Orientation != Velocity Vector != Acceleration Vector
To ensure there's no ambiguity here.
In spacecraft, the direction that the ship is facing is not necessarily the direction in which the ship is moving (but if the ship is accelerating, it usually is the direction in which acceleration is occurring).
Similarly, the direction in which the ship is moving is not necessarily the direction in which the ship is accelerating or facing.
Ship Velocity Vector can be changed without thrusting
But it still requires a momentum exchange with something.
A maneuver typical of this operation is called a gravity assist. The net result of a gravity assist changes the velocity of the ship relative to a third object (e.g. the Sun) but not the body performing the assist (e.g. Jupiter).
What exactly are you asking?
From your question and the comments, I think you want to know how to change spacecraft orientation (not velocity or acceleration vectors), without firing your engines.
If this is your question, then the answer is there are many methods of changing spacecraft orientation without (directly) affecting the spacecraft velocity and acceleration vectors.
- Thrusters / RCS
- Spin stabilization (this doesn't help you change orientation but it helps the spacecraft maintain a desired orientation).
- Momentum wheels (these are not gyroscopes)
- Control moment gyros (these are not moment wheels)
- Solar sails (and/or magnetic sails and/or Solar wind sails)
- Gravity-gradient stabilization (only appropriate when in orbit)
- Magnetic torquers (only appropriate when in a relatively strong magnetic field - this is not a magsail)
- Pure passive attitude control (gravity-gradient is one such passive attitude control, but there are others).
- Off center of mass thrusting (gimbal mounted engine or exhaust vane directed thrust)
This is complicated by the fact that every spacecraft ever designed has its main engine thrusting through the center of gravity.
So if you change a ships orientation while it is thrusting, you will change both its acceleration and velocity vectors.
There is no "turning radius" for spacecraft
Or more precisely the turning radius depends upon your current velocity and your thrust capabilities.
Forget 99.999% of everything you've ever seen about how objects move in space. Anything you've seen in movies or TV are wrong (and this includes supposedly accurate movies like Gravity - don't get me started).
Application of a thrust:
Other than the fact that usually the application of thrust is in the direction the craft is oriented, space craft velocity has nothing to do with spacecraft orientation.
You will probably require multiple attitude control systems. At least one of these will be a system that requires no fuel and little power. At least one of these will involve off-CG axis thrusting by your main propulsion system. The third will likely be a thrusting, reaction control system.
Since you're already aware of RCS, let's look at CMG (control moment gyros).
A CMG can apply the large amounts of torque required to change the orientation of your ship. It also doesn't use much power to do it. However, CMGs have a draw back:
At least three single-axis CMGs are necessary for control of
spacecraft attitude. However, no matter how many CMGs a spacecraft
uses, gimbal motion can lead to relative orientations that produce no
usable output torque along certain directions.
Meaning there are some orientation changes you can not do using only CMGs. To get around this limitation, a CMG attitude control system must use something like RCS.
Off-CG axis thrusting
Will impart rotation upon the spacecraft. By simply changing engine orientation you can cancel this rotation at any time you desire. The draw back is this is only available when firing your main engine. It will also change your velocity vector.