4] * u.rad).to(u.deg).value - drag_force_orbit[4].value)
# averaging over 5 last values in the way Curtis does
for check in solar_pressure_checks:
index = int(1.0 * check['t_days'] / tof.to(u.day).value * 4000)
delta_ecc, delta_inc, delta_raan, delta_argp = np.mean(delta_eccs[index - 5:index]), \
np.mean(delta_incs[index - 5:index]), np.mean(delta_raans[index - 5:index]), \
np.mean(delta_argps[index - 5:index])
assert_quantity_allclose([delta_ecc, delta_inc, delta_raan, delta_argp],
check['deltas_expected'], rtol=1e-1, atol=1e-4)
def init_state_obj(seed=None):
if not (seed == None):
np.random.seed(seed)
t_init = time.Time(datetime(2020, 3, 15, 0, 0, 0), scale='utc')
a = (Earth.R.value + 200000) * u.m # (Quantity) – Semi-major axis.
ecc = np.random.uniform(
0.001, 0.3) * u.dimensionless_unscaled # (Quantity) – Eccentricity.
inc = np.random.uniform(0, 180) * u.degree # (Quantity) – Inclination
raan = np.random.uniform(
0,
360) * u.degree # (Quantity) – Right ascension of the ascending node.
argp = np.random.uniform(
0, 360) * u.degree # (Quantity) – Argument of the pericenter.
nu = np.random.uniform(0, 360) * u.degree # (Quantity) – True anomaly.
epoch = t_init # (Time, optional) – Epoch, default to J2000.
plane = Planes.EARTH_EQUATOR # Fundamental plane of the frame.
return Orbit.from_classical(Earth,
a,
ecc,
inc,
raan,
argp,
nu,
epoch=epoch,
plane=plane)
def test_perifocal_points_to_perigee():
_d = 1.0 * u.AU # Unused distance
_ = 0.5 * u.one # Unused dimensionless value
_a = 1.0 * u.deg # Unused angle
ss = Orbit.from_classical(Sun, _d, _, _a, _a, _a, _a)
p, _, _ = ss.pqw()
assert_allclose(p, ss.e_vec / ss.ecc)
def _compute_results_array(a, ecc_0, ecc_f, inc_0, inc_f, argp, f):
k = Earth.k.decompose([u.km, u.s]).value
_, _, t_f = extra_quantities(k, a, ecc_0, ecc_f, inc_0, inc_f, argp, f)
# 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
)
r0, v0 = s0.rv()
combined_ei_accel = guidance_law(s0, ecc_f, inc_f, f)
# Propagate orbit
with ProgressResultsCallback(t_f) as res:
cowell(
k, r0.to(u.km).value, v0.to(u.km / u.s).value, t_f,
ad=combined_ei_accel,
callback=res,
nsteps=1000000
)
return res.get_results() # ~70 k rows, 7 columns, 3 MB in memory
def test_soyuz_standard_gto_numerical():
# Data from Soyuz Users Manual, issue 2 revision 0
r_a = (Earth.R + 35950 * u.km).to(u.km).value
r_p = (Earth.R + 250 * u.km).to(u.km).value
a = (r_a + r_p) / 2 # km
ecc = r_a / a - 1
argp_0 = (178 * u.deg).to(u.rad).value # rad
argp_f = (178 * u.deg + 5 * u.deg).to(u.rad).value # rad
f = 2.4e-7 # km / s2
k = Earth.k.to(u.km**3 / u.s**2).value
a_d, _, t_f = change_argp(k, a, ecc, argp_0, argp_f, f)
# Retrieve r and v from initial orbit
s0 = Orbit.from_classical(
Earth,
a * u.km, (r_a / a - 1) * u.one, 6 * u.deg,
188.5 * u.deg, 178 * u.deg, 0 * u.deg
)
# Propagate orbit
sf = s0.propagate(t_f * u.s, method=cowell, ad=a_d, rtol=1e-8)
assert_allclose(sf.argp.to(u.rad).value, argp_f, rtol=1e-4)
def test_bielliptic_maneuver(nu):
# Data from Vallado, example 6.2
alt_i = 191.34411 * u.km
alt_b = 503873.0 * u.km
alt_f = 376310.0 * u.km
_a = 0 * u.deg
ss_i = Orbit.from_classical(Earth,
Earth.R + alt_i,
ecc=0 * u.one,
inc=_a,
raan=_a,
argp=_a,
nu=nu)
# Expected output
expected_dv = 3.904057 * u.km / u.s
expected_t_pericenter = ss_i.time_to_anomaly(0 * u.deg)
expected_t_trans = 593.919803 * u.h
expected_total_time = expected_t_pericenter + expected_t_trans
man = Maneuver.bielliptic(ss_i, Earth.R + alt_b, Earth.R + alt_f)
assert_allclose(ss_i.apply_maneuver(man).ecc,
0 * u.one,
atol=1e-12 * u.one)
assert_quantity_allclose(man.get_total_cost(), expected_dv, rtol=1e-5)
assert_quantity_allclose(man.get_total_time(),
expected_total_time,
rtol=1e-6)
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.decompose([u.km, u.s]).value
_, _, t_f = extra_quantities(k, a, ecc_0, ecc_f, inc_0, inc_f, argp, f)
# 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)
r0, v0 = s0.rv()
optimal_accel = guidance_law(s0, ecc_f, inc_f, f)
# Propagate orbit
r, v = cowell(k,
r0.to(u.km).value,
v0.to(u.km / u.s).value,
t_f,
ad=optimal_accel,
nsteps=1000000)
sf = Orbit.from_vectors(Earth, r * u.km, v * u.km / u.s,
s0.epoch + t_f * u.s)
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 validate_coe2rv():
# Initial COE of the orbit
a, ecc, inc, raan, argp, nu = 8788e3, 0.1712, 2.6738, 4.4558, 0.3502, 0.4965
# Build Orekit orbit
k = C.IAU_2015_NOMINAL_EARTH_GM
epoch_00 = AbsoluteDate.J2000_EPOCH
gcrf_frame = FramesFactory.getGCRF()
ss0_orekit = KeplerianOrbit(a, ecc, inc, argp, raan, nu,
PositionAngle.TRUE, gcrf_frame, epoch_00, k)
# Build poliastro orbit
ss0_poliastro = Orbit.from_classical(
Earth,
a * u.m,
ecc * u.one,
inc * u.rad,
raan * u.rad,
argp * u.rad,
nu * u.rad,
)
# Retrieve Orekit final state vectors
r_orekit = ss0_orekit.getPVCoordinates().position.toArray() * u.m
v_orekit = ss0_orekit.getPVCoordinates().velocity.toArray() * u.m / u.s
# Retrieve poliastro final state vectors
r_poliastro, v_poliastro = ss0_poliastro.rv()
# Assert final state vector
assert_quantity_allclose(r_poliastro, r_orekit)
assert_quantity_allclose(v_poliastro, v_orekit)
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 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_propagating_to_certain_nu_is_correct():
# take an elliptic orbit
a = 1.0 * u.AU
ecc = 1.0 / 3.0 * u.one
_a = 0.0 * u.rad
nu = 10 * u.deg
elliptic = Orbit.from_classical(Sun, a, ecc, _a, _a, _a, nu)
elliptic_at_perihelion = elliptic.propagate_to_anomaly(0.0 * u.rad)
r_per, _ = elliptic_at_perihelion.rv()
elliptic_at_aphelion = elliptic.propagate_to_anomaly(np.pi * u.rad)
r_ap, _ = elliptic_at_aphelion.rv()
assert_quantity_allclose(norm(r_per), a * (1.0 - ecc))
assert_quantity_allclose(norm(r_ap), a * (1.0 + ecc))
# TODO: Test specific values
assert elliptic_at_perihelion.epoch > elliptic.epoch
assert elliptic_at_aphelion.epoch > elliptic.epoch
# test 10 random true anomaly values
for _ in range(10):
nu = np.random.uniform(low=0.0, high=2 * np.pi)
elliptic = elliptic.propagate_to_anomaly(nu * u.rad)
r, _ = elliptic.rv()
assert_quantity_allclose(norm(r), a * (1.0 - ecc ** 2) / (1 + ecc * np.cos(nu)))
def test_plot_maneuver():
# Data from Vallado, example 6.1
alt_i = 191.34411 * u.km
alt_f = 35781.34857 * u.km
_a = 0 * u.deg
ss_i = Orbit.from_classical(
attractor=Earth,
a=Earth.R + alt_i,
ecc=0 * u.one,
inc=_a,
raan=_a,
argp=_a,
nu=_a,
)
# Create the maneuver
man = Maneuver.hohmann(ss_i, Earth.R + alt_f)
# Plot the maneuver
fig, ax = plt.subplots()
plotter = StaticOrbitPlotter(ax=ax)
plotter.plot(ss_i, label="Initial orbit", color="blue")
plotter.plot_maneuver(ss_i, man, label="Hohmann maneuver", color="red")
return fig
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_solar_pressure(t_days, deltas_expected, sun_r):
# based on example 12.9 from Howard Curtis
with solar_system_ephemeris.set("builtin"):
j_date = 2_438_400.5 * u.day
tof = 600 * u.day
epoch = Time(j_date, format="jd", scale="tdb")
initial = Orbit.from_classical(
Earth,
10085.44 * u.km,
0.025422 * u.one,
88.3924 * u.deg,
45.38124 * u.deg,
227.493 * u.deg,
343.4268 * u.deg,
epoch=epoch,
)
# in Curtis, the mean distance to Sun is used. In order to validate against it, we have to do the same thing
sun_normalized = functools.partial(normalize_to_Curtis, sun_r=sun_r)
rr, vv = cowell(
Earth.k,
initial.r,
initial.v,
np.linspace(0, (tof).to(u.s).value, 4000) * u.s,
rtol=1e-8,
ad=radiation_pressure,
R=Earth.R.to(u.km).value,
C_R=2.0,
A_over_m=2e-4 / 100,
Wdivc_s=Wdivc_sun.value,
star=sun_normalized,
)
delta_eccs, delta_incs, delta_raans, delta_argps = [], [], [], []
for ri, vi in zip(rr.to(u.km).value, vv.to(u.km / u.s).value):
orbit_params = rv2coe(Earth.k.to(u.km**3 / u.s**2).value, ri, vi)
delta_eccs.append(orbit_params[1] - initial.ecc.value)
delta_incs.append((orbit_params[2] * u.rad).to(u.deg).value -
initial.inc.value)
delta_raans.append((orbit_params[3] * u.rad).to(u.deg).value -
initial.raan.value)
delta_argps.append((orbit_params[4] * u.rad).to(u.deg).value -
initial.argp.value)
# averaging over 5 last values in the way Curtis does
index = int(1.0 * t_days / tof.to(u.day).value * 4000 # type: ignore
)
delta_ecc, delta_inc, delta_raan, delta_argp = (
np.mean(delta_eccs[index - 5:index]),
np.mean(delta_incs[index - 5:index]),
np.mean(delta_raans[index - 5:index]),
np.mean(delta_argps[index - 5:index]),
)
assert_quantity_allclose(
[delta_ecc, delta_inc, delta_raan, delta_argp],
deltas_expected,
rtol=1e0, # TODO: Excessively low, rewrite test?
atol=1e-4,
)
def test_propagating_to_certain_nu_is_correct():
# Take an elliptic orbit
a = 1.0 * u.AU
ecc = 1.0 / 3.0 * u.one
_a = 0.0 * u.rad
nu = 10 * u.deg
elliptic = Orbit.from_classical(attractor=Sun,
a=a,
ecc=ecc,
inc=_a,
raan=_a,
argp=_a,
nu=nu)
elliptic_at_perihelion = elliptic.propagate_to_anomaly(0.0 * u.rad)
r_per, _ = elliptic_at_perihelion.rv()
elliptic_at_aphelion = elliptic.propagate_to_anomaly(np.pi * u.rad)
r_ap, _ = elliptic_at_aphelion.rv()
assert_quantity_allclose(norm(r_per), a * (1.0 - ecc))
assert_quantity_allclose(norm(r_ap), a * (1.0 + ecc))
# TODO: Test specific values
assert elliptic_at_perihelion.epoch > elliptic.epoch
assert elliptic_at_aphelion.epoch > elliptic.epoch
# Test 10 random true anomaly values
# TODO: Rework this test
for nu in np.random.uniform(low=-np.pi, high=np.pi, size=10):
elliptic = elliptic.propagate_to_anomaly(nu * u.rad)
r, _ = elliptic.rv()
assert_quantity_allclose(norm(r),
a * (1.0 - ecc**2) / (1 + ecc * np.cos(nu)))
def test_hohmann_maneuver(nu):
# Data from Vallado, example 6.1
alt_i = 191.34411 * u.km
alt_f = 35781.34857 * u.km
_a = 0 * u.deg
ss_i = Orbit.from_classical(Earth,
Earth.R + alt_i,
ecc=0 * u.one,
inc=_a,
raan=_a,
argp=_a,
nu=nu)
# Expected output
expected_dv = 3.935224 * u.km / u.s
expected_t_pericenter = ss_i.time_to_anomaly(0 * u.deg)
expected_t_trans = 5.256713 * u.h
expected_total_time = expected_t_pericenter + expected_t_trans
man = Maneuver.hohmann(ss_i, Earth.R + alt_f)
assert_quantity_allclose(man.get_total_cost(), expected_dv, rtol=1e-5)
assert_quantity_allclose(man.get_total_time(),
expected_total_time,
rtol=1e-5)
assert_quantity_allclose(ss_i.apply_maneuver(man).ecc,
0 * u.one,
atol=1e-14 * u.one)
def test_escape_velocity():
# TEST CASE 1:
# This is circular orbit, the escape velocity must be the same everywhere.
# Escape velocity for position on the ground is 11.179km/s (source BMW2, page 30)
o1 = Orbit.circular(Earth, 0*u.km)
v,vp,va = interplanetary.escape_vel(o1, False)
assert v == vp == va
assert np.abs(v - 11179 * u.m/u.s) < 1 * u.m / u.s
assert np.abs(vp - 11179 * u.m/u.s) < 1 * u.m / u.s
assert np.abs(va - 11179 * u.m/u.s) < 1 * u.m / u.s
# TEST CASE 2:
# Escape velocity for position at the altitude of 7000km is 7719km/s (source BMW2, page 30)
o2 = Orbit.circular(Earth, 7000*u.km)
v,vp,va = interplanetary.escape_vel(o2, False)
assert v == vp == va
assert np.abs(v - 7719 * u.m/u.s) < 1 * u.m / u.s
assert np.abs(vp - 7719 * u.m/u.s) < 1 * u.m / u.s
assert np.abs(va - 7719 * u.m/u.s) < 1 * u.m / u.s
o3 = Orbit.from_classical(Earth, Earth.R + 16000 * u.km, 0.5*u.one, 0*u.deg, 0*u.deg, 0*u.deg, 0*u.deg)
print_orb(o3)
v,vp,va = interplanetary.escape_vel(o3, False)
print(v, vp, va)
def test_sso_disposal_numerical(ecc_0, ecc_f):
a_0 = Earth.R.to(u.km).value + 900 # km
f = 2.4e-7 # km / s2, assumed constant
k = Earth.k.decompose([u.km, u.s]).value
_, t_f = extra_quantities(k, a_0, ecc_0, ecc_f, f)
# Retrieve r and v from initial orbit
s0 = Orbit.from_classical(Earth, a_0 * u.km, ecc_0 * u.one,
0 * u.deg, 0 * u.deg, 0 * u.deg, 0 * u.deg)
r0, v0 = s0.rv()
optimal_accel = guidance_law(s0, ecc_f, f)
# Propagate orbit
r, v = cowell(k,
r0.to(u.km).value,
v0.to(u.km / u.s).value,
t_f,
ad=optimal_accel,
nsteps=1000000)
sf = Orbit.from_vectors(Earth,
r * u.km,
v * u.km / u.s,
s0.epoch + t_f * u.s)
assert_allclose(sf.ecc.value, ecc_f, rtol=1e-4, atol=1e-4)
def test_default_time_for_new_state():
_d = 1.0 * u.AU # Unused distance
_ = 0.5 * u.one # Unused dimensionless value
_a = 1.0 * u.deg # Unused angle
_body = Sun # Unused body
expected_epoch = J2000
ss = Orbit.from_classical(_body, _d, _, _a, _a, _a, _a)
assert ss.epoch == expected_epoch
def test_sample_numpoints():
_d = 1.0 * u.AU # Unused distance
_ = 0.5 * u.one # Unused dimensionless value
_a = 1.0 * u.deg # Unused angle
_body = Sun # Unused body
ss = Orbit.from_classical(_body, _d, _, _a, _a, _a, _a)
positions = ss.sample(values=50)
assert len(positions) == 50
def test_apply_maneuver_changes_epoch():
_d = 1.0 * u.AU # Unused distance
_ = 0.5 * u.one # Unused dimensionless value
_a = 1.0 * u.deg # Unused angle
ss = Orbit.from_classical(Sun, _d, _, _a, _a, _a, _a)
dt = 1 * u.h
dv = [0, 0, 0] * u.km / u.s
orbit_new = ss.apply_maneuver([(dt, dv)])
assert orbit_new.epoch == ss.epoch + dt
def test_apply_zero_maneuver_returns_equal_state():
_d = 1.0 * u.AU # Unused distance
_ = 0.5 * u.one # Unused dimensionless value
_a = 1.0 * u.deg # Unused angle
ss = Orbit.from_classical(Sun, _d, _, _a, _a, _a, _a)
dt = 0 * u.s
dv = [0, 0, 0] * u.km / u.s
orbit_new = ss.apply_maneuver([(dt, dv)])
assert_allclose(orbit_new.r.to(u.km).value, ss.r.to(u.km).value)
assert_allclose(orbit_new.v.to(u.km / u.s).value, ss.v.to(u.km / u.s).value)
def test_sso_disposal_time_and_delta_v(ecc_0, ecc_f):
a_0 = Earth.R.to(u.km).value + 900 # km
f = 2.4e-7 # km / s2, assumed constant
expected_t_f = 29.697 # days, reverse-engineered
expected_delta_V = 0.6158 # km / s, lower than actual result
s0 = Orbit.from_classical(Earth, a_0 * u.km, ecc_0 * u.one,
0 * u.deg, 0 * u.deg, 0 * u.deg, 0 * u.deg)
_, delta_V, t_f = change_ecc_quasioptimal(s0, ecc_f, f)
assert_allclose(delta_V, expected_delta_V, rtol=1e-4)
assert_allclose(t_f / 86400, expected_t_f, rtol=1e-4)
def test_sample_with_nu_value():
_d = 1.0 * u.AU # Unused distance
_ = 0.5 * u.one # Unused dimensionless value
_a = 1.0 * u.deg # Unused angle
_body = Sun # Unused body
ss = Orbit.from_classical(_body, _d, _, _a, _a, _a, _a)
expected_r = [ss.r]
positions = ss.sample(values=ss.nu + [360] * u.deg)
r = positions.data.xyz.transpose()
assert_quantity_allclose(r, expected_r, rtol=1.e-7)
def test_3rd_body_Curtis(test_params):
# based on example 12.11 from Howard Curtis
body = test_params["body"]
with solar_system_ephemeris.set("builtin"):
j_date = 2454283.0 * u.day
tof = (test_params["tof"]).to(u.s).value
body_r = build_ephem_interpolant(
body,
test_params["period"],
(j_date, j_date + test_params["tof"]),
rtol=1e-2,
)
epoch = Time(j_date, format="jd", scale="tdb")
initial = Orbit.from_classical(Earth, *test_params["orbit"], epoch=epoch)
rr, vv = cowell(
Earth.k,
initial.r,
initial.v,
np.linspace(0, tof, 400) * u.s,
rtol=1e-10,
ad=third_body,
k_third=body.k.to(u.km ** 3 / u.s ** 2).value,
third_body=body_r,
)
incs, raans, argps = [], [], []
for ri, vi in zip(rr.to(u.km).value, vv.to(u.km / u.s).value):
angles = Angle(
rv2coe(Earth.k.to(u.km ** 3 / u.s ** 2).value, ri, vi)[2:5] * u.rad
) # inc, raan, argp
angles = angles.wrap_at(180 * u.deg)
incs.append(angles[0].value)
raans.append(angles[1].value)
argps.append(angles[2].value)
# averaging over 5 last values in the way Curtis does
inc_f, raan_f, argp_f = (
np.mean(incs[-5:]),
np.mean(raans[-5:]),
np.mean(argps[-5:]),
)
assert_quantity_allclose(
[
(raan_f * u.rad).to(u.deg) - test_params["orbit"][3],
(inc_f * u.rad).to(u.deg) - test_params["orbit"][2],
(argp_f * u.rad).to(u.deg) - test_params["orbit"][4],
],
[test_params["raan"], test_params["inc"], test_params["argp"]],
rtol=1e-1,
)
def test_sso_disposal_numerical(ecc_0, ecc_f):
a_0 = Earth.R.to(u.km).value + 900 # km
f = 2.4e-7 # km / s2, assumed constant
# Retrieve r and v from initial orbit
s0 = Orbit.from_classical(Earth, a_0 * u.km, ecc_0 * u.one,
0 * u.deg, 0 * u.deg, 0 * u.deg, 0 * u.deg)
a_d, _, t_f = change_ecc_quasioptimal(s0, ecc_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-4, atol=1e-4)
def test_propagation_hyperbolic_zero_time_returns_same_state():
ss0 = Orbit.from_classical(
Earth,
-27112.5464 * u.km,
1.25 * u.one,
0 * u.deg,
0 * u.deg,
0 * u.deg,
0 * u.deg,
)
r0, v0 = ss0.rv()
tof = 0 * u.s
ss1 = ss0.propagate(tof)
r, v = ss1.rv()
assert_allclose(r.value, r0.value)
assert_allclose(v.value, v0.value)
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)
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_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 test_soyuz_standard_gto_numerical():
# Data from Soyuz Users Manual, issue 2 revision 0
r_a = (Earth.R + 35950 * u.km).to(u.km).value
r_p = (Earth.R + 250 * u.km).to(u.km).value
a = (r_a + r_p) / 2 # km
ecc = r_a / a - 1
argp_0 = (178 * u.deg).to(u.rad).value # rad
argp_f = (178 * u.deg + 5 * u.deg).to(u.rad).value # rad
f = 2.4e-7 # km / s2
k = Earth.k.decompose([u.km, u.s]).value
optimal_accel = guidance_law(f)
_, t_f = extra_quantities(k, a, ecc, argp_0, argp_f, f)
# Retrieve r and v from initial orbit
s0 = Orbit.from_classical(
Earth,
a * u.km, (r_a / a - 1) * u.one, 6 * u.deg,
188.5 * u.deg, 178 * u.deg, 0 * u.deg
)
r0, v0 = s0.rv()
# Propagate orbit
r, v = cowell(k,
r0.to(u.km).value,
v0.to(u.km / u.s).value,
t_f,
ad=optimal_accel,
nsteps=1000000)
sf = Orbit.from_vectors(Earth,
r * u.km,
v * u.km / u.s,
s0.epoch + t_f * u.s)
assert_allclose(sf.argp.to(u.rad).value, argp_f, rtol=1e-4)
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.decompose([u.km, u.s]).value
_, _, t_f = extra_quantities(k, a, ecc_0, ecc_f, inc_0, inc_f, argp, f)
# 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
)
r0, v0 = s0.rv()
optimal_accel = guidance_law(s0, ecc_f, inc_f, f)
# Propagate orbit
r, v = cowell(k,
r0.to(u.km).value,
v0.to(u.km / u.s).value,
t_f,
ad=optimal_accel,
nsteps=1000000)
sf = Orbit.from_vectors(Earth,
r * u.km,
v * u.km / u.s,
s0.epoch + t_f * u.s)
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)
"""Example data.
"""
from astropy import time
from astropy import units as u
from poliastro.bodies import Sun, Earth
from poliastro.twobody import Orbit
# Taken from Plyades (c) 2012 Helge Eichhorn (MIT License)
iss = Orbit.from_vectors(
Earth,
[8.59072560e2, -4.13720368e3, 5.29556871e3] * u.km,
[7.37289205, 2.08223573, 4.39999794e-1] * u.km / u.s,
time.Time("2013-03-18 12:00", scale='utc')
)
molniya = Orbit.from_classical(
Earth,
26600 * u.km, 0.75 * u.one, 63.4 * u.deg,
0 * u.deg, 270 * u.deg, 80 * u.deg
)
churi = Orbit.from_classical(
Sun,
3.46250 * u.AU, 0.64 * u.one, 7.04 * u.deg,
50.1350 * u.deg, 12.8007 * u.deg, 63.89 * u.deg,
time.Time("2015-11-05 12:00", scale='utc')
)
from poliastro.twobody import Orbit
iss = Orbit.from_vectors(
Earth,
[8.59072560e2, -4.13720368e3, 5.29556871e3] * u.km,
[7.37289205, 2.08223573, 4.39999794e-1] * u.km / u.s,
time.Time("2013-03-18 12:00", scale="utc"),
)
"""ISS orbit example
Taken from Plyades (c) 2012 Helge Eichhorn (MIT License)
"""
molniya = Orbit.from_classical(
Earth, 26600 * u.km, 0.75 * u.one, 63.4 * u.deg, 0 * u.deg, 270 * u.deg, 80 * u.deg
)
"""Molniya orbit example"""
_r_a = Earth.R + 35950 * u.km
_r_p = Earth.R + 250 * u.km
_a = (_r_a + _r_p) / 2
soyuz_gto = Orbit.from_classical(
Earth, _a, _r_a / _a - 1, 6 * u.deg, 188.5 * u.deg, 178 * u.deg, 0 * u.deg
)
"""Soyuz geostationary transfer orbit (GTO) example
Taken from Soyuz User's Manual, issue 2 revision 0
"""