Orbiting in space Background
I'm making a game where a spaceship needs to orbit another object in space at a set distance.
Space is, unlike other game, like space is in reality. Friction less. (at least to my understanding)
Question
How do I calculate the direction and strength of the impulse that one "space ship" must emit in order to fall in to and maintain an orbit around another object?
Note on gravity
There is none in this simulation. Yet.
My own thoughts so far
To maintain the orbit, the impulse would always have to be directed directly towards the object.
I think my problem is how to fall into the orbit. What I do so far is I try to aim for a point 90 degrees off from my own incoming vector, and as I approach closer I turn towards the object and impulse towards it.
I think my problem is very related to that I do not keep to a maximum speed on my approach, this makes me fly wildly out of the orbit right away.
 A: If there is no gravity in your simulation, your thoughts are on the right lines.
The amount of centripetal force (=thrust) required to maintain a space-craft of mass m in circular orbit of radius r at speed v is $F=mv^2/r$.  Thrust has to be directed towards the centre of the circle and has to be maintained constantly - so unlike orbiting a planet using gravity, this could use up a lot of fuel.
First decide your orbital radius r and orbital period T.  Calculate the required orbital speed $v=2\pi r/T$.  Then head at this speed v for a point at distance r from the object making a 90 degree angle with the object and your current location - ie a tangent point on your intended orbit.  When you get there (not before, not after) turn on your thrust $F=mv^2/r$ towards the object.  If this exact amount of thrust is not maintained, you will not remain in a circular orbit.

In response to your comment 

And what if I am inside the desired orbital radius already?

There are a number of options, for example :


*

*(Probably easiest) Assuming you are not heading directly for the object, switch off all thrusters and drift until you are outside of the required orbit radius r.  Then use the above procedure.  

*(Quite difficult)  As you drift out towards the required orbit, gradually increase thrust towards the object to reduce your radial speed to zero when you reach the required orbit.  Then use a combination of thrust directed toward the object (radially) and to the side (tangentially) to increase tangential speed to v while maintaining the same orbital radius.   
