the idea think of smaller and smaller steps until it is almost continuous. you would need calculus to work it out. there may be a external gravitational field to add to the confusion
near earth or a large mass there is "escape velocity" which is the speed an object would have if if started with zero speed falling from a very very large distance where the gravity acceleration is much much less than at the surface
in this example the rocket would seem at first to move faster and faster and might be expected to exceed the speed of light
however from the point of view of the asteroid observer the very high speed ship and its fuel INCREASE IN APPARENT MASS as the energy increases and its acceleration slows
from the point of view of the ship the asteroid is moving away and is size and velocity through the empty space is DECREASING
Actually a very good question and requires a careful thought about the speed of the engine, the velocity of the exhaust relative to the engine and the velocities relative to the asteroid
neither ever sees the other go faster than light but they both appear to change
special relativity is REALLY WEIRD!!!