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(adsbygoogle = window.adsbygoogle || []).push({});

[itex]a = \frac{v^{r}}{r}[/itex]

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.

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# Moving a body into a circle of uniform motion

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