{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial 04: EGM2008 & Mass Gravity Models\n", "\n", "This tutorial demonstrates the high-fidelity gravitational mechanics modeled in `OpenGNC`, covering Two-Body, $J_2$, and full Spherical Harmonic perturbations (EGM2008).\n", "\n", "--- \n", "## Theory Prerequisites\n", "\n", "### 1. Two-Body Gravity\n", "The simplest model assuming Earth is a point mass. Acceleration is along the nadir vector:\n", "$$\n", "\\mathbf{a}_{2B} = -\\frac{\\mu}{r^3} \\mathbf{r}\n", "$$\n", "\n", "### 2. $J_2$ Oblateness\n", "Accounting for the equatorial bulge of the Earth via the dominant zonal harmonic $J_2$:\n", "$$\n", "a_{J_2, x} = \\frac{3}{2} J_2 \\frac{\\mu}{r^2} \\left(\\frac{R_E}{r}\\right)^2 \\frac{x}{r} \\left(5 \\frac{z^2}{r^2} - 1\\right)\n", "$$\n", "Adding this to $\\mathbf{a}_{2B}$ introduces **Nodal Precession** and **Apsidal Rotation**.\n", "\n", "### 3. Spherical Harmonics (EGM2008)\n", "For high-accuracy drag, decay, or orbital maintenance triggers, the Earth's potential $U$ is expanded into Associated Legendre Polynomials $P_{nm}$:\n", "$$\n", "U = \\frac{\\mu}{r} \\sum_{n=0}^{N} \\left(\\frac{R_E}{r}\\right)^n \\sum_{m=0}^{n} P_{nm}(\\sin\\phi) \\left( C_{nm}\\cos(m\\lambda) + S_{nm}\\sin(m\\lambda) \\right)\n", "$$\n", "\n", "---" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Gravity modules loaded.\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from opengnc.disturbances.gravity import TwoBodyGravity, J2Gravity, HarmonicsGravity\n", "from opengnc.propagators.cowell import CowellPropagator\n", "\n", "print(\"Gravity modules loaded.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Comparing Gravity Accelerations\n", "\n", "Let's evaluate the difference in acceleration magnitudes at a specific position in Low Earth Orbit (LEO) for Two-Body, $J_2$, and a Degree 10 Spherical Harmonic Model." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Two-Body Accel Magnitude: 8.425509 m/s^2\n", "J2 Gravity Accel Magnitude: 8.437274 m/s^2\n", "Degree 10 Accel Magnitude: 0.016811 m/s^2\n", "\n", "Effect of J2 alone: 0.011766 m/s^2\n", "Effect of Higher Order (10x10) over J2: 8.420463e+00 m/s^2\n" ] } ], "source": [ "# Spacecraft Position in ECI [m] (Approx 500km altitude)\n", "r_eci = np.array([6878137.0, 0.0, 0.0]) # Equatorial plane\n", "jd_epoch = 2451545.0 # J2000\n", "\n", "# 1. Initialize models\n", "gravity_2b = TwoBodyGravity()\n", "gravity_j2 = J2Gravity()\n", "gravity_harmonics = HarmonicsGravity(n_max=10, m_max=10) # Using N=10 for speed in validation\n", "\n", "# 2. Calculate Accelerations\n", "a_2b = gravity_2b.get_acceleration(r_eci)\n", "a_j2 = gravity_j2.get_acceleration(r_eci)\n", "a_har = gravity_harmonics.get_acceleration(r_eci, jd_epoch)\n", "\n", "print(f\"Two-Body Accel Magnitude: {np.linalg.norm(a_2b):.6f} m/s^2\")\n", "print(f\"J2 Gravity Accel Magnitude: {np.linalg.norm(a_j2):.6f} m/s^2\")\n", "print(f\"Degree 10 Accel Magnitude: {np.linalg.norm(a_har):.6f} m/s^2\")\n", "\n", "# Delta metrics\n", "delta_j2 = np.linalg.norm(a_j2 - a_2b)\n", "delta_har = np.linalg.norm(a_har - a_j2)\n", "print(f\"\\nEffect of J2 alone: {delta_j2:.6f} m/s^2\")\n", "print(f\"Effect of Higher Order (10x10) over J2: {delta_har:.6e} m/s^2\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Dynamic Impact: Orbit Precession\n", "\n", "The $J_2$ effect causes the right ascension of the ascending node (RAAN) to precess over time. Let's propagate a short orbit under $J_2$ and see the trajectory." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Propagated over 540 discrete steps.\n" ] } ], "source": [ "from opengnc.visualization.orbit import plot_orbit_3d\n", "\n", "# Initial Orbit State [m], [m/s]\n", "r_0 = np.array([6878137.0, 0.0, 0.0])\n", "v_0 = np.array([0.0, 7612.0 * np.cos(np.radians(45)), 7612.0 * np.sin(np.radians(45))]) # 45 deg inclination\n", "\n", "propagator = CowellPropagator()\n", "\n", "# Setup perturbation function for J2\n", "def j2_perturbation(t, r, v):\n", " # J2Gravity.get_acceleration already returns (TwoBody + J2)\n", " # propagator integrates (TwoBody + perturbation_acc_fn)\n", " # So we must return ONLY the perturbative acceleration\n", " return J2Gravity().get_acceleration(r) - TwoBodyGravity().get_acceleration(r)\n", "\n", "# Propagate for 1 Orbit (approx 5400 seconds)\n", "dt_span = 5400\n", "states = []\n", "steps = 540\n", "dt_step = dt_span / steps\n", "\n", "curr_r, curr_v = r_0, v_0\n", "for i in range(steps):\n", " states.append(curr_r.copy())\n", " # Single-step propagation workaround for demo loops or use integrate() directly\n", " # For simplicity, we can just use the internal integrator if desired, \n", " # but for visualization we want multiple points.\n", " curr_r, curr_v = propagator.propagate(curr_r, curr_v, dt_step, perturbation_acc_fn=j2_perturbation)\n", "\n", "states = np.array(states)\n", "print(f\"Propagated over {steps} discrete steps.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Visualization\n", "\n", "Using the `opengnc.visualization` module, we can display our 3D orbit around a spherical Earth model." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "colorscale": [ [ 0, "rgb(247,251,255)" ], [ 0.125, "rgb(222,235,247)" ], [ 0.25, "rgb(198,219,239)" ], [ 0.375, "rgb(158,202,225)" ], [ 0.5, "rgb(107,174,214)" ], [ 0.625, "rgb(66,146,198)" ], [ 0.75, "rgb(33,113,181)" ], [ 0.875, "rgb(8,81,156)" ], [ 1, "rgb(8,48,107)" ] ], "hoverinfo": "skip", "name": "Earth", "opacity": 0.3, "showscale": false, "type": "surface", "x": { "bdata": 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", "dtype": "f8", "shape": "60, 60" } }, { "line": { "color": "darkred", "width": 4 }, "mode": "lines", "name": "Orbit Path", "type": "scatter3d", "x": { "bdata": 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"#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "LEO orbit under J2 Disturbances" } } } }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Render the orbit in 3D\n", "fig = plot_orbit_3d(states, title=\"LEO orbit under J2 Disturbances\")\n", "fig.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.10.11" } }, "nbformat": 4, "nbformat_minor": 4 }