class TestHohmannCircular():
r1 = constants.earth.orbit_sma
r2 = constants.neptune.orbit_sma
ecc1, ecc2 = 0, 0
nu1, nu2 = 0, np.pi
mu = constants.sun.mu
dv1_true, dv2_true, tof_true, phase_angle_true = 11.65413, 4.05359, 9.66154e8, np.deg2rad(113.153)
dv1, dv2, tof, phase = maneuver.hohmann(r1, r2, ecc1, ecc2, nu1, nu2, mu)
def test_dv1(self):
np.testing.assert_allclose(self.dv1, self.dv1_true, rtol=1e-4)
def test_dv2(self):
np.testing.assert_allclose(self.dv2, self.dv2_true, rtol=1e-4)
def test_tof(self):
np.testing.assert_allclose(self.tof, self.tof_true, rtol=1e-4)
def test_tof(self):
np.testing.assert_allclose(self.phase, self.phase_angle_true, rtol=1e-4)
dv_bielliptical = dv1 + dv2 + dv3
tof_bielliptical = np.pi * (np.sqrt(ab1**3 / mu) + np.sqrt(ab2**3 / mu))
print('V1 : {} km/sec'.format(v1))
print('V2 : {} km/sec'.format(v2))
print('\nBielliptical transfer')
print('VT1a : {} km/sec'.format(vb1))
print('DV1 : {} km/sec'.format(dv1))
print('\nVT2a : {} km/sec'.format(vb1i))
print('VT2b : {} km/sec'.format(vb2i))
print('DV2 : {} km/sec'.format(dv2))
print('\nVT3b : {} km/sec'.format(vb2))
print('DV3 : {} km/sec'.format(dv3))
print('\nTOF : {} sec'.format(tof_bielliptical))
# hohmann transfer
at, pt, ecct = kepler.perapo2aecc(r1, r2)
vt1 = maneuver.vel_mag(r1, at, mu)
vt2 = maneuver.vel_mag(r2, at, mu)
dv1, dv2, tof, _ = maneuver.hohmann(r1, r2, 0, 0, 0, np.pi, mu)
print('\nHohmann Transfer')
print('VT1 : {} km/sec'.format(vt1))
print('VT2 : {} km/sec'.format(vt2))
print('DV1 : {} km/sec'.format(dv1))
print('DV2 : {} km/sec'.format(dv2))
print('TOF : {} sec'.format(tof))
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 a_p = kepler.period2sma(phasing_period, mu) rc = a_p * 2 - rb a_p, p_p, ecc_p = kepler.perapo2aecc(rc, rb) # hohmann from transfer ellipse to phasing orbit vt2 = maneuver.vel_mag(rb, a_t, mu)
# orbit 1 properties
a1, p1, ecc1 = kepler.perapo2aecc(ra, rb)
va1 = maneuver.vel_mag(ra, a1, mu)
vb1 = maneuver.vel_mag(rb, a1, mu)
# orbit 2 properties
a2, p2, ecc2 = kepler.perapo2aecc(rc, rd)
vc2 = maneuver.vel_mag(rc, a2, mu)
vd2 = maneuver.vel_mag(rd, a2, mu)
# A to C Hohmann trasnfer
at1, pt1, ecct1 = kepler.perapo2aecc(rc, ra)
vat = maneuver.vel_mag(ra, at1, mu)
vct = maneuver.vel_mag(rc, at1, mu)
dv1, dv2, tof1, _ = maneuver.hohmann(ra, rc, ecc1, ecc2, 0, 0, mu)
dvt1 = np.absolute(dv1) + np.absolute(dv2)
print('A to C hohmann transfer')
print('Semimajor axis : {} km'.format(at1))
print('Eccentricity : {} '.format(ecct1))
print('\nV1 at A : {} km/sec'.format(va1))
print('VT1 at A : {} km/sec'.format(vat))
print('DV1 : {} km/sec'.format(dv1))
print('\nV2 at C : {} km/sec'.format(vc2))
print('VT2 at C : {} km/sec'.format(vct))
print('DV2 : {} km/sec'.format(dv2))
print('TOF : {} sec'.format(tof1))
# B to D Hohmann trasnfer
at2, pt2, ecct2 = kepler.perapo2aecc(rb, rd)
vbt = maneuver.vel_mag(rb, at2, mu)
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))
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)
"""Hohmann Transfer example Problem 5 HW 5 2017
"""
from astro import constants, kepler, maneuver
import numpy as np
mu = constants.earth.mu
# initial orbit
r1 = 1.25 * constants.earth.radius
r2 = 6.6 * constants.earth.radius
at, pt, ecct = kepler.perapo2aecc(r1, r2)
v1 = maneuver.vel_mag(r1, r1, mu)
v2 = maneuver.vel_mag(r2, r2, mu)
dv1, dv2, tof, phase_angle = maneuver.hohmann(r1, r2, 0, 0, 0, np.pi, mu)
S = maneuver.synodic_period(r1, r2, mu)
print('V1 : {} km/sec'.format(v1))
print('DV1 : {} km/sec'.format(dv1))
print('V2 : {} km/sec'.format(v2))
print('DV2 : {} km/sec'.format(dv2))
print('TOF : {} sec = {} hr'.format(tof, tof / 3600))
print('Phase Angle : {} deg'.format(np.rad2deg(phase_angle)))
print('Synodic Period : {} sec = {} hr'.format(S, S / 3600))