def solution(infile='./data/RV2.txt', outfile='./data/RV2_solution.txt'):
"""Generate the solution that students should be able to match
"""
mu = constants.earth.mu
output_string = ''
with open(infile, 'r') as f:
line = f.readline().split()
while line:
r_in = np.array([float(i) for i in line[0:3]])
v_in = np.array([float(i) for i in line[3:6]])
dt = float(line[6])
# convert to coe
p, a, ecc, inc, raan, arg_p, nu, _, _, _, _ = kepler.rv2coe(
r_in, v_in, mu)
# propagate forward
E_f, M_f, nu_f = kepler.tof_delta_t(p, ecc, mu, nu, dt)
# compute elements at future time
prop_string = kepler.orbit_el(p, ecc, inc, raan, arg_p, nu_f, mu)
output_string += prop_string
line = f.readline().split()
with open(outfile, 'w') as f:
f.write(output_string)
def example_one():
re = constants.earth.radius
r = np.array([1.6772 * re, -1.6772 * re,
2.3719 * re]) # position in ECI in kilometers
v = np.array([3.1544, 2.4987, 0.4658]) # velocity in ECI in km/sec
a, ecc, inc, raan, argp, nu = kepler.rv2coe(r, v)
class TestEllipticalOribtProperties():
# test case from RV2COE Astro 321, MAE3145
r = np.array([8840.0, 646, 5455])
v = np.array([-0.695, 5.25, -1.65])
r_mag_true = 10407.6866
v_mag_true = 5.5469
r_per_true = 6260.5311
r_apo_true = 11134.4744
energy_true = -22.9147
period_true = 2.2423
sma_true = 8697.5027
ecc_true = 0.2802
inc_true = 33.9987
raan_true = 250.0287
arg_p_true = 255.5372
nu_true = 214.8548
mu = constants.earth.mu
p, a, ecc, inc, raan, arg_p, nu, _, _, _, _ = kepler.rv2coe(r, v, mu)
( a, h, period, sme, fpa, r_per, r_apo, r_ijk, v_ijk,
r_pqw, v_pqw, r_lvlh, v_lvlh, r, v, v_circ, v_esc,
E, M, n ) = kepler.elp_orbit_el(p,ecc,inc,raan,arg_p,nu,mu)
def test_r_mag(self):
np.testing.assert_allclose(np.linalg.norm(self.r_ijk), self.r_mag_true, rtol=1e-4)
def test_v_mag(self):
np.testing.assert_allclose(np.linalg.norm(self.v_ijk), self.v_mag_true, rtol=1e-4)
def test_r_per(self):
np.testing.assert_allclose(self.r_per, self.r_per_true, rtol=1e-4)
def test_r_apo(self):
np.testing.assert_allclose(self.r_apo, self.r_apo_true, rtol=1e-4)
def test_energy(self):
np.testing.assert_allclose(self.sme, self.energy_true, rtol=1e-4)
def test_period(self):
np.testing.assert_allclose(self.period*constants.sec2hr, self.period_true, rtol=1e-4)
def test_sma(self):
np.testing.assert_allclose(self.a, self.sma_true, rtol=1e-4)
def test_ecc(self):
np.testing.assert_allclose(self.ecc, self.ecc_true, rtol=1e-4)
def test_inc(self):
np.testing.assert_allclose(self.inc*constants.rad2deg, self.inc_true, rtol=1e-4)
def test_raan(self):
np.testing.assert_allclose(self.raan*constants.rad2deg, self.raan_true, rtol=1e-4)
def test_arg_p(self):
np.testing.assert_allclose(self.arg_p*constants.rad2deg, self.arg_p_true, rtol=1e-4)
class Testrv2coeRV1():
a_true = 8697.5027
ecc_true = 0.2802
p_true = a_true * ( 1 - ecc_true**2)
inc_true = np.deg2rad(33.9987)
raan_true = np.deg2rad(250.0287)
arg_p_true = np.deg2rad(255.5372)
nu_true = np.deg2rad(214.8548)
mu = 398600.5
r = np.array([8840, 646, 5455])
v = np.array([-0.6950, 5.250, -1.65])
p, a, ecc, inc, raan, arg_p, nu, m, arglat, truelon, lonper = kepler.rv2coe(r, v, mu)
def test_p(self):
np.testing.assert_allclose(self.p, self.p_true, rtol=1e-1)
def test_a(self):
np.testing.assert_allclose(self.a, self.p_true / (1 - self.ecc_true**2))
def test_ecc(self):
np.testing.assert_allclose(self.ecc, self.ecc_true, rtol=1e-4)
def test_inc(self):
np.testing.assert_allclose(self.inc, self.inc_true, rtol=1e-4)
def test_raan(self):
np.testing.assert_allclose(self.raan, self.raan_true)
def test_arg_p(self):
np.testing.assert_allclose(self.arg_p, self.arg_p_true, rtol=1e-4)
def test_nu(self):
np.testing.assert_allclose(self.nu, self.nu_true, rtol=1e-4)
def test_m(self):
E_true, M_true = kepler.nu2anom(self.nu, self.ecc)
np.testing.assert_allclose(self.m, M_true)
def test_arglat(self):
# argument of latitude isn't used for this case so it goes to zero
# np.testing.assert_allclose(self.arglat, self.nu_true + self.arg_p_true)
pass
def test_truelon(self):
# not used for inclined orbits - only special ones
# np.testing.assert_allclose(self.truelon, self.nu_true + self.raan_true + self.arg_p_true)
pass
def test_lonper(self):
# not really used for inclined orbits
# np.testing.assert_allclose(self.lonper, self.arg_p_true + self.raan_true)
pass
def test_rv2coe_project_example_one():
r = np.array([8840, 646, 5455])
v = np.array([-0.695, 5.25, -1.65])
a, ecc, inc, raan, argp, nu = kepler.rv2coe(r, v)
# expected values
a_exp = 8697.5027
ecc_exp = 0.2802
np.testing.assert_allclose(a, a_exp)
np.testing.assert_allclose(ecc, ecc_exp, rtol=1e-4)
class Testrv2coeEquatorialCircularHalf():
p_true = 6378.137 # km
ecc_true = 0.0
inc_true = 0.0
raan_true = 0.0
arg_p_true = 0.0
nu_true = np.pi
mu = 398600.5 # km^3 /sec^2
R_ijk_true = np.array([-p_true, 0,0])
V_ijk_true = np.sqrt(mu/p_true) * np.array([0,-1,0])
p, a, ecc, inc, raan, arg_p, nu, m, arglat, truelon, lonper = kepler.rv2coe(R_ijk_true, V_ijk_true, mu)
def test_p(self):
np.testing.assert_allclose(self.p, self.p_true)
def test_a(self):
np.testing.assert_allclose(self.a, self.p_true / (1 - self.ecc_true**2))
def test_ecc(self):
np.testing.assert_allclose(self.ecc, self.ecc_true)
def test_inc(self):
np.testing.assert_allclose(self.inc, self.inc_true)
def test_raan(self):
np.testing.assert_allclose(self.raan, self.raan_true)
def test_arg_p(self):
np.testing.assert_allclose(self.arg_p, self.arg_p_true)
def test_nu(self):
np.testing.assert_allclose(self.nu, self.nu_true)
def test_m(self):
E_true, M_true = kepler.nu2anom(self.nu, self.ecc)
np.testing.assert_allclose(self.m, M_true)
def test_arglat(self):
# argument of latitude isn't used for this case so it goes to zero
# np.testing.assert_allclose(self.arglat, self.nu_true + self.arg_p_true)
pass
def test_truelon(self):
np.testing.assert_allclose(self.truelon, self.nu_true + self.raan_true + self.arg_p_true)
def test_lonper(self):
np.testing.assert_allclose(self.lonper, self.arg_p_true + self.raan_true)
class Testrv2coePolarCircular():
p_true = 6378.137 # km
ecc_true = 0.0
inc_true = np.pi / 2
raan_true = 0.0
arg_p_true = 0.0
nu_true = 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_true) * np.array([0,0,1])
p, a, ecc, inc, raan, arg_p, nu, m, arglat, truelon, lonper = kepler.rv2coe(R_ijk_true, V_ijk_true, mu)
def test_p(self):
np.testing.assert_allclose(self.p, self.p_true)
def test_a(self):
np.testing.assert_allclose(self.a, self.p_true / (1 - self.ecc_true**2))
def test_ecc(self):
np.testing.assert_allclose(self.ecc, self.ecc_true)
def test_inc(self):
np.testing.assert_allclose(self.inc, self.inc_true)
def test_raan(self):
np.testing.assert_allclose(self.raan, self.raan_true)
def test_arg_p(self):
np.testing.assert_allclose(self.arg_p, self.arg_p_true)
def test_nu(self):
np.testing.assert_allclose(self.nu, self.nu_true)
def test_m(self):
E_true, M_true = kepler.nu2anom(self.nu, self.ecc)
np.testing.assert_allclose(self.m, M_true)
def test_arglat(self):
np.testing.assert_allclose(self.arglat, self.nu_true + self.arg_p_true)
def test_truelon(self):
np.testing.assert_allclose(self.truelon, self.nu_true + self.raan_true + self.arg_p_true)
def test_lonper(self):
np.testing.assert_allclose(self.lonper, self.arg_p_true + self.raan_true)
class Testrv2coeCurtis():
"""Using example 4.7 from Curtis
"""
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])
p, a, ecc, inc, raan, arg_p, nu, m, _, _, _= kepler.rv2coe(R_ijk_true, V_ijk_true, mu)
rtol = 1e-3
def test_p(self):
np.testing.assert_allclose(self.p, self.p_true, rtol=self.rtol)
def test_a(self):
np.testing.assert_allclose(np.absolute(self.a), self.p_true / (self.ecc_true**2 - 1), rtol=1e2)
def test_ecc(self):
np.testing.assert_allclose(self.ecc, self.ecc_true, rtol=1e-1)
def test_inc(self):
np.testing.assert_allclose(self.inc, self.inc_true, rtol=self.rtol)
def test_raan(self):
np.testing.assert_allclose(self.raan, self.raan_true, rtol=self.rtol)
def test_arg_p(self):
np.testing.assert_allclose(self.arg_p, self.arg_p_true, rtol=self.rtol)
def test_nu(self):
np.testing.assert_allclose(self.nu, self.nu_true, rtol=self.rtol)
def test_m(self):
E_true, M_true = kepler.nu2anom(self.nu, self.ecc)
np.testing.assert_allclose(self.m, M_true, rtol=self.rtol)
class Testrv2coeVallado():
p_true = 1.73527 * constants.earth.radius # km
ecc_true = 0.83285
inc_true = np.deg2rad(87.87)
raan_true = np.deg2rad(227.89)
arg_p_true = np.deg2rad(53.38)
nu_true = np.deg2rad(92.335)
mu = 398600.5 # km^3 /sec^2
R_ijk_true = np.array([6524.834, 6862.875, 6448.296])
V_ijk_true = np.array([4.901320, 5.533756, -1.976341])
p, a, ecc, inc, raan, arg_p, nu, m, _, _, _= kepler.rv2coe(R_ijk_true, V_ijk_true, mu)
rtol = 1e-3
def test_p(self):
np.testing.assert_allclose(self.p, self.p_true, rtol=self.rtol)
def test_a(self):
np.testing.assert_allclose(self.a, self.p_true / (1 - self.ecc_true**2), rtol=self.rtol)
def test_ecc(self):
np.testing.assert_allclose(self.ecc, self.ecc_true, rtol=self.rtol)
def test_inc(self):
np.testing.assert_allclose(self.inc, self.inc_true, rtol=self.rtol)
def test_raan(self):
np.testing.assert_allclose(self.raan, self.raan_true, rtol=self.rtol)
def test_arg_p(self):
np.testing.assert_allclose(self.arg_p, self.arg_p_true, rtol=self.rtol)
def test_nu(self):
np.testing.assert_allclose(self.nu, self.nu_true, rtol=self.rtol)
def test_m(self):
E_true, M_true = kepler.nu2anom(self.nu, self.ecc)
np.testing.assert_allclose(self.m, M_true, rtol=self.rtol)
etTwo = spice.str2et('Sep 15, 2005')
times = np.linspace(etOne, etTwo, 5000)
state = np.zeros((len(times), 6))
for ii, et in enumerate(times):
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()
def example_two():
r = np.array([6524.834, 6862.875,
6448.296]) # position in ECI in kilometers
v = np.array([4.901327, 5.53376, -1.976341]) # velocity in ECI in km/sec
kepler.rv2coe(r, v)
import numpy as np
from astro import kepler, constants
mu = constants.earth.mu
r = np.array([0, -26560, 0])
v = np.array([2.5, 0, 2.5])
p, a, ecc, inc, raan, arg_p, nu, m, arglat, truelon, lonper = kepler.rv2coe(
r, v, mu)
string = kepler.orbit_el(p, ecc, inc, raan, arg_p, nu, mu, False)
print(string)
def solution(meas_file='./data/COMFIX_tle_measurement.txt',
outfile='./data/COMFIX_tle_solution.txt'):
# read in the measurement data
fout = open(outfile, 'w')
with open(meas_file, 'r') as f:
l0 = f.readline().split()
l0 = [float(x) for x in l0]
while l0:
l1 = f.readline().split()
l1 = [float(x) for x in l1]
latgd, lon, alt, jd = np.deg2rad(l0[0]), np.deg2rad(
l0[1]), l0[2] / 1e3, l0[3]
satnum, rho, az, el, drho, daz, dele = l1[0], l1[1], np.deg2rad(
l1[2]), np.deg2rad(l1[3]), l1[4], np.deg2rad(
l1[5]), np.deg2rad(l1[6])
# GST, LST
gst, lst = time.gstlst(jd, lon)
# find satellite vector in SEZ
rho_sez, drho_sez = geodetic.rhoazel2sez(rho, az, el, drho, daz,
dele)
R_eci2ecef = geodetic.eci2ecef(jd)
R_ecef2eci = geodetic.ecef2eci(jd)
R_sez2ecef = transform.dcm_sez2ecef(latgd, lon, alt)
# find site vector in ECEF/ECI
site_ecef = geodetic.lla2ecef(latgd, lon, alt)
site_eci = R_ecef2eci.dot(site_ecef)
# transform satellite vector from SEZ to ECI
rho_ecef = R_sez2ecef.dot(rho_sez)
rho_eci = R_ecef2eci.dot(rho_ecef)
drho_ecef = R_sez2ecef.dot(drho_sez)
drho_eci = R_ecef2eci.dot(drho_ecef)
pos_eci = site_eci + rho_eci
vel_eci = drho_eci + np.cross(
np.array([0, 0, constants.earth.omega]), pos_eci)
# find orbital elements
p, a, ecc, inc, raan, arg_p, nu, _, _, _, _ = kepler.rv2coe(
pos_eci, vel_eci, constants.earth.mu)
# compute orbit properties
prop_string = kepler.orbit_el(p, ecc, inc, raan, arg_p, nu,
constants.earth.mu)
l0 = f.readline().split()
l0 = [float(x) for x in l0]
# output to text file
fout.write(
'#################### COMFIX SATELLITE {:g} ####################################\n\n'
.format(satnum))
fout.write(
'------------------------ INPUT DATA -------------------------------------------\n\n'
)
fout.write('LAT (deg) LON (deg) ALT (m) JD\n')
fout.write(
'{:<9.4f} {:<9.4f} {:<9.4f} {:<16.6f}\n\n'.format(
np.rad2deg(latgd), np.rad2deg(lon), alt * 1e3, jd))
fout.write(
'RHO (km) AZ (deg) EL (deg) DRHO (km/s) DAZ (deg/s) DEL (deg/s)\n'
)
fout.write(
'{:<9.4f} {:<6.4f} {:<6.4f} {:<6.4f} {:<6.4f} {:<6.4f}\n'
.format(rho, np.rad2deg(az), np.rad2deg(el), drho,
np.rad2deg(daz), np.rad2deg(dele)))
fout.write(
'------------------------- WORKING DATA ----------------------------------------\n\n'
)
fout.write('LAT (rad) LON (rad) ALT (m) JD\n')
fout.write(
'{:<9.4f} {:<9.4f} {:<9.4f} {:<16.6f}\n\n'.format(
latgd, lon, alt, jd))
fout.write(
'RHO (km) AZ (rad) EL (rad) DRHO (km/s) DAZ (rad/s) DEL (rad/s)\n'
)
fout.write(
'{:<9.4f} {:<6.4f} {:<6.4f} {:<6.4f} {:<6.4f} {:<6.4f}\n\n'
.format(rho, az, el, drho, daz, dele))
fout.write('GST = {:16.9f} rad = {:16.9f} deg\n'.format(
gst, np.rad2deg(gst)))
fout.write('LST = {:16.9f} rad = {:16.9f} deg\n\n'.format(
lst, np.rad2deg(lst)))
fout.write(
'---------------------------- VECTORS ------------------------------------------\n'
)
fout.write(
'{:9s} = {:13.4f} S {:13.4f} E {:13.4f} Z MAG = {:7.4f} km\n'.
format('rho_sez', rho_sez[0], rho_sez[1], rho_sez[2],
np.linalg.norm(rho_sez)))
fout.write(
'{:9s} = {:13.4f} I {:13.4f} J {:13.4f} K MAG = {:7.4f} km\n'.
format('rho_ecef', rho_ecef[0], rho_ecef[1], rho_ecef[2],
np.linalg.norm(rho_ecef)))
fout.write(
'{:9s} = {:13.4f} I {:13.4f} J {:13.4f} K MAG = {:7.4f} km\n'.
format('rho_eci', rho_eci[0], rho_eci[1], rho_eci[2],
np.linalg.norm(rho_eci)))
fout.write(
'{:9s} = {:13.4f} S {:13.4f} E {:13.4f} Z MAG = {:7.4f} km/s\n'
.format('drho_sez', drho_sez[0], drho_sez[1], drho_sez[2],
np.linalg.norm(drho_sez)))
fout.write(
'{:9s} = {:13.4f} I {:13.4f} J {:13.4f} K MAG = {:7.4f} km/s\n'
.format('drho_ecef', drho_ecef[0], drho_ecef[1], drho_ecef[2],
np.linalg.norm(drho_ecef)))
fout.write(
'{:9s} = {:13.4f} I {:13.4f} J {:13.4f} K MAG = {:7.4f} km/s\n'
.format('drho_eci', drho_eci[0], drho_eci[1], drho_eci[2],
np.linalg.norm(drho_eci)))
fout.write(
'{:9s} = {:13.4f} I {:13.4f} J {:13.4f} K MAG = {:7.4f} km\n'.
format('site_ecef', site_ecef[0], site_ecef[1], site_ecef[2],
np.linalg.norm(site_ecef)))
fout.write(
'{:9s} = {:13.4f} I {:13.4f} J {:13.4f} K MAG = {:7.4f} km\n'.
format('site_eci', site_eci[0], site_eci[1], site_eci[2],
np.linalg.norm(site_eci)))
fout.write(
'{:9s} = {:13.4f} I {:13.4f} J {:13.4f} K MAG = {:7.4f} km\n'.
format('pos_eci', pos_eci[0], pos_eci[1], pos_eci[2],
np.linalg.norm(pos_eci)))
fout.write(
'{:9s} = {:13.4f} I {:13.4f} J {:13.4f} K MAG = {:7.4f} km/s\n'
.format('vel_eci', vel_eci[0], vel_eci[1], vel_eci[2],
np.linalg.norm(vel_eci)))
fout.write(prop_string + '\n')
fout.close()
beta = np.arctan2(mag_dv_outofplane, mag_dv_inplane)
phi = np.arctan2(dv_lvlh[0], dv_lvlh[1])
alpha = phi-np.absolute(fpa)
print('Beta (out of plane) : {} deg'.format(np.rad2deg(beta)))
print('Phi (angle from theta_hat) : {} deg'.format(np.rad2deg(phi)))
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)
"""Problem 4 HW4 2017
"""
from astro import kepler, constants
import numpy as np
import matplotlib.pyplot as plt
re = constants.earth.radius
mu = constants.earth.mu
r = np.array([3 * re, 5 * re, 0])
v = np.array([-3.2, 2.0, 2.5])
p, a, ecc, inc, raan, arg_p, nu, _, _, _, _ = kepler.rv2coe(r, v, mu)
output = kepler.orbit_el(p, ecc, inc, raan, arg_p, nu, mu, True)
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, 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()
