Kepler plus drag

Backwards-integrate-dynamical-friction.ipynb

{
  "cells": [
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-04-26T15:52:40.069995Z",
          "end_time": "2022-04-26T15:52:40.085065Z"
        },
        "trusted": true
      },
      "cell_type": "code",
      "source": "from astropy.constants import G\nimport astropy.coordinates as coord\nimport astropy.units as u\nimport matplotlib as mpl\nimport matplotlib.pyplot as plt\n%matplotlib inline\nimport numpy as np\n\n# gala\nimport gala.coordinates as gc\nimport gala.dynamics as gd\nimport gala.integrate as gi\nimport gala.potential as gp\nfrom gala.units import solarsystem",
      "execution_count": 13,
      "outputs": []
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-04-26T15:49:24.183032Z",
          "end_time": "2022-04-26T15:49:24.195356Z"
        },
        "trusted": true
      },
      "cell_type": "code",
      "source": "sun = gp.KeplerPotential(m=1*u.Msun, units=solarsystem)",
      "execution_count": 7,
      "outputs": []
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-04-26T15:56:14.235289Z",
          "end_time": "2022-04-26T15:56:14.243403Z"
        },
        "trusted": true
      },
      "cell_type": "code",
      "source": "def F(t, w, sun, usys):\n    \"\"\"\n    Implement a simple friction force\n    \"\"\"\n    wdot = np.zeros_like(w)\n    wdot[:3] = w[3:]\n    \n    w = gd.PhaseSpacePosition.from_w(w, units=usys)\n    acc = sun.acceleration(w.xyz)\n    \n    # Fake drag force\n    v2 = np.sum(w.v_xyz**2, axis=0)\n    drag_F = 0.1/u.au * v2\n    acc += drag_F * -w.v_xyz / np.sqrt(v2)\n    \n    wdot[3:] = acc.decompose(usys).value\n    \n    return wdot",
      "execution_count": 33,
      "outputs": []
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-04-26T15:56:14.750638Z",
          "end_time": "2022-04-26T15:56:14.755731Z"
        },
        "trusted": true
      },
      "cell_type": "code",
      "source": "w0 = gd.PhaseSpacePosition(\n    pos=[1, 0, 0] * u.au,\n    vel=[0, 35, 0] * u.km/u.s,\n)",
      "execution_count": 34,
      "outputs": []
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-04-26T15:56:15.032200Z",
          "end_time": "2022-04-26T15:56:15.037655Z"
        },
        "trusted": true
      },
      "cell_type": "code",
      "source": "integ = gi.LeapfrogIntegrator(\n    F, \n    func_args=(sun, sun.units), \n    func_units=sun.units\n)",
      "execution_count": 35,
      "outputs": []
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-04-26T15:56:49.570018Z",
          "end_time": "2022-04-26T15:56:49.932993Z"
        },
        "trusted": true
      },
      "cell_type": "code",
      "source": "orbit = integ.run(w0, dt=1e-2*u.yr, t1=0, t2=1*u.yr)\norbit.plot();",
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 864x288 with 3 Axes>",
            "image/png": 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          },
          "metadata": {
            "image/png": {
              "width": 872,
              "height": 296
            }
          }
        }
      ]
    },
    {
      "metadata": {
        "ExecuteTime": {
          "start_time": "2022-04-26T15:56:46.706411Z",
          "end_time": "2022-04-26T15:56:47.063057Z"
        },
        "trusted": true
      },
      "cell_type": "code",
      "source": "orbit_back = integ.run(orbit[-1], dt=-1e-2*u.yr, t1=orbit.t[-1], t2=0)\norbit_back.plot();",
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 864x288 with 3 Axes>",
            "image/png": 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          },
          "metadata": {
            "image/png": {
              "width": 872,
              "height": 296
            }
          }
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "name": "conda-env-gala-dev-py",
      "display_name": "Python [conda env:gala-dev]",
      "language": "python"
    },
    "toc": {
      "nav_menu": {},
      "number_sections": true,
      "sideBar": true,
      "skip_h1_title": false,
      "base_numbering": 1,
      "title_cell": "Table of Contents",
      "title_sidebar": "Contents",
      "toc_cell": false,
      "toc_position": {},
      "toc_section_display": true,
      "toc_window_display": false
    },
    "language_info": {
      "name": "python",
      "version": "3.9.4",
      "mimetype": "text/x-python",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "pygments_lexer": "ipython3",
      "nbconvert_exporter": "python",
      "file_extension": ".py"
    },
    "gist": {
      "id": "",
      "data": {
        "description": "Kepler plus drag",
        "public": true
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}