What's the terminal velocity of an object accelerated by a constant force in interstellar space Terminal Velocity is the velocity at which a the gravitational acceleration and the drag of the air cancel each other out to zero change in velocity. While one might think that space as a vacuum, it really isn't. The interstellar medium has densities between 10^-4 and 10^6 molecules per cube centimetre. Assuming an indestructible object is accelerated constantly with a force of $F$, what will be its terminal velocity? The relativistic effects evolved in this make this above my pay grade. An optimal answer would provide me with a formula for the terminal velocity depending on the objects acceleration. 
 A: A way to calculate a "worst case" limit (ignoring for example the cosmic microwave background) would be to assume that every particle the vehicle hits is simply reflected.  We know that the average mass density $D$ of the intergalactic medium is something less than $10^{-27} kg/m3$.  Classically, a vehicle with cross sectional area of $A$, moving at a speed of $V$ relative to that medium would result in a "frictional" force of $2 A V D$.  Terminal velocity $V_t$ would be the velocity $V$ at which the accelerating force $F$ is equal to the frictional force: $$F = 2AVD$$ or terminal velocity $$V_t = F/(2AD)$$
If the force is large and the cross section is small, then relativistic effects can come into play, requiring a correction term which will make D effectively larger (thus increasing the effective $F$ and will also add a velocity-dependent term to $2AVD$ which further increases the effective $F$.
A: The air resistance formula says that the resistance is proportional to the density of the medium and the square of the velocity. The density of the interstellar medium varies, but let us assume it is 10-16 the density of air. That would suggest that the terminal velocity might be 108 times the terminal velocity of an object falling through air, assuming the force were comparable to 1g, which would mean that c might be the limiting factor rather than the resistance due to the medium.
