def test_parabolic(self):
"""Shouldn't work since parabolas have infinite a
"""
a = np.infty
ecc = 1
p = kepler.semilatus_rectum(a, ecc)
np.testing.assert_allclose(p, 0)
def test_planar_orbit_intersection():
ecc1 = 0.75
p1 = kepler.semilatus_rectum(4.5*constants.earth.radius, ecc1)
a2, p2, ecc2 = kepler.perapo2aecc(2 * constants.earth.radius, 6 * constants.earth.radius)
dargp = np.deg2rad(35)
nu = maneuver.planar_conic_orbit_intersection(p1, p2, ecc1, ecc2, dargp)
np.testing.assert_allclose(nu, np.deg2rad(110.342156))
def j2dragpert(inc0, ecc0, n0, ndot2, mu=398600.5, re=6378.137, J2=0.00108263):
"""Perturbed Kepler Propogator including J2 and drag
Inputs:
inc0 - initial inclination (radians)
ecc0 - initial eccentricity (unitless)
n0 - initial mean motion (rad/sec)
ndot2 - mean motion rate divided by 2 (rad/sec^2)
Outputs:
raandot - nodal rate (rad/sec)
argdot - argument of periapsis rate (rad/sec)
eccdot - eccentricity rate (1/sec)
adot - semi major axis rate (km/sec)
Globals: None
Constants:
mu - 398600.5 Earth gravitational parameter in km^3/sec^2
re - 6378.137 Earth radius in km
J2 - 0.00108263 J2 perturbation factor
Coupling:
kepler.semilatus_rectum - compute semilatus rectum
Author: C2C Shankar Kulumani USAFA/CS-19 719-333-4741
12 5 2014 - modified to remove global varaibles
17 Jun 2017 - Now in Python for awesomeness
29 Nov 2017 - Include drag effect on a, ecc
References:
Vallado
"""
# calculate initial semi major axis and semilatus rectum
a0 = (mu / n0**2) ** (1 / 3)
p0 = kepler.semilatus_rectum(a0, ecc0)
# mean motion with J2
nvec = n0 * (1 + 1.5 * J2 * (re / p0)**2 *
np.sqrt(1 - ecc0**2) * (1 - 1.5 * np.sin(inc0)**2))
# eccentricity rate
eccdot = (-2 * (1 - ecc0) * 2 * ndot2) / (3 * nvec)
# calculate nodal rate
raandot = (-1.5 * J2 * (re / p0)**2 * np.cos(inc0)) * nvec
# argument of periapsis rate
argdot = (1.5 * J2 * (re / p0)**2 * (2 - 2.5 * np.sin(inc0)**2)) * nvec
# semi major axis rate
adot = - 2 / 3 * a0 / nvec * 2 * ndot2
return (raandot, argdot, eccdot, adot)
def j2dragpert(inc0, ecc0, n0, ndot2, mu=398600.5, re=6378.137, J2=0.00108263):
"""Perturbed Kepler Propogator including J2 and drag
Inputs:
inc0 - initial inclination (radians)
ecc0 - initial eccentricity (unitless)
n0 - initial mean motion (rad/sec)
ndot2 - mean motion rate divided by 2 (rad/sec^2)
Outputs:
raandot - nodal rate (rad/sec)
argdot - argument of periapsis rate (rad/sec)
eccdot - eccentricity rate (1/sec)
adot - semi major axis rate (km/sec)
Globals: None
Constants:
mu - 398600.5 Earth gravitational parameter in km^3/sec^2
re - 6378.137 Earth radius in km
J2 - 0.00108263 J2 perturbation factor
Coupling:
kepler.semilatus_rectum - compute semilatus rectum
Author: C2C Shankar Kulumani USAFA/CS-19 719-333-4741
12 5 2014 - modified to remove global varaibles
17 Jun 2017 - Now in Python for awesomeness
29 Nov 2017 - Include drag effect on a, ecc
References:
Vallado
"""
# calculate initial semi major axis and semilatus rectum
a0 = (mu / n0**2)**(1 / 3)
p0 = kepler.semilatus_rectum(a0, ecc0)
# mean motion with J2
nvec = n0 * (1 + 1.5 * J2 * (re / p0)**2 * np.sqrt(1 - ecc0**2) *
(1 - 1.5 * np.sin(inc0)**2))
# eccentricity rate
eccdot = (-2 * (1 - ecc0) * 2 * ndot2) / (3 * nvec)
# calculate nodal rate
raandot = (-1.5 * J2 * (re / p0)**2 * np.cos(inc0)) * nvec
# argument of periapsis rate
argdot = (1.5 * J2 * (re / p0)**2 * (2 - 2.5 * np.sin(inc0)**2)) * nvec
# semi major axis rate
adot = -2 / 3 * a0 / nvec * 2 * ndot2
return (raandot, argdot, eccdot, adot)
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
def test_hyperbolic(self):
a = -8000
ecc = 1.5
p = kepler.semilatus_rectum(a, ecc)
np.testing.assert_allclose(p, a * (1 - ecc**2))
def test_elliptical(self):
a = 8000
ecc = 0.5
p = kepler.semilatus_rectum(a, ecc)
np.testing.assert_allclose(p, a * (1 - ecc**2))
def test_circular(self):
a = 8000
ecc = 0
p = kepler.semilatus_rectum(a, ecc)
np.testing.assert_allclose(p, a)
"""Problem 3 HW4 2017
"""
from astro import kepler, constants
import numpy as np
import matplotlib.pyplot as plt
# 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)
""" from astro import constants, kepler, maneuver import numpy as np import matplotlib.pyplot as plt import pdb ra = 7000 rb = 14000 mu = constants.earth.mu # define hyperbolic arrival orbit va1 = 12 e_h = va1**2 / 2 - mu / ra a_h = -mu / e_h / 2 ecc_h = ra / np.absolute(a_h) + 1 p_h = kepler.semilatus_rectum(np.absolute(a_h), ecc_h) nu_h = 0 # hohmann transfer from hyperbolic orbit to circular orbit rb a_t, p_t, ecc_t = kepler.perapo2aecc(ra, rb) vt1 = maneuver.vel_mag(ra, a_t, mu) dva1, _, toft, phaset = maneuver.hohmann(ra, rb, ecc_h, 0, 0, 0, mu) # final orbit mean motion n2 = np.sqrt(mu / rb**3) angle = n2 * toft p2 = 2 * np.pi * np.sqrt(rb**3 / mu) phasing_period = p2 - toft # design of phasing orbit
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
import numpy as np
from astro import constants, maneuver, kepler, transform
import matplotlib.pyplot as plt
from kinematics import attitude
import pdb
mu = constants.earth.mu
re2km = constants.re2km
deg2rad = constants.deg2rad
rad2deg = constants.rad2deg
# initial orbit
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
mu = constants.sun.mu
a_e = constants.earth.orbit_sma
a_n = constants.neptune.orbit_sma
km2au = constants.km2au
ecc_e = 0
ecc_n = 0
# circular earth velocity
v_1 = np.sqrt(mu / a_e)
v_2 = np.sqrt(mu / a_n)
# transfer orbit
a_t = .5 * (a_e + a_n)
ecc_t = a_n / a_t - 1
p_t = kepler.semilatus_rectum(a_t, ecc_t)
# velocity of transfer orbit at initial and final orbit
sme_t = -mu / (2 * a_t)
vt_1 = np.sqrt(2 * (sme_t + mu / a_e))
vt_2 = np.sqrt(2 * (sme_t + mu / a_n))
(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))
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