const PI = Math.PI; const SOLAR_MASS = 4 * PI * PI; const DAYS_PER_YEAR = 365.24; function Body(x, y, z, vx, vy, vz, mass) { this.x = x; this.y = y; this.z = z; this.vx = vx; this.vy = vy; this.vz = vz; this.mass = mass; } function Jupiter() { return new Body( 4.84143144246472090e+00, -1.16032004402742839e+00, -1.03622044471123109e-01, 1.66007664274403694e-03 * DAYS_PER_YEAR, 7.69901118419740425e-03 * DAYS_PER_YEAR, -6.90460016972063023e-05 * DAYS_PER_YEAR, 9.54791938424326609e-04 * SOLAR_MASS ); } function Saturn() { return new Body( 8.34336671824457987e+00, 4.12479856412430479e+00, -4.03523417114321381e-01, -2.76742510726862411e-03 * DAYS_PER_YEAR, 4.99852801234917238e-03 * DAYS_PER_YEAR, 2.30417297573763929e-05 * DAYS_PER_YEAR, 2.85885980666130812e-04 * SOLAR_MASS ); } function Uranus() { return new Body( 1.28943695621391310e+01, -1.51111514016986312e+01, -2.23307578892655734e-01, 2.96460137564761618e-03 * DAYS_PER_YEAR, 2.37847173959480950e-03 * DAYS_PER_YEAR, -2.96589568540237556e-05 * DAYS_PER_YEAR, 4.36624404335156298e-05 * SOLAR_MASS ); } function Neptune() { return new Body( 1.53796971148509165e+01, -2.59193146099879641e+01, 1.79258772950371181e-01, 2.68067772490389322e-03 * DAYS_PER_YEAR, 1.62824170038242295e-03 * DAYS_PER_YEAR, -9.51592254519715870e-05 * DAYS_PER_YEAR, 5.15138902046611451e-05 * SOLAR_MASS ); } function Sun() { return new Body(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, SOLAR_MASS); } const bodies = Array(Sun(), Jupiter(), Saturn(), Uranus(), Neptune()); function offsetMomentum() { let px = 0; let py = 0; let pz = 0; const size = bodies.length; for (let i = 0; i < size; i++) { const body = bodies[i]; const mass = body.mass; px += body.vx * mass; py += body.vy * mass; pz += body.vz * mass; } const body = bodies[0]; body.vx = -px / SOLAR_MASS; body.vy = -py / SOLAR_MASS; body.vz = -pz / SOLAR_MASS; } function advance(dt) { const size = bodies.length; for (let i = 0; i < size; i++) { const bodyi = bodies[i]; let vxi = bodyi.vx; let vyi = bodyi.vy; let vzi = bodyi.vz; for (let j = i + 1; j < size; j++) { const bodyj = bodies[j]; const dx = bodyi.x - bodyj.x; const dy = bodyi.y - bodyj.y; const dz = bodyi.z - bodyj.z; const d2 = dx * dx + dy * dy + dz * dz; const mag = dt / (d2 * Math.sqrt(d2)); const massj = bodyj.mass; vxi -= dx * massj * mag; vyi -= dy * massj * mag; vzi -= dz * massj * mag; const massi = bodyi.mass; bodyj.vx += dx * massi * mag; bodyj.vy += dy * massi * mag; bodyj.vz += dz * massi * mag; } bodyi.vx = vxi; bodyi.vy = vyi; bodyi.vz = vzi; } for (let i = 0; i < size; i++) { const body = bodies[i]; body.x += dt * body.vx; body.y += dt * body.vy; body.z += dt * body.vz; } } function energy() { let e = 0; const size = bodies.length; for (let i = 0; i < size; i++) { const bodyi = bodies[i]; e += 0.5 * bodyi.mass * ( bodyi.vx * bodyi.vx + bodyi.vy * bodyi.vy + bodyi.vz * bodyi.vz ); for (let j = i + 1; j < size; j++) { const bodyj = bodies[j]; const dx = bodyi.x - bodyj.x; const dy = bodyi.y - bodyj.y; const dz = bodyi.z - bodyj.z; const distance = Math.sqrt(dx * dx + dy * dy + dz * dz); e -= (bodyi.mass * bodyj.mass) / distance; } } return e; } const n = +50000000; offsetMomentum(); console.log(energy().toFixed(9)); const start = Date.now(); for (let i = 0; i < n; i++) { advance(0.01); } const end = Date.now(); console.log(energy().toFixed(9)); console.log("elapsed:",end-start);