Moving a body into a circle of uniform motion

[dexwiz]

I am trying to make a game where a drone approaches a ship, that may be moving, and then orbits it at a set distance. I know that if the drone is already moving in a circle of uniform motion then I use

$a = \frac{v^{r}}{r}$

I then take that magnitude and an angle derived from atan2 with cos and sin to find the x and y components of the acceleration. That works fine.

But how can I calculate the acceleration of the drone that is approaching the ship, still outside of the orbit radius that needs to move into an orbit. I have tried calculating a point for the drones to chase and just move towards that and it usually just ends up giving me some sort of slingshot. I really trying to stay away from giving the ship and drone mass, defining a G constant, and giving the drone thrusters. I just want a simple model to move from approaching the ship to orbiting the ship.

 

[Naty1]

Seems like you can utilize this approach:

http://en.wikipedia.org/wiki/Orbital_speed

More generally, seems like your approach at distance r needs to match linear velocity with orbital velocity...equal speed to orbital speed and tangent at distance r...