{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Visualizing advancement of perihelion in Schwarzschild space-time" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import astropy.units as u\n", "\n", "from plotly.offline import init_notebook_mode\n", "\n", "from einsteinpy.plotting import GeodesicPlotter\n", "from einsteinpy.coordinates import SphericalDifferential\n", "from einsteinpy.bodies import Body\n", "from einsteinpy.geodesic import Geodesic" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/vnd.plotly.v1+html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "init_notebook_mode(connected=True)\n", "# Essential when using Jupyter Notebook (May skip in Jupyter Lab)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Defining various parameters\n", " - Mass of the attractor(M)\n", " - Initial position and velocity vectors of test partcle" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "Attractor = Body(name=\"BH\", mass=6e24 * u.kg, parent=None)\n", "sph_obj = SphericalDifferential(130*u.m, np.pi/2*u.rad, -np.pi/8*u.rad,\n", " 0*u.m/u.s, 0*u.rad/u.s, 1900*u.rad/u.s)\n", "Object = Body(differential=sph_obj, parent=Attractor)\n", "geodesic = Geodesic(body=Object, time=0 * u.s, end_lambda=0.002, step_size=5e-8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the trajectory" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "marker": { "color": "#ffcc00", "line": { "width": 2 }, "size": 10 }, "mode": "markers", "name": "attractor", "type": "scatter", "x": [ 0 ], "y": [ 0 ] }, { "marker": { "color": "#313b6e", "line": { "width": 2 }, "size": 5 }, "mode": 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