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This actually started with a something of an amorous note sent to a lady friend, with the general idea that there is always a (small) gravitational force experienced between two people and if you make everything else disappear, the two will always(eventually) find each other.

So, that of course made the geek in my curious to derive the equation describing the length of time(and final velocity out of morbid curiosity) that it would take two objects with space, with no other gravitational influences to "find each other"(intersect).

I started looking at the basic kinematic equations but soon found myself out my depth when looking at the complexity introduced by acceleration not being constant.

Thanks.

P.S.

The note actually was a hit.