How to detect if a ball will collide with another, and the normal vector of the collision?

So I have a 2D game involving balls (circles) colliding. I want to be able to detect if two balls will collide before it happens, and the normal vector of the collision if a collision is going to happen. Take a look at the below picture:

Essentially a normalized vector represented by the red arrow is what I am interested in knowing. How can I figure that out any frame most efficiently, given I know the following:

• The blue ball has a current initial velocity


• The ball ball is pulled down by a constant gravity


• The green ball does not move


• The sizes and location of both balls