{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial 12: Analytical Orbital Maneuvers\n", "\n", "This tutorial covers standard impulsive orbital maneuvers using analytical formulations from circular to circular/elliptical orbits.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Theory Prerequisite\n", "\n", "### 1.1 Hohmann Transfer\n", "A two-impulse maneuver that moves a spacecraft between two coplanar circular orbits of different radii using an elliptical transfer orbit.\n", "\n", "- **Semi-major axis**: $a_{\\text{trans}} = (r_1 + r_2) / 2$\n", "- **First Burn (Perigee)**: $\\Delta V_1 = | v_{\\text{trans, p}} - v_{c1} |$\n", "- **Second Burn (Apogee)**: $\\Delta V_2 = | v_{c2} - v_{\\text{trans, a}} |$\n", "- **Total Delta-V**: $\\Delta V_{\\text{tot}} = \\Delta V_1 + \\Delta V_2$\n", "\n", "### 1.2 Bi-Elliptic Transfer\n", "A three-impulse maneuver that can be more fuel-efficient than a Hohmann transfer when the ratio of the final radius to the initial radius ($r_2 / r_1$) is greater than **15.58**.\n", "\n", "- **Step 1**: Propel to intermediate apogee $r_b > r_2$.\n", "- **Step 2**: Circularize/raise perigee at $r_b$ to target $r_2$.\n", "- **Step 3**: De-circularize at $r_2$ (retrograde) from $r_b$ transfer to circular $r_2$ (Wait, standard bi-elliptic usually raises perigee or apogee. The toolkit splits it into $r_1 \\rightarrow r_b \\rightarrow r_2$)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Imports successful.\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from opengnc.guidance.maneuvers import hohmann_transfer, bi_elliptic_transfer, plane_change\n", "\n", "print(\"Imports successful.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Demonstration: Hohmann vs Bi-Elliptic\n", "\n", "We will compare the Delta-V requirements for a Hohmann transfer and a Bi-Elliptic transfer between a low Earth orbit (LEO) and a high Earth orbit (HEO)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initial Orbit Radius: 6778.00 km\n", "Final Orbit Radius: 42164.00 km\n", "\n", "--- Hohmann Transfer ---\n", "Delta-V 1: 2.3975 km/s\n", "Delta-V 2: 1.4565 km/s\n", "Total Delta-V: 3.8540 km/s\n", "Transfer Time: 5.29 hours\n", "\n", "--- Bi-Elliptic Transfer ---\n", "Intermediate Radius rb: 63246.00 km\n", "Delta-V 1: 2.6382 km/s\n", "Delta-V 2: 1.1408 km/s\n", "Delta-V 3: 0.2935 km/s\n", "Total Delta-V: 4.0725 km/s\n", "Transfer Time: 25.78 hours\n" ] } ], "source": [ "r1 = 6378.0 + 400.0 # LEO: 400 km altitude\n", "r2 = 6378.0 + 35786.0 # GEO: 35786 km altitude\n", "mu = 398600.4418 # Earth gravitational parameter\n", "\n", "print(f\"Initial Orbit Radius: {r1:.2f} km\")\n", "print(f\"Final Orbit Radius: {r2:.2f} km\")\n", "\n", "# 1. Hohmann Transfer\n", "dv1_h, dv2_h, t_h = hohmann_transfer(r1, r2, mu)\n", "dv_tot_h = dv1_h + dv2_h\n", "\n", "print(\"\\n--- Hohmann Transfer ---\")\n", "print(f\"Delta-V 1: {dv1_h:.4f} km/s\")\n", "print(f\"Delta-V 2: {dv2_h:.4f} km/s\")\n", "print(f\"Total Delta-V: {dv_tot_h:.4f} km/s\")\n", "print(f\"Transfer Time: {t_h / 3600:.2f} hours\")\n", "\n", "# 2. Bi-Elliptic Transfer (using intermediate rb)\n", "rb = r2 * 1.5 # Higher intermediate apogee\n", "dv1_b, dv2_b, dv3_b, t_b = bi_elliptic_transfer(r1, r2, rb, mu)\n", "dv_tot_b = dv1_b + dv2_b + dv3_b\n", "\n", "print(\"\\n--- Bi-Elliptic Transfer ---\")\n", "print(f\"Intermediate Radius rb: {rb:.2f} km\")\n", "print(f\"Delta-V 1: {dv1_b:.4f} km/s\")\n", "print(f\"Delta-V 2: {dv2_b:.4f} km/s\")\n", "print(f\"Delta-V 3: {dv3_b:.4f} km/s\")\n", "print(f\"Total Delta-V: {dv_tot_b:.4f} km/s\")\n", "print(f\"Transfer Time: {t_b / 3600:.2f} hours\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 Efficiency Threshold Comparison\n", "\n", "Bi-elliptic is better for large radius ratios ($r_2 / r_1 > 15.58$). Let's plot the total Delta-V vs Radius Ratio." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "r_ratios = np.linspace(2, 40, 50)\n", "dv_hohmann = []\n", "dv_bi_elliptic = []\n", "rb_multiplier = 4.0 # rb = r2 * rb_multiplier\n", "\n", "for ratio in r_ratios:\n", " r_f = r1 * ratio\n", " dv1, dv2, _ = hohmann_transfer(r1, r_f, mu)\n", " dv_hohmann.append(dv1 + dv2)\n", " \n", " r_b = r_f * rb_multiplier\n", " dv1_b, dv2_b, dv3_b, _ = bi_elliptic_transfer(r1, r_f, r_b, mu)\n", " dv_bi_elliptic.append(dv1_b + dv2_b + dv3_b)\n", "\n", "plt.figure(figsize=(10, 5))\n", "plt.plot(r_ratios, dv_hohmann, 'r-', label='Hohmann')\n", "plt.plot(r_ratios, dv_bi_elliptic, 'b--', label=f'Bi-Elliptic (rb = {rb_multiplier} * r2)')\n", "plt.axvline(x=15.58, color='k', linestyle=':', label='Theoretical Threshold (15.58)')\n", "plt.xlabel('Radius Ratio $(r_2 / r_1)$')\n", "plt.ylabel('Total Delta-V [km/s]')\n", "plt.title('Hohmann vs Bi-Elliptic Efficiency')\n", "plt.legend()\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Plane Change Maneuver\n", "\n", "Changing the inclination of an orbit requires an out-of-plane burn." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Circular Velocity: 7.6686 km/s\n", "Delta-V for 10 deg Plane Change at LEO: 1.3367 km/s\n", "Total Hohmann (LEO to GEO) was: 3.8540 km/s\n", "Plane changes at high velocity (low altitude) are expensive!\n" ] } ], "source": [ "v_circ = np.sqrt(mu / r1) # circular velocity at LEO\n", "delta_i = np.radians(10.0) # 10 degrees inclination change\n", "\n", "dv_plane = plane_change(v_circ, delta_i)\n", "\n", "print(f\"Circular Velocity: {v_circ:.4f} km/s\")\n", "print(f\"Delta-V for 10 deg Plane Change at LEO: {dv_plane:.4f} km/s\")\n", "print(f\"Total Hohmann (LEO to GEO) was: {dv_tot_h:.4f} km/s\")\n", "print(\"Plane changes at high velocity (low altitude) are expensive!\")" ] } ], "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 }