The thing about Newtonian gravitational physics is that when we put it into a system like this, it will create some odd behaviour.
The most pressing problem for us was that somehow we realized (by using the system for a long time) that particles started disappearing. We needed to find out why.
After some digging in the code we realised that if the particles, in one frame, is extremely close to a hand, it's speed will be (by the laws of physics) be divided by 1/r squared. What this means is that if the distance between the hand and the particle is, for example, 0.000001, the particle will get a speed that easily surpasses light speed. That means, in our world, that the particle never ever will be seen again, as it has flown far, far away...
The solution required multiple edits to the "physical laws" of our system.
First, if the distance that is about to be calculated is lower than 0.01, we set it to 0.01. This essentialy is a speed limitation.
Second, if the particle flies outside the screen, not only does it stop, but its coordinate is moved back to the edge (e.g. the particle moves to x = 900, but max of x (the edge) is 105, so we set it to 105).
Third, If a particle reaches an extremely high velocity, we gradually reduce its speed (deceleration) by a factor of 0.9 each frame to a linear max velocity that we have set. This third solution actually is not really a requirement, but rather something that creates a really aesthetically pleasing effect behind the hands' interaction. Check out this video: