{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Three-Body Problem\n", "by [Paulo Marques](http://pmarques.eu), 2014/03/13\n", "\n", "Updated 2016/02/15 for supporting Julia 0.4. Thanks [mbeltagy](https://github.com/mbeltagy) for the contribution.\n", "\n", "---\n", "\n", "## Introduction\n", "This notebook implements a numeric simulation of the [three-body problem](http://en.wikipedia.org/wiki/Three-body_problem). This is \n", "done using the [Julia Language](http://julialang.org) and the [Sundials](https://github.com/JuliaLang/Sundials.jl) library. \n", "\n", "The problem corresponds to determine the trajectories of three bodies in space under the influence of their mutual gravity forces (e.g., the motion of the Sun, Moon and Earth, taken together). Isaac Newton was the first person to try to solve this problem. In 1887, Bruns and PoincarĂ© showed that there is no general analytical closed solution for this problem. In fact, the motion of the three bodies is generally non-repeating! That's pretty amazing.\n", "\n", "![Planets](http://upload.wikimedia.org/wikipedia/commons/thumb/5/56/1e6m_comparison_Mars_Mercury_Moon_Pluto_Haumea_-_no_transparency.png/600px-1e6m_comparison_Mars_Mercury_Moon_Pluto_Haumea_-_no_transparency.png)\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Universal Law of Gravitation\n", "\n", "Newton taught us that two bodies with masses $m_0$ and $m_1$ attract themselves with a force proportional to their masses and inversionally proportional to the square of their distance $d$. This is called the [Universal Law of Gravitation](http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation). Mathematically this is expressed by: \n", "\n", "$$F = G \\frac{m_0 \\, m_1}{d^2}$$\n", "\n", "where $G$ is the gravitational constant. But, if we want to consider the movement of three bodies in space, we'll need to formulate this in terms of vector calculus. Let's suppose that mass $m_0$ is at position $\\vec{r_0}$ and $m_1$ at position $\\vec{r_1}$. This is shown in the next diagram (which also shows a mass $m_2$ and its position -- for now, assume it doesn't exist):\n", "\n", "![System](files/imgs/system.png)\n", "\n", "In this case, the law of gravitation can be formulated as:\n", "\n", "$$\\vec{F_{01}} = - G \\frac{m_0 m_1}{{\\vert \\vec{r_0} - \\vec{r_1} \\vert}^2} \\hat{r_{01}}$$\n", "\n", "where $\\vec{F_{01}}$ is the force exerted on $m_1$ due to $m_0$ and $\\hat{r_{01}}$ is the unit vector from $m_0$ to $m_1$:\n", "\n", "$$\\hat{r_{01}} = \\frac{\\vec{r_1} - \\vec{r_0}}{\\vert \\vec{r_1} - \\vec{r_0} \\vert}$$\n", "\n", "By simple manipulation we can write:\n", "\n", "$$\\vec{F_{01}} = - G \\, m_0 \\, m_1 \\frac{\\vec{r_1} - \\vec{r_0}}{{\\vert \\vec{r_1} - \\vec{r_0} \\vert}^3}$$\n", "\n", "Finally, there's an important thing that we also know: force equals mass times accelaration (Newton's second law) and that accelaration is the second derivative of position:\n", "\n", "$$\\vec{F} = m \\frac{d^2\\vec{r}}{dt^2}$$\n", "\n", "Thus we can write:\n", "\n", "$$m_1 \\frac{d^2\\vec{r_1}}{dt^2} = - G \\, m_0 \\, m_1 \\frac{\\vec{r_1} - \\vec{r_0}}{{\\vert \\vec{r_1} - \\vec{r_0} \\vert}^3}$$\n", "\n", "If we only had two bodies this would be great. But, with three bodies, we need to consider all the interactions and forces. Since we are calculating the accelaration of $m_1$ we just need to add the force corresponding to $\\vec{F_{21}}$:\n", "\n", "$$m_1 \\frac{d^2\\vec{r_1}}{dt^2} = - G \\, m_0 \\, m_1 \\frac{\\vec{r_1} - \\vec{r_0}}{{\\vert \\vec{r_1} - \\vec{r_0} \\vert}^3} \\\n", " - G \\, m_2 \\, m_1 \\frac{\\vec{r_1} - \\vec{r_2}}{{\\vert \\vec{r_1} - \\vec{r_2} \\vert}^3}$$\n", "\n", "---\n", "# Equations for Three Bodies\n", "\n", "From the last equation above and by symmetry we get the follwing three equations:\n", "\n", "$$\\frac{d^2\\vec{r_0}}{dt^2} = G \\, m_1 \\frac{\\vec{r_1} - \\vec{r_0}}{{\\vert \\vec{r_1} - \\vec{r_0} \\vert}^3} + \\\n", " G \\, m_2 \\frac{\\vec{r_2} - \\vec{r_0}}{{\\vert \\vec{r_2} - \\vec{r_0} \\vert}^3}$$\n", "\n", "$$\\frac{d^2\\vec{r_1}}{dt^2} = G \\, m_0 \\frac{\\vec{r_0} - \\vec{r_1}}{{\\vert \\vec{r_0} - \\vec{r_1} \\vert}^3} + \\\n", " G \\, m_2 \\frac{\\vec{r_2} - \\vec{r_1}}{{\\vert \\vec{r_2} - \\vec{r_1} \\vert}^3}$$\n", "\n", "$$\\frac{d^2\\vec{r_2}}{dt^2} = G \\, m_0 \\frac{\\vec{r_0} - \\vec{r_2}}{{\\vert \\vec{r_0} - \\vec{r_2} \\vert}^3} + \\\n", " G \\, m_1 \\frac{\\vec{r_1} - \\vec{r_2}}{{\\vert \\vec{r_1} - \\vec{r_2} \\vert}^3}$$\n", " \n", "These can be integrated numerically. Let's do so.\n", "\n", "---\n", "\n", "Let's start by importing a ploting library and a differential equation solver." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "using PyPlot\n", "using Sundials" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we need to define a function $\\dot{g} = f(t, g)$ where $g$ is a function of time $t$ and $\\dot{g}$ represents its derivative. Using the Sundials library this is done by defining a function f(t, g, gdot). The function should update the return parameter gdot with the derivative of g(t) at time t. Note that this design is not particularly great -- it would be much better if we could just return gdot. (Note that typically $\\dot{g} = f(t, g)$ is written as $\\dot{y} = f(t, y)$. We are not doing so because we'll be using $x$ and $y$ to denote coordinates.)\n", "\n", "Looking at the equations above it's easy to see that both y and ydot are going to be 12-entry vectors. We are going to work in two dimentions: X and Y. Thus, each vector $\\vec{r_k(t)}$ is going to correspond to two coordinates: $\\vec{r_k(t)} = (x_k(t), y_k(t))$. Since we have 3 of these position vectors this corresponds to 6 entries. Since the differencial equations above are of second order, we will need the derivatives of each one of $\\vec{r_k(t)}$, which corresponds to the bodies velocities $\\vec{v_k(t)}$. Since we have 3 bodies, each with an X and Y velocity, we get 6 other entries.\n", "\n", "So, let's write this function using the 3 differential equations above. For simplicity, we'll assume that $G=1$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "function f(t, g, gdot)\n", " # Extract the position and velocity vectors from the g array\n", " r0, v0 = g[1:2], g[3:4]\n", " r1, v1 = g[5:6], g[7:8]\n", " r2, v2 = g[9:10], g[11:12]\n", " \n", " # The derivatives of the position are simply the velocities\n", " dr0 = v0\n", " dr1 = v1\n", " dr2 = v2\n", " \n", " # Now calculate the the derivatives of the velocities, which are the accelarations\n", " # Start by calculating the distance vectors between the bodies (assumes m0, m1 and m2 are global variables)\n", " # Slightly rewriten the expressions dv0, dv1 and dv2 comprared to the normal equations so we can reuse d0, d1 and d2\n", " d0 = (r2 - r1) / ( norm(r2 - r1)^3.0 )\n", " d1 = (r0 - r2) / ( norm(r0 - r2)^3.0 )\n", " d2 = (r1 - r0) / ( norm(r1 - r0)^3.0 ) \n", " \n", " dv0 = m1*d2 - m2*d1\n", " dv1 = m2*d0 - m0*d2\n", " dv2 = m0*d1 - m1*d0\n", " \n", " # Reconstruct the derivative vector\n", " gdot[:] = [dr0; dv0; dr1; dv1; dr2; dv2]\n", "end;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For running a simulation we just need to setup the mass of each body, its initial position and velocity. As a sanity check we are also calculating the center of gravity at the end, for each time step, to make sure it's not \"drifting\" (which would violate the laws of physics)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Masses of the bodies\n", "m0 = 5.0\n", "m1 = 4.0\n", "m2 = 3.0\n", "\n", "# Initial positions and velocities of each body (x0, y0, vx0, vy0) \n", "gi0 = [ 1.0; -1.0; 0.0; 0.0]\n", "gi1 = [ 1.0; 3.0; 0.0; 0.0]\n", "gi2 = [-2.0; -1.0; 0.0; 0.0]\n", "\n", "# Simulation from time t=0 to t=30\n", "tf = 30.0\n", "dt = 500\n", "t = collect(linspace(0.0, tf, round(Int,tf*dt)))\n", "g0 = [gi0; gi1; gi2]\n", "res = Sundials.cvode(f, g0, t, reltol=1e-10)\n", "\n", "# Extract the position and velocity vectors from the solution\n", "r0, v0, r1, v1, r2, v2 = res[:,1:2], res[:,3:4], res[:,5:6], res[:,7:8], res[:,9:10], res[:,11:12]\n", "\n", "# Calculate the center of mass\n", "cx = [(r0[i,1]*m0 + r1[i,1]*m1 + r2[i,1]*m2) / (m0 + m1 + m2) for i=1:length(t)]\n", "cy = [(r0[i,2]*m0 + r1[i,2]*m1 + r2[i,2]*m2) / (m0 + m1 + m2) for i=1:length(t)]\n", "\n", "# Write the results to file if we want to do something with them later on (e.g., create some videos)\n", "# writecsv(\"results.csv\", res);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we need a function that allows us to plot the trajectory over time. We'll call it plot_trajectory and will pass as parameter the start time and stop time to plot." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "function plot_trajectory(t1, t2)\n", " t1i = round(Int,(length(t)-1) * t1/tf) + 1\n", " t2i = round(Int,(length(t)-1) * t2/tf) + 1\n", " \n", " # Plot the initial and final positions\n", " # In these vectors, the first coordinate will be X and the second Y\n", " X = 1\n", " Y = 2\n", " \n", " figure(figsize=(6,6))\n", " plot(r0[t1i,X], r0[t1i,Y], \"ro\")\n", " plot(r0[t2i,X], r0[t2i,Y], \"rs\")\n", " plot(r1[t1i,X], r1[t1i,Y], \"go\")\n", " plot(r1[t2i,X], r1[t2i,Y], \"gs\")\n", " plot(r2[t1i,X], r2[t1i,Y], \"bo\")\n", " plot(r2[t2i,X], r2[t2i,Y], \"bs\")\n", " \n", " # Plot the trajectories\n", " plot(r0[t1i:t2i,X], r0[t1i:t2i,Y], \"r-\")\n", " plot(r1[t1i:t2i,X], r1[t1i:t2i,Y], \"g-\")\n", " plot(r2[t1i:t2i,X], r2[t1i:t2i,Y], \"b-\")\n", " \n", " # Plot cente of mass\n", " plot(cx[t1i:t2i], cy[t1i:t2i], \"kx\")\n", " \n", " # Setup the axis and titles\n", " xmin = minimum([r0[t1i:t2i,X]; r1[t1i:t2i,X]; r2[t1i:t2i,X]]) * 1.10\n", " xmax = maximum([r0[t1i:t2i,X]; r1[t1i:t2i,X]; r2[t1i:t2i,X]]) * 1.10\n", " ymin = minimum([r0[t1i:t2i,Y]; r1[t1i:t2i,Y]; r2[t1i:t2i,Y]]) * 1.10\n", " ymax = maximum([r0[t1i:t2i,Y]; r1[t1i:t2i,Y]; r2[t1i:t2i,Y]]) * 1.10\n", " \n", " axis([xmin, xmax, ymin, ymax])\n", " title(@sprintf \"3-body simulation for t=[%.1f .. %.1f]\" t1 t2)\n", "end;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot the trajectory from 0 to 10 time units." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_trajectory(0, 10);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's pretty crazy! The trajectory of each body is drawn in a different color. The start position is marked by a small circle and the end position by a square. The center of gravity is marked with a black X. As you can see the behavior is pretty insane. \"Almost collisions\" and unstable aperiodic trajectories.\n", "\n", "And it goes on and on..." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_trajectory(10, 20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It almost looks like they are dancing..." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_trajectory(20, 30);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## Videos \n", "I've also decided to make three small videos containing the simulation.\n", "[The videos weren't generated here because (i)Julia's support for doing this is not great...] \n", "\n", "Look at all the close encounters!" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Function for creating an embedded video given a filename\n", "function html_video(filename)\n", " base64_video = base64encode(open(readbytes, filename))\n", " \"\"\"