Using velocity verlet algorithm for nbody simulation results in planet leaving orbit

Question

I'm new to computational physics and attempting an n-Body simulator in java but for some reason the planet in orbit leaves the orbit when it reaches the fastest accelaration aka the closest point to the other planet. I'm testing the velocity verlet algorithm for two bodies at the moment. I'm not quite sure what I'm doing wrong but here is the site im using to learn the Velocity Verlet algorithm. And here is my code:

    public void move(float simSpeed, Planet planet) {
        float deltaT = Gdx.graphics.getDeltaTime() * simSpeed;

        float deltaX = planet.getPos().x - this.pos.x;
        float deltaY = planet.getPos().y - this.pos.y;
        float alpha = (float) Math.toDegrees(Math.atan2(deltaY, deltaX));

        float distance = (float) Math.sqrt(Math.pow(deltaX, 2) + Math.pow(deltaY, 2));
        float F = MainScreen.G * this.m * planet.getM() / (distance * distance);
        this.force.x = F * MathUtils.cosDeg(alpha);
        this.force.y = F * MathUtils.sinDeg(alpha);

        this.pos.x += this.vel.x * deltaT + 0.5f * (this.force.x / this.m) * deltaT * deltaT;
        this.pos.y += this.vel.y * deltaT + 0.5f * (this.force.y / this.m) * deltaT * deltaT;

        this.vel.x += (this.force.x / this.m) * deltaT;
        this.vel.y += (this.force.y / this.m) * deltaT;

    }

EDIT: the code works fine if I use simple Newtonian equations without any integration.

Answer 1

There are two sources for such an error, if the exact solution is known to stay bounded.

• Verlet becomes catastrophically incorrect in singular situations, that is, if two objects become close in a N-body simulation or any other with potentials with singularities.

• "Sequential Verlet" is not Verlet, nor is it second order, nor is it symplectic. You get a complicated first order method with the ensuing error sources.

For expansion on these ideas see

• About using Verlet in a many-particle molecular dynamics simulation https://stackoverflow.com/questions/29374247/lennard-jones-potential-simulation
• forcing singularities with catastrophic consequences by starting a star cluster at zero velocity https://stackoverflow.com/questions/65753463/n-body-simulation-python
• Verlet for N-body in C++ with Eigen https://stackoverflow.com/questions/64190036/how-can-i-update-c-class-members-with-a-function