Propagating an orbit

Mubody also allows to provide the initial conditions (IC) vector of the satellite (position and velocity) and integrate the equations of motion directly to obtain the trajectory.

from mubody.mission import Mission
import matplotlib.pyplot as plt

First, we generate an analytic orbit so we can compare it with the trajectory integrated from the IC.

upm_a = Mission(mission_time=365*86400)
upm_a.AO()

We can plot the trajectory and save the figure in a variable to reuse it later.

fig = upm_a.plot_trajectory()

plt.show()

Now, we can retrieve the initial conditions from the previous case and reuse it in a new mission. The trajectory of the satellite, and therefore its initial conditions, are expressed in a given coodinate frame. By default, the coordinate frame of the CRTBP is Synodic and centered in the second Lagrange point of the the Sun-Earth/Moon system.

IC, frame = upm_a.sat.orbit.IC()
print(frame)
print(IC)

SEML2Synodic
[[-1.20000000e+08]
[-1.68941915e-06]
[-3.31550837e-06]
[-2.21489493e-13]
[ 1.57392553e+02]
[-1.19105000e+02]]

With the IC and its corresponding frame, we can integrate the motion for the desired time and plot it along with the analytic orbit.

upm_b = Mission(mission_time=180*86400)
upm_b.IC(IC=IC, IC_frame=frame)
fig = upm_b.plot_trajectory(fig=fig)

plt.show()

As it can be seen in the figure, the unstability of the motion around the libration point, which is not present in the analytic solution, drives the satellite away from the region when the equations of motion are integrated directly, even if the IC are the same.