Java – how to move objects at speed correctly?

I recently started playing Android and decided to try to make a basic physical simulator, but I encountered a small problem

I have ball's object. Each ball has a velocity vector. The way I move it is to add the position of each ball to the position of the ball. It works well before I notice the problem with this method

When I tried to apply gravity to the ball, I noticed that when the two balls were close to each other, one of them was fast

After some debugging, I found the reason for this. The following is an example of my calculation of gravity and acceleration:

    //for each ball that isn't this ball
    for (Ball ball : Ball.balls)
        if (ball != this) {
            double m1 = this.getMass();
            double m2 = ball.getMass();
            double distance = this.getLocation().distance(ball.getLocation());
            double Fg = 6.674*((m1*m2)/(distance * distance));
            Vector direction = ball.getLocation().subtract(this.getLocation()).toVector();
            Vector gravity = direction.normalize().multiply(Fg / mass);
            this.setVeloctity(this.getVeLocity().add(gravity));
        }

That's the problem – when the ball gets very close, the gravity becomes very high (as it should be), so the speed becomes very high, but because I add a vector to each scale position, and the value of the vector is very high, a ball is ejected

This reminds me of my question - is there a better way to move objects than adding vectors? Also, is there a better way to deal with gravity?

I appreciate any help you offer

resolvent:

You can try this:

acceleration.y = force.y / MASS; //to get the acceleration
force.y = MASS * GRAVITY_Constant; // to get the force
displacement.y = veLocity.y * dt + (0.5f * acceleration.y * dt * dt); //Verlet integration for y displacment
position.y += displacement.y * 100; //Now cal to position
new_acceleration.y = force.y / MASS; //cau the new acc
avg_acceleration.y = 0.5f * (new_acceleration.y + acceleration.y); //get the avg
veLocity.y += avg_acceleration.y * dt; // Now cal the veLocity from the avg

(acceleration, velocity, displacement and position) is the vector of the ball

*Note (DT = delta time, that is, the difference time between the current frame and the previous frame