# Would ejecting propellant close to light speed result a '"dream engine"?

"Dream engine" I assume as pictured in the old science fiction: a single stage rocket that can take off from the Earth and then freely travel at least over Solar system, landing multiple times wherever it needs without refueling.

The rationale is, the mass increases with the speed. Hence by ejecting with velocity close to speed of light we can convert hydrogen atoms into something more like cannon balls by mass. Hence the rocket would require very little mass of propellant.

The energy problem remains obviously unsolved but at least we do not longer need a lot of mass.

• There's really no such thing as "close to light speed". If you're in an inertial reference frame, light speed will be equal regardless of which inertial frame you're in. You can only have "close to light speed" with respect to another body, in which case that other body is "close to light speed" with respect to you. Sep 12 at 13:27
• Yeah baby LHC in space!!! Sep 12 at 13:29
• With respect to the rocket
– h22
Sep 12 at 13:30
• There 's one slight caveat: If you lift off with such an engine, everybody who happens to be behind your rocket (no matter how far) will get a neat dose of radiation applied at them. Sep 12 at 13:50
• Also "Mass increases with speed" is a way of describing relativistic effects that most physics texts dropped in the 90's, in favor of using relativistic momentum and relativistic kinetic energy, and invariant mass. Sep 12 at 17:24

On the other hand, using faster and faster exhaust velocities pays off even in the total absence of relativistic effects. Taking the basic equation for momentum $$p = m v$$ we can see that you can always trade propellant mass for exhaust velocity to gain the same amount of momentum. Unfortunately, $$E = \frac{1}{2}m v^2$$ says that we need to increase our power by a factor of 4 to double the velocity and to halve the mass. This quadratic behavior limits us in reaching extremely high exhaust speeds (among other things as the size of the engines).