import numpy.linalg as lg
import matplotlib.pyplot as plt
import scipy.io as spio
MU = 398600
RE = 6380
omega_earth = 2 * np.pi / 86164
f = 3.35e-3
# Orbit A
init_cond = [7000, 0.01, 45, 0, -65, 0]
theta_g_i = 0
t_0 = 0
P = 2 * np.pi * np.sqrt(init_cond[0]**3 / MU) # seconds
print(P)
[r_a, v_a] = sf.elm2cart(init_cond, MU)
[r, v] = sf.orbit_prop_rk(r_a, v_a, t_0, P * 3, 60)
time_series = np.arange(0, 3 * P, 60)
step = 0
phi_gd = np.empty(np.shape(time_series))
lam = np.empty(np.shape(time_series))
for t_n in time_series:
theta_g = theta_g_i + omega_earth * (t_n - t_0)
r_ecf = np.matmul(sf.R3(theta_g), r[step, :])
r_norm = lg.norm(r_ecf)
phi_gc = np.arcsin(r_ecf[2] / r_norm)
lam[step] = np.arctan2(r_ecf[1], r_ecf[0])
phi_gd[step] = np.arctan2(np.tan(phi_gc), (1 - f)**2)
step = step + 1
# Convert to degrees
lam = np.multiply(lam, 180 / np.pi)
import space_functions as sf
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
elements = [70000, 0.01, 20, 180, 25, 0]
r_0, v_0 = sf.elm2cart(elements, sf.earth.mu)
T0 = 2451545.0 * 86400
TF = ((2451545.0 + 365.25) * 86400 - T0)
T0 = 0
dT = .5 * 86400
time_series = np.arange(0, 365.25, 0.5)
print("Starting Propagation")
r_vec, v_vec = sf.orbit_prop_3body_RV(r_0, v_0, T0, TF, dT)
print("Propagation Complete!")
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot3D(r_vec[:, 0], r_vec[:, 1], r_vec[:, 2])
elements = np.empty([np.shape(r_vec)[0], 6])
for i in range(np.shape(r_vec)[0]):
elements[i, :] = sf.cart2elm(r_vec[i, :], v_vec[i, :], sf.earth.mu)
print(np.shape(elements))
fig, ax = plt.subplots(3, sharex=True)
elementals = ["a[km]", "e", "i[deg]", "RAAN[deg]", "Arg Periapsis [deg]"]
import space_functions as sf
import numpy as np
import matplotlib.pyplot as plt
elements = [7000, 0, 75, 0, 0, 0]
rho_0 = [2.5e-2, 0, 0]
rho_dot_0 = [-1e-3, 0, 0]
# part a
print("5.1: ")
r_t, v_t = sf.elm2cart(elements, sf.earth.mu)
r_t_norm = np.linalg.norm(r_t)
R = np.divide(r_t, r_t_norm)
h = np.cross(r_t, v_t)
W = np.divide(h, np.linalg.norm(h))
S = np.cross(W, R)
Q_ijk = np.transpose(np.squeeze([R, S, W]))
rho_ijk = np.matmul(Q_ijk, rho_0)
rho_dot_ijk = np.matmul(Q_ijk, rho_dot_0)
r_c = r_t + rho_ijk
v_c = v_t + rho_dot_ijk
print(r_c, v_c)
# part b
print("5.2: ")
Ang_vel = h / r_t_norm**2
rho_dot_rel = np.multiply(
1000, np.matmul(np.transpose(Q_ijk),
rho_dot_0 - np.cross(Ang_vel, rho_ijk)))
import space_functions as sf
import matplotlib.pyplot as plt
import numpy as np
from colorama import Fore
MU = 398600
a = 500000
e = 0.3
i = 50
RAAN = 350
arg_peri = 90
anomaly = 0
r_0, v_0 = sf.elm2cart([a, e, i, RAAN, arg_peri, anomaly], MU)
T0 = 2451545.0 * 86400
tf = ((2451545.0 + 365.25) * 86400 - T0)
T0 = 0
dt = .5 * 86400
time_series = np.arange(T0, tf, dt) - T0
r_vec, v_vec = sf.orbit_prop_3body(r_0, v_0, T0, tf, dt)
elements = np.empty([np.shape(r_vec)[0], 6])
for i in range(np.shape(r_vec)[0]):
elements[i, :] = sf.cart2elm(r_vec[i, :], v_vec[i, :], MU)
print(np.shape(elements))
import numpy as np
import numpy.linalg as lg
import space_functions as sf
MU = 398600.4415
RE = 6378.1363
JDos = 0.00108248
f = 3.353e-3
E_i = [8000, 0.1, 50, 45, 300, 0]
E_f = [8500, 0.15294, 50, 45, 300, 0]
r_i, v_i = sf.elm2cart(E_i, MU)
r_f, v_f = sf.elm2cart(E_f, MU)
delta_v = v_f-v_i
print("∆v:")
print(delta_v)
v_r = np.dot(delta_v, r_i/lg.norm(r_i))
v_p = np.sqrt(lg.norm(delta_v)**2-v_r**2)
print("|∆v_r|: "+str(v_r)+" km/s |∆v_⊥|: "+str(v_p)+" km/s")
MU = 398600.4415
J2 = 0.0010826267
J3 = -0.0000025327
class conditions:
p_srp = 4.57e-6 * 1000**2
C_r = 1.5
A_m = 0.1 / 1000**2
C_D = 2
url = 'https://raw.githubusercontent.com/ggb367/Spring-2020/master/366L/hw7/density.csv'
density_table = pd.read_csv(url)
epoch = 2458200.5 # days
r_0, v_0 = sf.elm2cart([6800, 0.005, 71, 300, 78, 0], MU)
r_vec, v_vec = sf.orbit_prop_all_pert(r_0, v_0, 0, 86400, 30, conditions)
r_bad, v_bad = sf.orbit_prop_rk(r_0, v_0, 0, 86400, 30)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot3D(r_vec[:, 0], r_vec[:, 1], r_vec[:, 2])
ax.plot3D(r_bad[:, 0], r_bad[:, 1], r_bad[:, 2])
print("With Perts:")
print("The Final Position is: ", r_vec[-1, :], "The Final Velocity is: ",
v_vec[-1, :])
print("Without Perts:")
print("The Final Position is: ", r_bad[-1, :], "The Final Velocity is: ",
v_bad[-1, :])
import math as m
import matplotlib.pyplot as plt
import numpy as np
import numpy.linalg as lg
import space_functions as sf
MU = 398600.4415
# E - [a, e, i, RAAN, omega, nu]
elements = [26000, 0.72, 75, 90, 270,
0] # time since periapsis passage is 0 for #1 so nu is 0
# #1
r_0, v_0 = sf.elm2cart(elements, MU)
print("This is r:")
print(r_0)
print("This is v:")
print(v_0)
#2
time_series = np.arange(0, 86400 * 3, 20)
nu_0 = 0
r_norm = lg.norm(r_0)
h = np.cross(r_0, v_0)
h_norm = lg.norm(h)
eccent = np.cross(v_0, h) / MU - np.divide(r_0, r_norm)
eccent_norm = lg.norm(eccent)
a = (r_norm *
(1 + eccent_norm * np.cos(nu_0))) / (1 - eccent_norm**2) # semimajor axis
import space_functions as sf
import numpy as np
import numpy.linalg as lg
import matplotlib.pyplot as plt
r_earth = [1, 0, 0]
_, v_earth = sf.elm2cart([1, 0, 0, 0, 0, 0], 1)
print(v_earth)
t = []
C3 = []
u = np.arange(5, 170, 5)
for step in u:
r_mars, v_mars = sf.elm2cart([1.524, 0, 1.85, 0, 0, step], 1)
mu_sun = 1
t_m = 1
a_min, e_min, t_abs, v_0 = sf.Lambert_MinEng(r_earth, r_mars)
t.append(t_abs)
v_inf = lg.norm(v_0-v_earth)
C3.append(v_inf**2)
plt.plot(u, t)
plt.xlabel("u_mars, deg")
plt.ylabel("Time [TU]")
plt.title("Argument of Latitude of Mars vs. Absolute Minimum Time of Flight")
plt.figure()
plt.xlabel("u_mars, deg")
plt.ylabel("C_3 [AU^2/TU^2]")
plt.title("Argument of Latitude of Mars vs. Departure C_3")
plt.plot(u, C3)
# plt.yscale('log')
plt.show()