return {

{80.f, 50, 5.972e24f, {0.f, 0.f, 0.f}, {0.f, 0.f, 0.0f}, {0.f, 0.f, 0.f}},

{20.f, 50, 7.348e22f, {-500.f, 0.f, 0.f}, {0.f, 75.f, 50.f}, {0.f, 0.f, 0.f}},

{20.f, 50, 7.348e22f, {600.f, 0.f, 0.f}, {0.f, -68.f, -30.f}, {0.f, 0.f, 0.f}},

{10.f, 50, 1e22f, {0.f, 500.f, 0.f}, {0.f, -60.f, 0.f}, {0.f, 0.f, 0.f}},

{15.f, 50, 2e22f, {800.f, -400.f, 200.f}, {-70.f, 55.f, -10.f},{0.f, 0.f, 0.f}},

{25.f, 50, 1e23f, {1500.f, 1500.f, -1500.f}, {0.f, 0.f, 0.f}, {0.f, 0.f, 0.f}},

{5.f, 50, 1e21f, {-300.f, -300.f, -300.f}, {45.f, 45.f, 45.f}, {0.f, 0.f, 0.f}},

{5.f, 50, 1e21f, {300.f, 300.f, 300.f}, {-45.f, -45.f, -45.f},{0.f, 0.f, 0.f}},

};

const int N_STEPS = 2500;

const float DT = 1.0f / 60.0f;

std::vector<Planet> initial = loadScene("scene.json");

if (initial.empty()) {

std::cout << "Using default hardcoded scene.\n";

initial = defaultScene();

}

const char* names[] = { "explicit_euler", "semi_implicit_euler", "leapfrog", "rk4" };

std::array<std::vector<float>, 4> errors;

for (int integ = 0; integ < 4; ++integ) {

std::vector<Planet> planets = initial;

float E0 = totalEnergy(planets);

std::cout << "Running " << names[integ] << "...\n";

for (int step = 0; step < N_STEPS; ++step) {

calculateMovement(planets, DT, integ);

checkAllCollisions(planets);

float err = (E0 != 0.0f) ? std::abs((totalEnergy(planets) - E0) / E0) : 0.0f;

errors[integ].push_back(err);

}

}

std::ofstream csv("docs/energy_errors.csv");

csv << "time_s";

for (const char* name : names) csv << "," << name;

csv << "\n";

for (int s = 0; s < N_STEPS; ++s) {

csv << (s + 1) * DT;

for (int i = 0; i < 4; ++i) csv << "," << errors[i][s];

csv << "\n";

}

std::cout << "Written docs/energy_errors.csv (" << N_STEPS << " steps, dt=" << DT << ")\n";

return 0;