Visualizing advance of perihelion of a test particle in Schwarzschild space-time

Importing the required modules

[1]:

import numpy as np
import astropy.units as u
from einsteinpy.plotting import ScatterGeodesicPlotter

Defining various parameters

  • Mass of the attractor(M)

  • Initial position and velocity vectors of test partcle

[2]:

M = 6e24 * u.kg
pos = [130*u.m, np.pi/2*u.rad, -np.pi/8*u.rad]
vel = [0*u.m/u.s, 0*u.rad/u.s, 1900*u.rad/u.s]

Plotting the trajectory

[3]:

%matplotlib inline
obj = ScatterGeodesicPlotter(M)
obj.plot(pos, vel, 0.002, 5e-8)
obj.show()
../_images/examples_Visualizing_advance_of_perihelion_of_a_test_particle_in_Schwarzschild_space-time_5_0.png

It can be seen that the orbit advances along the azimuth angle on each revolution of test partcle .