💿🐜 Antkeeper source code
https://antkeeper.com
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78 lines
2.4 KiB
78 lines
2.4 KiB
/*
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* Copyright (C) 2021 Christopher J. Howard
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*
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* This file is part of Antkeeper source code.
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*
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* Antkeeper source code is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Antkeeper source code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "celestial-mechanics.hpp"
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#include "math/angles.hpp"
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#include <cmath>
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namespace ast
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{
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double solve_kepler(double ec, double ma, double tolerance, std::size_t iterations)
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{
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// Approximate eccentric anomaly, E
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double e0 = ma + ec * std::sin(ma) * (1.0 + ec * std::cos(ma));
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// Iteratively converge E0 and E1
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for (std::size_t i = 0; i < iterations; ++i)
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{
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double e1 = e0 - (e0 - ec * std::sin(e0) - ma) / (1.0 - ec * std::cos(e0));
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double error = std::abs(e1 - e0);
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e0 = e1;
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if (error < tolerance)
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break;
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}
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return e0;
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}
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double3 orbital_elements_to_ecliptic(const orbital_elements& elements, double ke_tolerance, std::size_t ke_iterations)
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{
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// Calculate semi-minor axis, b
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double b = elements.a * std::sqrt(1.0 - elements.ec * elements.ec);
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// Solve Kepler's equation for eccentric anomaly, E
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double ea = solve_kepler(elements.ec, elements.ma, ke_tolerance, ke_iterations);
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// Calculate radial distance, r; and true anomaly, v
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double xv = elements.a * (std::cos(ea) - elements.ec);
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double yv = b * std::sin(ea);
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double r = std::sqrt(xv * xv + yv * yv);
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double v = std::atan2(yv, xv);
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// Calculate true longitude, l
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double l = elements.w + v;
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// Transform vector (r, 0, 0) from local coordinates to ecliptic coordinates
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// = Rz(-omega) * Rx(-i) * Rz(-l) * r
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double cos_om = std::cos(elements.om);
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double sin_om = std::sin(elements.om);
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double cos_i = std::cos(elements.i);
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double cos_l = std::cos(l);
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double sin_l = std::sin(l);
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return double3
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{
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r * (cos_om * cos_l - sin_om * sin_l * cos_i),
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r * (sin_om * cos_l + cos_om * sin_l * cos_i),
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r * sin_l * std::sin(elements.i)
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};
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}
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} // namespace ast
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