JavaScript recursion: Maximum call stack size exceeded

I have a recursive function for moving some circles on a canvas. Overed circle is enlarged (zoom in) and all the other circles is pushed away. Pushed circles push other circles and so on until zooming is complete.

I get an error "Maximum call stack size exceeded", and I understand the problem, but I just don't know how to solve it... I found three possible solutions for solving recursion problems in general:

1. Change recursion to iteration
2. Use memoization
3. Use SetTimeout

But I think that I can use none of them:

1. I can not implement iteration because of unknown count of operations needed
2. I don't understand memoization well enough, but I think it does not fit either (or maybe I'm wrong and someone could told me differently?)
3. I can not use SetTimeout, because it should be blocking function calls at this particular animation.

How do I fix this problem?

// Pushes circles aside when some other circle leans on these circles (on zoom in)
var moveCirclesAside = function(circle1, circleToSkip, groupOfMoves) {
    var count = circles.length;
    for (var i = 0; i < count; i++) {

        // Skip the same circle
        if (i == circle1.i) {
            continue;
        }

        // Also skip the circle which was intended not to move any further
        if (circleToSkip != null && i == circleToSkip.i) {
            continue;
        }

        // Get second circle
        var circle2 = circles[i];

        // Calculate a distance between two circles
        var dx = circle2.x - circle1.x;
        var dy = circle2.y - circle1.y;
        var distance = Math.sqrt((dx * dx) + (dy * dy));

        // If circles already collided need to do some moving...
        if (distance <= circle1.r + circle2.r + OD.config.circleSpacing) {

            // Get collision angles
            var a