Retrograde Motion

In retrograde motion, the stars are orbitting the main galaxy $M$ in the opposite direction (counterclockwise) with respect to the motion of the disrupting galaxy $S$. This was done simply by flipping the minus sign on the $x$- and $y$-velocity components to get $v_x = -vsin(\theta)$ and $v_y = vcos(\theta)$. Other than that, the calculations are the exact same, with no need to change anything else.



In [1]:

    
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns
import timeit
from scipy.integrate import odeint
from IPython.html.widgets import interact, fixed
from moviepy.video.io.bindings import mplfig_to_npimage
import moviepy.editor as mpy









    



:0: FutureWarning: IPython widgets are experimental and may change in the future.
WARNING:py.warnings:/usr/local/lib/python3.4/dist-packages/skimage/filter/__init__.py:6: skimage_deprecation: The `skimage.filter` module has been renamed to `skimage.filters`.  This placeholder module will be removed in v0.13.
  warn(skimage_deprecation('The `skimage.filter` module has been renamed '

Constants



In [2]:

    
gamma = 4.4983169634398597e4
tsteps = 1000
t = np.linspace(0,1.5,tsteps)
M = 10
S = 10
whichplot='retro'

Function Imports



In [3]:

    
from derivsfunc import *
from initialconditions import *
from solutions import ode_solutions
from staticplotter import *
from retromoviemaker import *;

Calling functions to ensure all variables and whatever else is available



In [4]:

    
direct_ic(M,gamma)
parabolic_ic(M,S,gamma)
ics(M,S,gamma)
ode_solutions(t,tsteps,M,S,gamma);

Static plots at different time intervals

Note: This is not a representation of the entire time frame. These plots show the disrupting galaxy and a few of it's after effects.

In the retrograde passage case, the stars aren't as willing to give up their orbit around $M$. Since the stars and $S$ are moving in opposite directions, the stars have inertia in a different direction, thus resisting the pull of $S$. A large majority of the stars stay in their initial shell, but get a little clumped up. We see most of the effect of $S$ in the outer two shells where the outermost shell even folds in on itself.



In [5]:

    
plot_static(t,whichplot, tsteps, M, S, gamma)

Visualization of the Motion



In [6]:

    
retro_animation.ipython_display(fps=60)









    









    Out[6]: