class TestHNEVector_elliptical_equatorial():
r, v, _, _ = kepler.coe2rv(10000, 0.2, 0, 0, 0, 0, constants.earth.mu)
h, n, e = kepler.hne_vec(r, v, constants.earth.mu)
def test_h_vec(self):
np.testing.assert_allclose(self.h, np.array([0, 0, 1]))
def test_n_vec(self):
np.testing.assert_allclose(self.n, np.zeros(3))
def test_e_vec(self):
np.testing.assert_allclose(self.e, np.array([1, 0, 0]))
def test_coe2rv_polar_circular():
"""Test COE to RV for polar circular orbit around Earth"""
p = 6378.137 # km
ecc = 0.0
inc = np.pi/2
raan = 0.0
arg_p = 0.0
nu = 0.0
mu = 398600.5 # km^3 /sec^2
R_ijk_true = np.array([6378.137,0,0])
V_ijk_true = np.sqrt(mu/p) * np.array([0.0,0.0,1])
R_ijk, V_ijk, R_pqw, V_pqw = kepler.coe2rv(p,ecc,inc,raan,arg_p,nu, mu)
np.testing.assert_array_almost_equal(R_ijk_true,R_ijk)
np.testing.assert_array_almost_equal(V_ijk_true,V_ijk)
def test_coe2rv_curtis():
"""Test COE to RV for Curtis example 4.3"""
p_true = 80000**2/398600
ecc_true = 1.4
inc_true = np.deg2rad(30)
raan_true = np.deg2rad(40)
arg_p_true = np.deg2rad(60)
nu_true = np.deg2rad(30)
mu = 398600 # km^3 /sec^2
R_ijk_true = np.array([-4040, 4815, 3629])
V_ijk_true = np.array([-10.39, -4.772, 1.744])
R_ijk, V_ijk, R_pqw, V_pqw = kepler.coe2rv(p_true,ecc_true,inc_true,raan_true,arg_p_true,nu_true, mu)
np.testing.assert_allclose(R_ijk,R_ijk_true, rtol=1e0)
np.testing.assert_allclose(V_ijk,V_ijk_true, rtol=1e0)
def test_coe2rv_vallado():
"""Test COE to RV for Vallado example 2-6"""
p_true = 1.735272 * constants.earth.radius # km
ecc_true = 0.832853
inc_true = np.deg2rad(87.87)
raan_true = np.deg2rad(227.89)
arg_p_true = np.deg2rad(53.38)
nu_true = np.deg2rad(92.336)
mu = 398600.5 # km^3 /sec^2
R_ijk_true = np.array([6525.5454,6861.7313, 6449.0585])
V_ijk_true = np.array([4.902227, 5.533085, -1.975757])
R_ijk, V_ijk, R_pqw, V_pqw = kepler.coe2rv(p_true,ecc_true,inc_true,raan_true,arg_p_true,nu_true, mu)
np.testing.assert_allclose(R_ijk,R_ijk_true, rtol=1e-4)
np.testing.assert_allclose(V_ijk,V_ijk_true, rtol=1e-4)
def roadster_coe(jd):
"""Output the COES of the roadster at the given JD
"""
epoch = 2458190.500000000
ecc = 2.560214125839113E-01 # eccentricy
per = 9.860631722474498E-01 * au2km # periapsis
inc = 1.078548455272089E+00 * deg2rad # inclination
raan = 3.171871226218810E+02 * deg2rad #
arg_p = 1.774087594994931E+02 * deg2rad
jd_per = 2458153.531206728425
mean_motion = 6.459332187157216E-01 * deg2rad * sec2day
mean_anom = 2.387937163002724E+01 * deg2rad
E, nu, count = kepler.kepler_eq_E(mean_anom, ecc)
nu = 4.031991175737090E+01 * deg2rad
sma = 1.325391871387247E+00 * au2km
apo = 1.664720570527044E+00 * au2km
period = 5.573331570030891E+02 * day2sec
# compute some other elements
p = kepler.semilatus_rectum(sma, ecc)
deltat = (jd - epoch) * day2sec
# propogate from epoch to JD and find nu
Ef, Mf, nuf = kepler.tof_delta_t(p, ecc, constants.sun.mu, nu, deltat)
roadster_coe = planets.COE(p=p,
ecc=ecc,
inc=inc,
raan=raan,
argp=arg_p,
nu=nuf)
# compute the vector in J2000 Ecliptic frame
r_ecliptic, v_ecliptic, r_pqw, v_pqw = kepler.coe2rv(
p, ecc, inc, raan, arg_p, nuf, constants.sun.mu)
return roadster_coe, r_ecliptic, v_ecliptic
# initial orbit parameters
a_1 =6*re2km
ecc_1 = .5
nu_0 = 0
p_1 = a_1*(1-ecc_1**2)
# desired orbit altitude - location of manuever
r_1 = 7.6*re2km
# find intersection of original orbit and desired orbit - true anomaly
nu_1 = kepler.nu_solve(p_1, ecc_1, r_1)
# conditions of orbit just prior to burn
print('Initial Orbit prior to manuever')
kepler.orbit_el(p_1, ecc_1, 0, 0, 0, nu_1[0], mu, 'True')
_,_, r1_pqw, v1_pqw= kepler.coe2rv(p_1, ecc_1, 0, 0, 0, nu_1[0], mu)
fpa1 = kepler.fpa_solve(nu_1[0], ecc_1)
# properties of desired orbit at manuever point
r_2 = r_1
ecc_2 = 0
_,_, r2_pqw, v2_pqw= kepler.coe2rv(r_2, ecc_2, 0, 0, 0, nu_1[0], mu)
delta_v, alpha, beta = manuever.delta_v_solve_planar(np.linalg.norm(v1_pqw),
np.linalg.norm(v2_pqw),
fpa1, 0)
print('Delta V: {} km/sec'.format(delta_v))
print('Alpha: {} deg, Beta: {} deg'.format(np.rad2deg(alpha), np.rad2deg(beta)))
# final orbit properties
print('Final Orbit after manuever')
kepler.orbit_el(r_2, ecc_2, 0, 0, 0, nu_1[0], mu, 'True')
def tle_update(self, jd_span, mu=398600.5):
"""Update the state of satellite given a JD time span
This procedure uses the method of general perturbations to update
classical elements from epoch to a future time for inclined elliptical
orbits. It includes the effects due to first order secular rates
(second order for mean motion) caused by drag and J2.
Author: C2C Shankar Kulumani USAFA/CS-19 719-333-4741
Inputs:
deltat - elapsed time since epoch (sec)
n0 - mean motion at epoch (rad/sec)
ndot2 - mean motion rate divided by 2 (rad/sec^2)
ecc0 - eccentricity at epoch (unitless)
eccdot - eccentricity rate (1/sec)
raan0 - RAAN at epoch (rad)
raandot - RAAN rate (rad/sec)
argp0 - argument of periapsis at epoch (rad)
argdot - argument of periapsis rate (rad/sec)
mean0 - mean anomaly at epoch
Outputs:
n - mean motion at epoch + deltat (rad/sec)
ecc - eccentricity at epoch + deltat (unitless)
raan - RAAN at epoch + deltat (rad)
argp - argument of periapsis at epoch + deltat (rad)
nu - true anomaly at epoch + deltat (rad)
Globals: None
Constants: None
Coupling:
newton.m
References:
Astro 321 PREDICT LSN 24-25
"""
deltat = (jd_span - self.epoch_jd) * day2sec
# epoch orbit parameters
n0 = self.n0
ecc0 = self.ecc0
ndot2 = self.ndot2
nddot6 = self.nddot6
raan0 = self.raan0
argp0 = self.argp0
mean0 = self.mean0
inc0 = self.inc0
adot = self.adot
eccdot = self.eccdot
raandot = self.raandot
argpdot = self.argpdot
_, nu0, _ = kepler.kepler_eq_E(mean0, ecc0)
a0 = kepler.n2a(n0, mu)
M0, E0 = kepler.nu2anom(nu0, ecc0)
# propogated elements
a1 = a0 + adot * deltat # either use this or compute a1 from n1 instead
ecc1 = ecc0 + eccdot * deltat
raan1 = raan0 + raandot * deltat
argp1 = argp0 + argpdot * deltat
inc1 = inc0 * np.ones_like(ecc1)
n1 = n0 + ndot2 * 2 * deltat
# a1 = kepler.n2a(n1, mu)
p1 = kepler.semilatus_rectum(a1, ecc1)
M1 = M0 + n0 * deltat+ ndot2 *deltat**2 + nddot6 *deltat**3
M1 = attitude.normalize(M1, 0, 2 * np.pi)
E1, nu1, _ = kepler.kepler_eq_E(M1, ecc1)
# convert to vectors
r_eci, v_eci, _, _ = kepler.coe2rv(p1, ecc1, inc1, raan1, argp1, nu1, mu)
# save all of the variables to the object
self.jd_span = jd_span
self.coe = COE(n=n1, ecc=ecc1, raan=raan1, argp=argp1, mean=M1,
E=E1, nu=nu1, a=a1, p=p1, inc=inc1)
self.r_eci = r_eci
self.v_eci = v_eci
return 0
ecc_i = .4
a_i = 6 * re2km
nu_i = 90 * deg2rad
p_i = kepler.semilatus_rectum(a_i, ecc_i)
inc_i = 0
raan_i = 0
arg_p_i = 0
mag_dv = 0.75
alpha = -60 * deg2rad
# calculate orbital elements
print('Initial Orbit')
kepler.orbit_el(p_i, ecc_i, inc_i, raan_i, arg_p_i, nu_i, mu, 'True')
_, _, rpqw_i, vpqw_i = kepler.coe2rv(p_i, ecc_i, inc_i, raan_i, arg_p_i, nu_i,
mu)
fpa_i = kepler.fpa_solve(nu_i, ecc_i)
# convert delta v and alpha into various reference frames
(dv_vnc, dv_lvlh) = maneuver.delta_v_vnc(mag_dv, alpha, 0, fpa_i)
# transform delta v to pqw frame
R_lvlh2pqw = transform.dcm_lvlh2pqw(nu_i)
dv_pqw = R_lvlh2pqw.dot(dv_lvlh)
print('DV : {} V {} C {} N km/sec'.format(dv_vnc[0], dv_vnc[1], dv_vnc[2]))
print('DV : {} R {} T {} H km/sec'.format(dv_lvlh[0], dv_lvlh[1], dv_lvlh[2]))
print('DV : {} P {} Q {} W km/sec'.format(dv_pqw[0], dv_pqw[1], dv_pqw[2]))
# properties of new orbit
rf, vf, fpaf = maneuver.single_impulse(np.linalg.norm(rpqw_i),
np.linalg.norm(vpqw_i), fpa_i, mag_dv,
def tle_update(self, jd_span, mu=398600.5):
"""Update the state of satellite given a JD time span
This procedure uses the method of general perturbations to update
classical elements from epoch to a future time for inclined elliptical
orbits. It includes the effects due to first order secular rates
(second order for mean motion) caused by drag and J2.
Author: C2C Shankar Kulumani USAFA/CS-19 719-333-4741
Inputs:
deltat - elapsed time since epoch (sec)
n0 - mean motion at epoch (rad/sec)
ndot2 - mean motion rate divided by 2 (rad/sec^2)
ecc0 - eccentricity at epoch (unitless)
eccdot - eccentricity rate (1/sec)
raan0 - RAAN at epoch (rad)
raandot - RAAN rate (rad/sec)
argp0 - argument of periapsis at epoch (rad)
argdot - argument of periapsis rate (rad/sec)
mean0 - mean anomaly at epoch
Outputs:
n - mean motion at epoch + deltat (rad/sec)
ecc - eccentricity at epoch + deltat (unitless)
raan - RAAN at epoch + deltat (rad)
argp - argument of periapsis at epoch + deltat (rad)
nu - true anomaly at epoch + deltat (rad)
Globals: None
Constants: None
Coupling:
newton.m
References:
Astro 321 PREDICT LSN 24-25
"""
deltat = (jd_span - self.epoch_jd) * day2sec
# epoch orbit parameters
n0 = self.n0
ecc0 = self.ecc0
ndot2 = self.ndot2
nddot6 = self.nddot6
raan0 = self.raan0
argp0 = self.argp0
mean0 = self.mean0
inc0 = self.inc0
adot = self.adot
eccdot = self.eccdot
raandot = self.raandot
argpdot = self.argpdot
_, nu0, _ = kepler.kepler_eq_E(mean0, ecc0)
a0 = kepler.n2a(n0, mu)
M0, E0 = kepler.nu2anom(nu0, ecc0)
# propogated elements
a1 = a0 + adot * deltat # either use this or compute a1 from n1 instead
ecc1 = ecc0 + eccdot * deltat
raan1 = raan0 + raandot * deltat
argp1 = argp0 + argpdot * deltat
inc1 = inc0 * np.ones_like(ecc1)
n1 = n0 + ndot2 * 2 * deltat
# a1 = kepler.n2a(n1, mu)
p1 = kepler.semilatus_rectum(a1, ecc1)
M1 = M0 + n0 * deltat + ndot2 * deltat**2 + nddot6 * deltat**3
M1 = attitude.normalize(M1, 0, 2 * np.pi)
E1, nu1, _ = kepler.kepler_eq_E(M1, ecc1)
# convert to vectors
r_eci, v_eci, _, _ = kepler.coe2rv(p1, ecc1, inc1, raan1, argp1, nu1,
mu)
# save all of the variables to the object
self.jd_span = jd_span
self.coe = COE(n=n1,
ecc=ecc1,
raan=raan1,
argp=argp1,
mean=M1,
E=E1,
nu=nu1,
a=a1,
p=p1,
inc=inc1)
self.r_eci = r_eci
self.v_eci = v_eci
return 0
mu = constants.mars.mu
deg2rad = constants.deg2rad
rad2deg = constants.rad2deg
# initial orbit elements
a = 5*r_mars
ecc =.5
p = kepler.semilatus_rectum(a, ecc)
inc = 30*deg2rad
raan = 45*deg2rad
arg_p = -60*deg2rad
nu = 120*deg2rad
print('Initial Mars Orbit')
kepler.orbit_el(p,ecc,inc,raan,arg_p,nu,mu,'True')
r_inertial, v_inertial, _, _ = kepler.coe2rv(p, ecc, inc, raan, arg_p, nu, mu)
fpa = kepler.fpa_solve(nu, ecc)
# delta v in inertial coordinates
dv_inertial = np.array([0.1,-0.25,0.2])
# form rotation matrix to go from mars inertial frame to LVLH frame
dcm_mci2pqw = transform.dcm_eci2pqw_coe(raan, inc, arg_p)
dcm_pqw2lvlh = transform.dcm_pqw2lvlh(nu)
dv_lvlh = dcm_pqw2lvlh.dot(dcm_mci2pqw).dot(dv_inertial)
print('Delta V : {} rhat {} that {} hhat km/sec'.format(dv_lvlh[0], dv_lvlh[1], dv_lvlh[2]))
mag_dv = np.linalg.norm(dv_lvlh)
mag_dv_outofplane = dv_lvlh[2]
mag_dv_inplane = np.linalg.norm(dv_lvlh[0:1])
print('Percentage out of plane : {} %'.format(mag_dv_outofplane / mag_dv * 100))