Subject: Why don't binary systems collide when observing from within the system?

Imagine two planets revolving about each other, and an observer some distance 
away which let's say doesn't affect the two planets. Being the observer, I know 
they have a force towards one another because they have mass, and I can see them 
revolving around each other so they must have a centrifugal force outwards, and 
let's say they're distance from each other is such that these two forces are 
equal in magnitude. What I do not understand is, if the observer is now ON one 
of the planets, (and let's say the planets are rotating so that they face each 
other constantly) the other planet which can be seen from observer does not 
appear to be moving at all, why does it seem in this case the two planets should 
collide when it is the same scenario as before?

Re: Why don't binary systems collide when observing from within the system?