Attempt at a better version of n-body for PHP

n-body-test.php

<?php

/* The Computer Language Benchmarks Game
   https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
    Contributed by George Peter Banyard
*/

final class Body {
    private const SOLAR_MASS = 4 * M_PI * M_PI;
    private const DAYS_PER_YEAR = 365.24;

    public float $x;
    public float $y;
    public float $z;
    public float $vx;
    public float $vy;
    public float $vz;
    public float $mass;

    public function __construct(
        float $x,
        float $y,
        float $z,
        float $vx,
        float $vy,
        float $vz,
        float $mass
    ) {
        $this->x = $x;
        $this->y = $y;
        $this->z = $z;
        $this->vx = $vx;
        $this->vy = $vy;
        $this->vz = $vz;
        $this->mass = $mass;
    }

    public function offsetMomentum(float $px, float $py, float $pz): self
    {
        $this->vx = -$px / self::SOLAR_MASS;
        $this->vy = -$py / self::SOLAR_MASS;
        $this->vz = -$pz / self::SOLAR_MASS;
        return $this;
    }

    public static function jupiter(): self
    {
        return new self(
            4.84143144246472090e+00,
            -1.16032004402742839e+00,
            -1.03622044471123109e-01,
            1.66007664274403694e-03 * self::DAYS_PER_YEAR,
            7.69901118419740425e-03 * self::DAYS_PER_YEAR,
            -6.90460016972063023e-05 * self::DAYS_PER_YEAR,
            9.54791938424326609e-04 * self::SOLAR_MASS,
        );
    }

    public static function saturn(): self
    {
        return new self(
            8.34336671824457987e+00,
            4.12479856412430479e+00,
            -4.03523417114321381e-01,
            -2.76742510726862411e-03 * self::DAYS_PER_YEAR,
            4.99852801234917238e-03 * self::DAYS_PER_YEAR,
            2.30417297573763929e-05 * self::DAYS_PER_YEAR,
            2.85885980666130812e-04 * self::SOLAR_MASS,
        );
    }

    public static function uranus(): self
    {
        return new self(
            1.28943695621391310e+01,
            -1.51111514016986312e+01,
            -2.23307578892655734e-01,
            2.96460137564761618e-03 * self::DAYS_PER_YEAR,
            2.37847173959480950e-03 * self::DAYS_PER_YEAR,
            -2.96589568540237556e-05 * self::DAYS_PER_YEAR,
            4.36624404335156298e-05 * self::SOLAR_MASS
        );
    }

    public static function neptune(): self
    {
        return new self(
            1.53796971148509165e+01,
            -2.59193146099879641e+01,
            1.79258772950371181e-01,
            2.68067772490389322e-03 * self::DAYS_PER_YEAR,
            1.62824170038242295e-03 * self::DAYS_PER_YEAR,
            -9.51592254519715870e-05 * self::DAYS_PER_YEAR,
            5.15138902046611451e-05 * self::SOLAR_MASS
        );
    }

    public static function sun(): self
    {
        return new self(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, self::SOLAR_MASS);
    }

}

final class NBodySystem {
    private array $bodies;

    public function __construct(Body ...$bodies)
    {
        $px = 0.0;
        $py = 0.0;
        $pz = 0.0;

        foreach ($bodies as $body) {
            $px += $body->vx * $body->mass;
            $py += $body->vy * $body->mass;
            $pz += $body->vz * $body->mass;
        }
        $bodies[0]->offsetMomentum($px, $py, $pz);

        $this->bodies = $bodies;
    }

    public function advance(float $dt): void
    {
        foreach ($this->bodies as $index => $referenceBody) {
            $nbBodies = count($this->bodies);
            for ($i = $index + 1; $i < $nbBodies; ++$i) {
                $body = $this->bodies[$i];
                $dx = $referenceBody->x - $body->x;
                $dy = $referenceBody->y - $body->y;
                $dz = $referenceBody->z - $body->z;

                $distance² = $dx**2 + $dy**2 + $dz**2;
                $distance = sqrt($distance²);
                $magnitude = $dt / ($distance² * $distance);

                $referenceBody->vx -= $dx * $body->mass * $magnitude;
                $referenceBody->vy -= $dy * $body->mass * $magnitude;
                $referenceBody->vz -= $dz * $body->mass * $magnitude;

                $body->vx += $dx * $referenceBody->mass * $magnitude;
                $body->vy += $dy * $referenceBody->mass * $magnitude;
                $body->vz += $dz * $referenceBody->mass * $magnitude;
            }
        }

        foreach ($this->bodies as $body) {
            $body->x += $dt * $body->vx;
            $body->y += $dt * $body->vy;
            $body->z += $dt * $body->vz;
        }
    }

    public function energy(): float
    {
        $e = 0.0;

        foreach ($this->bodies as $index => $referenceBody) {
            $e += 0.5 * $referenceBody->mass * (
                $referenceBody->vx * $referenceBody->vx
                + $referenceBody->vy * $referenceBody->vy
                + $referenceBody->vz * $referenceBody->vz
            );
            $nbBodies = count($this->bodies);
            for ($i = $index + 1; $i < $nbBodies; ++$i) {
                $body = $this->bodies[$i];
                $dx = $referenceBody->x - $body->x;
                $dy = $referenceBody->y - $body->y;
                $dz = $referenceBody->z - $body->z;

                $distance = sqrt($dx**2 + $dy**2 + $dz**2);
                $e -= ($referenceBody->mass * $body->mass) / $distance;
            }
        }

        return $e;
    }
}

$n = $argv[1];

$system = new NBodySystem(Body::sun(), Body::jupiter(), Body::saturn(), Body::uranus(), Body::neptune());

printf("%0.9f\n", $system->energy());
$start = hrtime(true);
for ($i = 0; $i < $n; ++$i) {
    $system->advance(0.01);
}
printf("%0.9f\n", $system->energy());