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Aside from the theory of Special Relativity, is there a theoretical limit on velocity for spaceships powered by ion engines. I think there is but I do not understand why because unbalanced forces should always create accelerations.

They do. The limiting problem is that you run out of fuel, unless you are talking about the famous (and hypothetical) Bussard ramrocket. The limits you may be thinking about are the basic practical limits to your final rocket velocity, beyond your more mundane engineering limits relating to overcoming internal friction in your motor, powering life support, inefficiencies in your control of the fuel flow, and faulty O-ring gaskets... These limits are related to the exhaust velocity of the rocket and the ratio of the fueled to empty rocket weight. You can get to higher speeds in principle by (a) using a higher velocity exhaust (this shoves more momentum out back for every gram of fuel you use up), which is the principal advantage of ion rockets (which use electric fields to accelerate heavy ions out back) over chemical rockets; or (b) getting a higher fueled/empty ratio by either building real thin rockets or multiple stage rockets, so you throw away non-fuel mass when you are done with it. I think Robert Goddard was one of the first to really exploit the latter idea, and of course it dominates modern rocketry. If you use a solar sail and power your vehicle by light pressure, there is no upper limit (besides c) on your velocity, but you will run out of the solar system before you get going too fast.

christopher grayce

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