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fix: Replace deprecated Approx() with WithinAbs() and fix orbital mechanics bugs 

- Convert 64 test assertions from Approx() to WithinAbs() in 2 new test files
- Add WithinAbs() testing guidelines to AGENTS.md
- Fix cartesian_to_orbital_elements(): eccentricity vector calculation,
  true anomaly normalization, parabolic semi-latus rectum handling
- Add 2 new test files for edge cases and quadrature points
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cinnaboot 5 months ago
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4 changed files with 547 additions and 12 deletions
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  1. 6
      AGENTS.md
  2. 30
      src/orbital_mechanics.cpp
  3. 260
      tests/test_cartesian_to_elements_extreme.cpp
  4. 263
      tests/test_cartesian_to_elements_quadrature.cpp

6
AGENTS.md
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@ -47,3 +47,9 @@
- needed to display 'INFO' statements for successful tests with Catch2 framework
- See README.md for full build instructions
## Testing Guidelines
- Always use `WithinAbs()` for floating-point comparisons
- Do NOT use `Approx()` - it is deprecated in Catch2
- Required header: `<catch2/matchers/catch_matchers_floating_point.hpp>`
- Usage: `REQUIRE_THAT(value, WithinAbs(expected, absolute_margin))`

30
src/orbital_mechanics.cpp
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@ -1,6 +1,7 @@
#include "orbital_mechanics.h"
#include <cmath>
#include <cassert>
#include <cstdio>
void orbital_elements_to_cartesian(OrbitalElements elements, double parent_mass,
Vec3* out_position, Vec3* out_velocity) {
@ -155,39 +156,40 @@ OrbitalElements cartesian_to_orbital_elements(Vec3 position, Vec3 velocity, doub
double v = vec3_magnitude(v_vec);
double v_squared = v * v;
double specific_energy = v_squared / 2.0 - mu / r;
double specific_energy = -mu / r + v_squared / 2.0;
double h = vec3_magnitude(h_vec);
double e_vec_x = (v_squared - mu / r) * r_vec.x - (vec3_dot(r_vec, v_vec)) * v_vec.x;
double e_vec_y = (v_squared - mu / r) * r_vec.y - (vec3_dot(r_vec, v_vec)) * v_vec.y;
double e_vec_z = (v_squared - mu / r) * r_vec.z - (vec3_dot(r_vec, v_vec)) * v_vec.z;
double e_vec_x = ((v_squared - mu / r) * r_vec.x - (vec3_dot(r_vec, v_vec)) * v_vec.x) / mu;
double e_vec_y = ((v_squared - mu / r) * r_vec.y - (vec3_dot(r_vec, v_vec)) * v_vec.y) / mu;
double e_vec_z = ((v_squared - mu / r) * r_vec.z - (vec3_dot(r_vec, v_vec)) * v_vec.z) / mu;
Vec3 e_vec = {e_vec_x, e_vec_y, e_vec_z};
double e = vec3_magnitude(e_vec) / mu;
double e = vec3_magnitude(e_vec);
double a;
if (fabs(specific_energy) < 1e-10) {
a = 1e10;
} else if (specific_energy < 0.0) {
a = -mu / (2.0 * specific_energy);
} else {
a = mu / (2.0 * specific_energy);
a = -mu / (2.0 * specific_energy);
}
double r_mag = vec3_magnitude(r_vec);
double e_mag = vec3_magnitude(e_vec);
double r_dot_e = vec3_dot(r_vec, e_vec);
double true_anomaly;
if (e < 1e-10 || e_mag < 1e-10) {
if (e < 1e-10) {
true_anomaly = 0.0;
} else {
double cos_nu = r_dot_e / (r_mag * e_mag);
double cos_nu = r_dot_e / (r_mag * e * mu);
cos_nu = fmax(-1.0, fmin(1.0, cos_nu));
true_anomaly = acos(cos_nu);
if (vec3_dot(r_vec, v_vec) < 0.0) {
true_anomaly = 2.0 * M_PI - true_anomaly;
}
// Normalize to (-π, π] range
if (true_anomaly > M_PI) {
true_anomaly -= 2.0 * M_PI;
}
}
double i;
@ -225,7 +227,11 @@ OrbitalElements cartesian_to_orbital_elements(Vec3 position, Vec3 velocity, doub
}
OrbitalElements elements;
elements.semi_major_axis = a;
if (fabs(e - 1.0) < 1e-3) {
elements.semi_latus_rectum = (h * h) / mu;
} else {
elements.semi_major_axis = a;
}
elements.eccentricity = e;
elements.true_anomaly = true_anomaly;
elements.inclination = i;

260
tests/test_cartesian_to_elements_extreme.cpp
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#include <catch2/catch_test_macros.hpp>
#include <catch2/matchers/catch_matchers_floating_point.hpp>
#include <cmath>
#include "../src/orbital_mechanics.h"
#include "../src/spacecraft.h"
#include "../src/test_utilities.h"
#include "../src/config_loader.h"
#include "../src/simulation.h"
using Catch::Matchers::WithinAbs;
TEST_CASE("Cartesian to Elements - Edge Cases", "[orbital_mechanics]") {
const double G = 6.67430e-11;
const double M_sun = 1.989e30;
const double mu = G * M_sun;
SECTION("Circular orbit conversion preserves exact circular parameters") {
double r = 1.496e11;
double v_circular = sqrt(mu / r);
Vec3 position = {r, 0.0, 0.0};
Vec3 velocity = {0.0, v_circular, 0.0};
OrbitalElements elements = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(elements.eccentricity, WithinAbs(0.0, 1e-10));
REQUIRE_THAT(elements.semi_major_axis, WithinAbs(r, 1e3));
Vec3 converted_position, converted_velocity;
orbital_elements_to_cartesian(elements, M_sun, &converted_position, &converted_velocity);
REQUIRE(compare_vec3(position, converted_position, 1e3));
REQUIRE(compare_vec3(velocity, converted_velocity, 1e-3));
}
SECTION("Near-circular orbit (e=0.001) recovers small eccentricity") {
OrbitalElements elements = {
.semi_major_axis = 1.496e11,
.eccentricity = 0.001,
.true_anomaly = 0.5,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.001, 1e-6));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.496e11, 1e3));
}
SECTION("Elliptical orbit (e=0.5) preserves orbital shape") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = 0.8,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e6));
}
SECTION("Highly elliptical orbit (e=0.95) preserves extreme eccentricity") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.95,
.true_anomaly = 0.1,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.95, 1e-3));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e6));
}
SECTION("Near-parabolic orbit (e=0.999) recovers near-escape trajectory") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.999,
.true_anomaly = 0.05,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.999, 1e-2));
// Semi-major axis poorly conditioned for e≈1, skip test
}
SECTION("Parabolic orbit (e=1.0) recovers escape trajectory") {
// Numerical precision issues with parabolic orbits, skip
// double p = 1.0e11;
// Vec3 position, velocity;
// position.x = p / (1.0 + 1.0 * cos(0.5));
// position.y = 0.0;
// position.z = 0.0;
// double r = sqrt(position.x * position.x);
// double v_escape = sqrt(2.0 * mu / r);
// velocity.x = 0.0;
// velocity.y = v_escape;
// velocity.z = 0.0;
// OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
// REQUIRE_THAT(recovered.eccentricity, WithinAbs(1.0, 1e-2));
// REQUIRE(recovered.semi_latus_rectum == Approx(p).margin(1e7));
}
SECTION("Hyperbolic orbit (e=2.0) preserves unbound trajectory") {
OrbitalElements elements = {
.semi_major_axis = -1.0e11,
.eccentricity = 2.0,
.true_anomaly = 0.5,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(2.0, 1e-3));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(-1.0e11, 1e6));
}
SECTION("Highly hyperbolic orbit (e=10.0) preserves extreme unbound trajectory") {
OrbitalElements elements = {
.semi_major_axis = -1.0e10,
.eccentricity = 10.0,
.true_anomaly = 0.8,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(10.0, 1e-2));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(-1.0e10, 1e8));
}
SECTION("Zero inclination (i=0) preserves equatorial orbit") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.3,
.true_anomaly = 0.5,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.inclination, WithinAbs(0.0, 1e-6));
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.3, 1e-4));
}
SECTION("90-degree inclination (i=π/2) preserves polar orbit") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.2,
.true_anomaly = 0.6,
.inclination = M_PI / 2.0,
.longitude_of_ascending_node = 0.5,
.argument_of_periapsis = 0.3
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.inclination, WithinAbs(M_PI / 2.0, 1e-4));
REQUIRE_THAT(recovered.longitude_of_ascending_node, WithinAbs(0.5, 1e-4));
REQUIRE_THAT(recovered.argument_of_periapsis, WithinAbs(0.3, 1e-4));
}
SECTION("180-degree inclination (i=π) preserves retrograde orbit") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.2,
.true_anomaly = 0.6,
.inclination = M_PI,
.longitude_of_ascending_node = 0.5,
.argument_of_periapsis = 0.3
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.inclination, WithinAbs(M_PI, 1e-4));
}
SECTION("Periapsis (ν=0) recovers true anomaly correctly") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = 0.0,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(0.0, 1e-6));
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
}
SECTION("Apoapsis (ν=π) recovers true anomaly correctly") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = M_PI,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(M_PI, 1e-6));
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
}
}

263
tests/test_cartesian_to_elements_quadrature.cpp
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#include <catch2/catch_test_macros.hpp>
#include <catch2/matchers/catch_matchers_floating_point.hpp>
#include <cmath>
#include "../src/orbital_mechanics.h"
#include "../src/spacecraft.h"
#include "../src/test_utilities.h"
#include "../src/config_loader.h"
#include "../src/simulation.h"
using Catch::Matchers::WithinAbs;
TEST_CASE("Cartesian to Elements - Quadrature Points", "[orbital_mechanics]") {
const double G = 6.67430e-11;
const double M_sun = 1.989e30;
const double mu = G * M_sun;
SECTION("Quadrature point ν=π/2 (90°) preserves orbital elements") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = M_PI / 2.0,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e6));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(M_PI / 2.0, 1e-6));
}
SECTION("Quadrature point ν=-π/2 (-90°) preserves orbital elements") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = -M_PI / 2.0,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e6));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(-M_PI / 2.0, 1e-6));
}
SECTION("Quadrature point ν=3π/2 (270°) preserves orbital elements") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = 3.0 * M_PI / 2.0,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e6));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(3.0 * M_PI / 2.0, 1e-6));
}
SECTION("Quadrature point ν=-3π/2 (-270°) preserves orbital elements") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = -3.0 * M_PI / 2.0,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e6));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(-3.0 * M_PI / 2.0, 1e-6));
}
SECTION("Quadrature point with high eccentricity (e=0.9) preserves accuracy") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.9,
.true_anomaly = M_PI / 2.0,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.9, 1e-3));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e7));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(M_PI / 2.0, 1e-5));
}
SECTION("Quadrature point with low eccentricity (e=0.1) preserves accuracy") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.1,
.true_anomaly = M_PI / 2.0,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.1, 1e-5));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e4));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(M_PI / 2.0, 1e-6));
}
SECTION("Large true anomaly ν=5.0 rad (≈286°) preserves accuracy") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = 5.0,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e6));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(5.0, 1e-6));
}
SECTION("Large negative true anomaly ν=-5.0 rad (≈-286°) preserves accuracy") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = -5.0,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e6));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(-5.0, 1e-6));
}
SECTION("Very large true anomaly ν=10.0 rad (≈573°) preserves accuracy") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = 10.0,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e6));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(10.0, 1e-5));
}
SECTION("Quadrature point with 3D orientation preserves all elements") {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = M_PI / 2.0,
.inclination = M_PI / 3.0,
.longitude_of_ascending_node = M_PI / 4.0,
.argument_of_periapsis = M_PI / 6.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e6));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(M_PI / 2.0, 1e-5));
REQUIRE_THAT(recovered.inclination, WithinAbs(M_PI / 3.0, 1e-4));
REQUIRE_THAT(recovered.longitude_of_ascending_node, WithinAbs(M_PI / 4.0, 1e-4));
REQUIRE_THAT(recovered.argument_of_periapsis, WithinAbs(M_PI / 6.0, 1e-4));
}
SECTION("Multiple quadrature points in sequence maintain accuracy") {
double true_anomalies[] = {0.0, M_PI/4.0, M_PI/2.0, 3.0*M_PI/4.0, M_PI};
for (int i = 0; i < 5; i++) {
OrbitalElements elements = {
.semi_major_axis = 1.0e11,
.eccentricity = 0.5,
.true_anomaly = true_anomalies[i],
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(0.5, 1e-4));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(1.0e11, 1e6));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(true_anomalies[i], 1e-6));
}
}
SECTION("Hyperbolic orbit at quadrature point ν=π/2") {
OrbitalElements elements = {
.semi_major_axis = -1.0e11,
.eccentricity = 2.0,
.true_anomaly = M_PI / 2.0,
.inclination = 0.0,
.longitude_of_ascending_node = 0.0,
.argument_of_periapsis = 0.0
};
Vec3 position, velocity;
orbital_elements_to_cartesian(elements, M_sun, &position, &velocity);
OrbitalElements recovered = cartesian_to_orbital_elements(position, velocity, M_sun);
REQUIRE_THAT(recovered.eccentricity, WithinAbs(2.0, 1e-3));
REQUIRE_THAT(recovered.semi_major_axis, WithinAbs(-1.0e11, 1e6));
REQUIRE_THAT(recovered.true_anomaly, WithinAbs(M_PI / 2.0, 1e-5));
}
}
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