{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Copyright (c) 2024 Massachusetts Institute of Technology\n", "\n", "SPDX-License-Identifier: MIT" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Propagate a Satellite\n", "\n", "In this example we will use `astroforge` to propagate a geostationary satellite using two separate force models." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Defining the Satellite\n", "\n", "In `astroforge`, a satellite is simply defined by its position and velocity. The coordinate system used is *TETED* (True Equinox and True Equator of Date, see [here](https://docs.astropy.org/en/stable/api/astropy.coordinates.TETE.html) and [here](https://en.wikipedia.org/wiki/Equatorial_coordinate_system#Primary_direction)), and the units are km and km/s.\n", "\n", "Our geostationary satellite will lie on the x-axis, with its velocity pointing in the y direction." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "GM = 398600.4418 # Geocentric gravitational constant (km**3 / s**2)\n", "r0 = 42164.0 # Geostationary distance from Earth's center (km)\n", "v0 = np.sqrt(GM / r0) # Speed (km/s)\n", "\n", "x0 = np.array([r0, 0, 0, 0, v0, 0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the position and velocity are defined together in a six-element array." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Defining the Propagation Parameters\n", "\n", "We must next decide how we want to propagate the satellite. We'll define a series of times (in seconds, starting at 0) at which we'll record the satellite's state.\n", "\n", "We will also define how precisely to solve the differential equations within our propagators by setting an absolute tolerance (`atol`) and a relative tolerance (`rtol`). For more information, see [here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# We'll take 1000 evenly spaced observations for one day (86400 seconds)\n", "t_eval = np.linspace(0.0, 86400.0, 1000)\n", "\n", "atol = 1e-9\n", "rtol = 1e-9" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Selecting a Force Model and Propagating\n", "\n", "When propagating an orbit, you can typically choose between fast, low-precision force models or high-precision models that take longer to compute. Force models also vary in how they handle atmospheric drag and solar radiation pressure (SRP). The choice you make depends on your specific modeling needs.\n", "\n", "In `astroforge`, we currently offer three different force models:\n", "1. `kepler`, a simple two-body model that ignores the effects of air resistance and SRP.\n", "2. `F_mp`, a medium-fidelity force model including J2 perturbations and perturbations from the sun and moon.\n", "3. `F_mp_srp`, a medium-fidelity model using an 8x8 spherical harmonic Earth gravity model, sun and moon perturbations, and a SRP model.\n", "\n", "For inputs, both `kepler` and `F_mp` only require the time (expressed as a Modified Julian Date) and the satellite's six-element state vector. `F_mp_srp` requires 3 additional time-constant coefficients defining the SRP model (please see the API documentaiton for `force_models._models.F_mp_srp` for more details.)\n", "\n", "In this example, we will compare the performances of `kepler` and `F_mp`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Two-body propagation took 14.50363 seconds.\n", "Medium Precision propagation took 19.24923 seconds.\n" ] } ], "source": [ "import time\n", "import astroforge as af\n", "\n", "t0 = time.time()\n", "x_kepler = af.propagators.propagator(af.force_models.kepler, x0, t_eval, atol=atol, rtol=rtol)\n", "t_kepler = time.time() - t0\n", "\n", "t0 = time.time()\n", "x_mp = af.propagators.propagator(af.force_models.F_mp, x0, t_eval, atol=atol, rtol=rtol)\n", "t_mp = time.time() - t0\n", "\n", "print(f\"Two-body propagation took {t_kepler:.5f} seconds.\")\n", "print(f\"Medium Precision propagation took {t_mp:.5f} seconds.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The outputs of our propagations, `x_kepler` and `x_mp` are Nx6 numpy arrays, where N is the number of timesteps (in our case, 1000). Each row of this array is the 6-element state vector at the corresponding timestep." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1000, 6)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x_kepler.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's plot the two orbits to see if we can spot any differences." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Z-axis (km)')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "fig, (ax1, ax2, ax3) = plt.subplots(3, sharex=True)\n", "fig.suptitle(\"Comparing Two-Body and Medium Precision Propagators\")\n", "\n", "ax1.plot(t_eval, x_kepler[:,0], \"b\", lw=2, label=\"Kepler\")\n", "ax1.plot(t_eval, x_mp[:,0], \"g\", lw=2, label=\"Medium Precision\")\n", "ax1.set_ylabel(\"X-axis (km)\")\n", "ax1.legend()\n", "\n", "ax2.plot(t_eval, x_kepler[:,1], \"b\", lw=2, label=\"Kepler\")\n", "ax2.plot(t_eval, x_mp[:,1], \"g\", lw=2, label=\"Medium Precision\")\n", "ax2.set_ylabel(\"Y-axis (km)\")\n", "\n", "ax3.plot(t_eval, x_kepler[:,2], \"b\", lw=2, label=\"Kepler\")\n", "ax3.plot(t_eval, x_mp[:,2], \"g\", lw=2, label=\"Medium Precision\")\n", "ax3.set_ylabel(\"Z-axis (km)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Well, look at that! The differences in the X and Y axes are too small to see at this scale, but it's obvious that the Kepler propagator misses some very slight disturbances in the Z-axis due to the perturbations included in the Medium Precision model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "kernelspec": { "display_name": "maddg", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.7" } }, "nbformat": 4, "nbformat_minor": 2 }