class TestConicOrbitEquatorial():
p = 7000 # km
ecc = 0.0
inc = 0.0
raan = 0.0
arg_p = 0.0
nu_i = 0.0
nu_f = 0.0
mu = constants.earth.mu
(state_eci, state_pqw, state_lvlh, state_sat_eci, state_sat_pqw,
state_sat_lvlh) = kepler.conic_orbit(p, ecc, inc, raan, arg_p, nu_i, nu_f,
mu)
def test_x_axis(self):
np.testing.assert_allclose(self.state_sat_eci[0], self.p)
def test_y_axis(self):
np.testing.assert_allclose(self.state_sat_eci[1], 0)
def test_z_axis(self):
np.testing.assert_allclose(self.state_sat_eci[2], 0)
def test_circular_orbit(self):
np.testing.assert_allclose(np.linalg.norm(self.state_eci[:, 0:3],
axis=1), self.p)
def test_lvlh_radial_velocity(self):
np.testing.assert_allclose(self.state_lvlh[:, 3], 0)
def test_lvlh_tangential_velocity(self):
np.testing.assert_allclose(self.state_lvlh[:, 4], np.sqrt(self.mu/self.p))
class TestConicOrbitParabolic():
p = 10000 # km
ecc = 1.0
inc = 0.0
raan = 0.0
arg_p = 0.0
nu_i = 0.0
nu_f = 0.0
(state_eci, state_pqw, state_lvlh, state_sat_eci, state_sat_pqw,
state_sat_lvlh) = kepler.conic_orbit(p, ecc, inc, raan, arg_p, nu_i, nu_f)
def test_x_axis(self):
np.testing.assert_allclose(self.state_sat_eci[0], self.p/2)
def test_y_axis(self):
np.testing.assert_allclose(self.state_sat_eci[1], 0)
def test_z_axis(self):
np.testing.assert_allclose(self.state_sat_eci[2], 0)
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')
# create the plot
# generate a plot of the orbit
_, state_pqw1, _, _, sat_pqw1, _ = kepler.conic_orbit(p_1, ecc_1, 0, 0, 0, nu_1[0], nu_1[0], mu)
_, state_pqw2, _, _, sat_pqw2, _ = kepler.conic_orbit(r_2, ecc_2, 0, 0, 0, 0, 0, mu)
# rotate the second orbit by the change in argument of perigee
fig, ax = plt.subplots()
ax.plot(state_pqw1[:, 0], state_pqw1[:, 1], label='Initial')
ax.plot(state_pqw2[:, 0], state_pqw2[:, 1], label='Final')
ax.plot([0, sat_pqw1[0]], [0, sat_pqw1[1]], 'b.-', markersize=10)
ax.set_title('Single Impulse Manuever')
ax.set_xlabel(r'$\hat p$')
ax.set_ylabel(r'$\hat q$')
plt.legend()
plt.show()
# define orbital elements
a = 3 * constants.earth.radius
ecc = 0.4
p = kepler.semilatus_rectum(a, ecc)
inc = np.deg2rad(28.5)
raan = np.deg2rad(45)
argp = np.deg2rad(90)
nu = np.deg2rad(235)
mu = constants.earth.mu
re = constants.earth.radius
output = kepler.orbit_el(p, ecc, inc, raan, argp, nu, mu, True)
# generate a plot of orbit plane
# plot the orbit
state_eci, state_pqw, state_lvlh, state_sat_eci, state_sat_pqw, state_sat_lvlh = kepler.conic_orbit(
p, ecc, inc, raan, argp, nu, nu)
fig, ax = plt.subplots()
ax.plot(state_pqw[:, 0], state_pqw[:, 1])
ax.plot(re * np.cos(np.linspace(0, 2 * np.pi)),
re * np.sin(np.linspace(0, 2 * np.pi)))
ax.plot([0, state_sat_pqw[0]], [0, state_sat_pqw[1]], 'b-', linewidth=3)
ax.plot(state_sat_pqw[0], state_sat_pqw[1], 'b.', markersize=20)
ax.set_xlabel(r'$\hat p$')
ax.set_ylabel(r'$\hat q$')
plt.axis('equal')
plt.show()
with open('prob3_sol.txt', 'w') as f:
f.write(output)
r_lvlh[0], r_lvlh[1], r_lvlh[2], v_lvlh[0], v_lvlh[1], v_lvlh[2]))
# get orbital paramters
param_string = kepler.orbit_el(sat.coe.p, sat.coe.ecc, sat.coe.inc,
sat.coe.raan, sat.coe.argp, sat.coe.nu,
constants.earth.mu)
answer_file.write('\n{} {}\n{}'.format(sat.satname, sat.satnum,
param_string))
print(sat.satname, sat.satnum)
print(param_string)
# create the plot of the orbit in the PQW reference frame
pos_eci, sat_eci, pos_pqw, sat_pqw = kepler.conic_orbit(
sat.coe.p, sat.coe.ecc, sat.coe.inc, sat.coe.raan, sat.coe.argp,
sat.coe.nu, sat.coe.nu)
fig, ax = plt.subplots()
ax.plot(pos_pqw[:, 0], pos_pqw[:, 1])
ax.plot(sat_pqw[0], sat_pqw[1], 'bo', markersize=9)
ax.plot(0, 0, 'ko', markersize=20)
ax.set_title(sat.satname)
ax.set_xlabel(r'$ \hat p (km)$')
ax.set_ylabel(r'$ \hat q (km)$')
plt.axis('equal')
plt.grid()
plt.savefig(str(sat.satnum) + '.pdf')
ofile.close()
answer_file.close()
print('V1 : {} km/sec'.format(va1))
print('DV1 : {} km/sec'.format(np.absolute(dva1)))
print('TOF : {} sec = {} hr'.format(toft, toft / 3600))
print('\nPhasing Orbit')
print('Period Phasing : {} sec'.format(phasing_period))
print('Phasing orbit : a = {} km, ecc = {}'.format(a_p, ecc_p))
print('\nTransfer from hohmann ellipse to phasing orbit')
print('DV2 : {} km/sec'.format(dvb1))
print('\nTransfer from phasing orbit to final orbit')
print('DV3 : {} km/sec'.format(dvb2))
# generate a plot of the orbit
_, state_pqw1, _, _, sat_pqw1, _ = kepler.conic_orbit(np.absolute(p_h), ecc_h,
0, 0, 0, -np.deg2rad(10),
np.deg2rad(10), mu)
_, state_pqw2, _, _, sat_pqw2, _ = kepler.conic_orbit(p_t, ecc_t, 0, 0, 0, 0,
0, mu)
_, state_pqw3, _, _, sat_pqw3, _ = kepler.conic_orbit(rb, 0, 0, 0, 0, 0, 0, mu)
_, state_pqw4, _, _, sat_pqw4, _ = kepler.conic_orbit(p_p, ecc_p, 0, 0, 0, 0,
0, mu)
# rotate new orbit
fig, ax = plt.subplots()
ax.plot(state_pqw1[:, 0], state_pqw1[:, 1], label='Initial')
ax.plot(state_pqw2[:, 0], state_pqw2[:, 1], label='Transfer')
ax.plot(state_pqw3[:, 0], state_pqw3[:, 1], label='Final')
ax.plot(state_pqw4[:, 0], state_pqw4[:, 1], label='Phasing')
print('Orbital Elements just before burn')
kepler.orbit_el(p, ecc, 0, 0, 0, nuf, mu, True)
out = kepler.elp_orbit_el(p, ecc, 0, 0, 0, nuf, mu)
r1 = np.linalg.norm(out[7])
v1 = np.linalg.norm(out[8])
fpa1 = out[4]
# compute burn
rf, vf, fpaf = manuever.single_impulse(r1, v1, fpa1, delta_v, alpha)
an, pn, eccn, nun = manuever.rvfpa2orbit_el(rf, vf, fpaf, mu)
delta_arg_p = nuf - nun
print('Orbital Elements after burn')
kepler.orbit_el(pn, eccn, 0, 0, delta_arg_p, nun, mu, True)
# generate a plot of the orbit
_, state_pqw1, _, _, sat_pqw1, _ = kepler.conic_orbit(p, ecc, 0, 0, 0, nuf, nuf, mu)
_, state_pqw2, _, _, sat_pqw2, _ = kepler.conic_orbit(pn, eccn, 0, 0, 0, nun, nun, mu)
# rotate the second orbit by the change in argument of perigee
rot_old2new = attitude.rot3(delta_arg_p)
state_pqw2 = rot_old2new.dot(state_pqw2[:, 0:3].T).T
sat_pqw2 = rot_old2new.dot(sat_pqw2[0:3])
fig, ax = plt.subplots()
ax.plot(state_pqw1[:, 0], state_pqw1[:, 1], label='Initial')
ax.plot(state_pqw2[:, 0], state_pqw2[:, 1], label='Final')
ax.plot([0, sat_pqw2[0]], [0, sat_pqw2[1]], 'b.-', markersize=10)
ax.set_title('Single Impulse Manuever')
ax.set_xlabel(r'$\hat p$')
ax.set_ylabel(r'$\hat q$')
state[ii, :], _ = spice.spkezr('Cassini', et, 'J2000', 'None',
'SATURN BARYCENTER')
initial_state = state[0, :]
# comppute position/velocity in the orbital plane
print('Cassini pos: {} km'.format(initial_state[0:3]))
print('Cassini vel: {} km/sec'.format(initial_state[3:6]))
# compute some orbital elements of the vehicle
mu = constants.saturn.mu
p, a, ecc, inc, raan, arg_p, nu, m, arglat, truelon, lonper = kepler.rv2coe(
initial_state[0:3], initial_state[3:6], mu)
kepler.orbit_el(p, ecc, inc, raan, arg_p, nu, mu, print_flag=True)
# students should generate a plot of the orbit (conic equation)
pos_inertial, sat_inertial, pos_pqw, sat_pqw = kepler.conic_orbit(
p, ecc, inc, raan, arg_p, nu, nu)
rsaturn = constants.saturn.radius
pqw_fig, pqw_ax = plt.subplots()
pqw_ax.plot(pos_pqw[:, 0] / rsaturn, pos_pqw[:, 1] / rsaturn)
pqw_ax.plot(sat_pqw[0] / rsaturn, sat_pqw[1] / rsaturn, 'bo', markersize=10)
pqw_ax.plot(0, 0, 'bo', markersize=20)
pqw_ax.set_xlabel(r'$\hat p (r_{\saturn})$')
pqw_ax.set_ylabel(r'$\hat q (r_{\saturn})$')
pqw_ax.set_title(r'Cassini Orbit in Perifocal Reference Frame')
pqw_ax.grid()
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(state[:, 0] / rsaturn, state[:, 1] / rsaturn, state[:, 2] / rsaturn,
'b-')
ax.set_title(r'Cassini Sep 15, 2004 to Sep 15, 2005')
mu_e = constants.earth.mu
r_p = 1000 + re
ecc = 1.05
nu = np.deg2rad(90)
nu_1 = np.deg2rad(90)
nu_2 = np.deg2rad(150)
a, p = kepler.hyp_per2sma(r_p, ecc)
# compute orbit properties
print("Properties at nu=90")
output = "Properties at nu=90 deg\n"
output += kepler.orbit_el(p, ecc, 0, 0, 0, nu, mu_e, True)
# plot the orbit
state_eci, state_pqw, state_lvlh, state_sat_eci, state_sat_pqw, state_sat_lvlh = kepler.conic_orbit(
p, ecc, 0, 0, 0, -np.deg2rad(135), np.deg2rad(135))
# orbit properties at second nu
print("Properties at nu=150")
output += "Properties at nu=150 deg\n"
output += kepler.orbit_el(p, ecc, 0, 0, 0, np.deg2rad(150), mu_e, True)
# time of flight
tof = kepler.tof_nu(p, ecc, nu_1, nu_2, mu_e)
print('Time of flight from 90 to 150 deg: {} sec = {} hrs'.format(
tof, tof / 3600))
output += 'Time of flight from 90 to 150 deg: {} sec = {} hrs'.format(
tof, tof / 3600)
fig, ax = plt.subplots()
ax.plot(state_pqw[:, 0], state_pqw[:, 1])
# properties of new orbit
rf, vf, fpaf = maneuver.single_impulse(np.linalg.norm(rpqw_i),
np.linalg.norm(vpqw_i), fpa_i, mag_dv,
alpha)
nu_f = maneuver.nu_solve(rf, vf, fpaf, mu)
print('V2 : {} km/sec'.format(vf))
print('FPAf : {} deg'.format(np.rad2deg(fpaf)))
delta_arg_p = nu_i - nu_f
print('Final orbit after maneuver')
a_f, p_f, ecc_f, nu_f = maneuver.rvfpa2orbit_el(rf, vf, fpaf, mu)
kepler.orbit_el(p_f, ecc_f, inc_i, raan_i, arg_p_i, nu_f, mu, 'True')
# generate a plot of the orbit
_, state_pqw1, _, _, sat_pqw1, _ = kepler.conic_orbit(p_i, ecc_i, 0, 0, 0,
nu_i, nu_i, mu)
_, state_pqw2, _, _, sat_pqw2, _ = kepler.conic_orbit(p_f, ecc_f, 0, 0, 0,
nu_f, nu_f, mu)
rot_old2new = attitude.rot3(delta_arg_p)
state_pqw2 = rot_old2new.dot(state_pqw2[:, 0:3].T).T
sat_pqw2 = rot_old2new.dot(sat_pqw2[0:3])
# rotate new orbit
fig, ax = plt.subplots()
ax.plot(state_pqw1[:, 0], state_pqw1[:, 1], label='Initial')
ax.plot(state_pqw2[:, 0], state_pqw2[:, 1], label='Final')
ax.plot([0, sat_pqw1[0]], [0, sat_pqw1[1]], 'b.', markersize=10)
ax.set_title('Single Impulse - Maneuver at 90')
(dv_a, dv_b, tof, phase_angle) = maneuver.hohmann(
a_e, a_n, ecc_e, ecc_n, 0, np.pi, mu)
print('Initial Orbit Velocity : {} km/sec'.format(v_1))
print('Final Orbit Velocity : {} km/sec'.format(v_2))
print('Transfer SMA : {} km Eccentricity : {}'.format(a_t, ecc_t))
print('Transfer Periapsis velocity : {} km/sec'.format(vt_1))
print('Transfer Apoapsis velocity : {} km/sec'.format(vt_2))
print('Delta V1 : {} km/sec'.format(dv_a))
print('Delta V2 : {} km/sec'.format(dv_b))
print('TOF : {} sec = {} day = {} yr'.format(tof, tof/86400, tof/86400/365.25))
print('Phase : {} deg'.format(np.rad2deg(phase_angle)))
# generate a plot of the orbit
_, state_pqw1, _, _, sat_pqw1, _ = kepler.conic_orbit(a_e, 0, 0, 0, 0, 0, 0, mu)
_, state_pqw2, _, _, sat_pqw2, _ = kepler.conic_orbit(a_n, 0, 0, 0, 0, np.pi, np.pi, mu)
_, state_pqw3, _, _, sat_pqw3, _ = kepler.conic_orbit(p_t, ecc_t, 0, 0, 0, 0, np.pi, mu)
fig, ax = plt.subplots()
ax.plot(state_pqw1[:, 0], state_pqw1[:, 1], label='Earth')
ax.plot(state_pqw2[:, 0], state_pqw2[:, 1], label='Neptune')
ax.plot(state_pqw3[:, 0], state_pqw3[:, 1], label='Transfer')
ax.set_title('Hohmann Transfer')
ax.set_xlabel(r'$\hat p$')
ax.set_ylabel(r'$\hat q$')
plt.axis('equal')
plt.legend()
plt.show()
rp, = ax.plot(roadster_ecliptic[0],
roadster_ecliptic[1],
marker='o',
color='r')
mcp, = ax.plot(mercury_ecliptic[0], mercury_ecliptic[1], marker='o', color='c')
vp, = ax.plot(venus_ecliptic[0], venus_ecliptic[1], marker='o', color='m')
ep, = ax.plot(earth_ecliptic[0], earth_ecliptic[1], marker='o', color='g')
mp, = ax.plot(mars_ecliptic[0], mars_ecliptic[1], marker='x', color='b')
# draw conic orbits
mercury_inertial, _, _, _, _, _ = kepler.conic_orbit(mercury_coe.p,
mercury_coe.ecc,
mercury_coe.inc,
mercury_coe.raan,
mercury_coe.argp,
0,
2 * np.pi,
mu=constants.sun.mu)
venus_inertial, _, _, _, _, _ = kepler.conic_orbit(venus_coe.p,
venus_coe.ecc,
venus_coe.inc,
venus_coe.raan,
venus_coe.argp,
0,
2 * np.pi,
mu=constants.sun.mu)
earth_inertial, _, _, _, _, _ = kepler.conic_orbit(earth_coe.p,
earth_coe.ecc,
earth_coe.inc,
earth_coe.raan,
print('Alpha (angle from Vhat) : {} deg'.format(np.rad2deg(alpha)))
r_initial = r_inertial
v_initial = v_inertial
r_final = r_initial
v_final = dv_inertial+v_initial
# find orbital elements of new orbit
( p_n,a_n,ecc_n,inc_n,raan_n,arg_p_n,nu_n,_,_,_,_) = kepler.rv2coe(r_final,v_final, mu)
print('Final Orbit')
kepler.orbit_el(p_n,ecc_n,inc_n,raan_n,arg_p_n,nu_n,mu,'True')
# generate a plot of the orbit
state_mci1, state_pqw1, _, sat_mci1, _, _ = kepler.conic_orbit(p, ecc, inc, raan, arg_p, nu, nu, mu)
state_mci2, state_pqw2, _, sat_mci2,_, _ = kepler.conic_orbit(p_n, ecc_n, inc_n, raan_n, arg_p_n, nu_n, nu_n, mu)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(state_mci1[:, 0],state_mci1[:, 1], state_mci1[:, 2], label='Initial')
ax.plot(state_mci2[:, 0],state_mci2[:, 1], state_mci2[:, 2], label='Final')
ax.plot([0, sat_mci1[0]], [0, sat_mci1[1]], [0, sat_mci1[2]], 'b.-', markersize=10)
ax.scatter(0, 0, 0,s=1000)
ax.set_title('Single Impulse Manuever')
ax.set_xlabel(r'$\hat x$')
ax.set_ylabel(r'$\hat y$')
ax.set_zlabel(r'$\hat z$')
plt.axis('equal')
plt.legend()