Why can't a nuclear reactor be used as a rocket motor? Nuclear fission, and potentially fusion, reactors generate vast amounts of energy, primarily as heat.  What stops us from harnessing that energy to propel spacecraft at or above escape velocity from Earth?
I am aware that once a craft reaches escape velocity, we can power the craft with small reactors, Some craft are then accelerated with electronic ion accelerators. 
My question is simply what restricts launching from the surface of Earth something powered by fission or fusion as the sole fuel.
 A: There have been designs for such things. Try searching "nuclear salt water rocket" (or just go to the wikipedia page...). 
Paper with a design (PDF link): http://path-2.narod.ru/design/base_e/nswr.pdf. 
The author does not suggest it as a ascent or descent stage (presumably because the radioactive exhaust would make you unpopular with anyone who wanted to live near the landing or takeoff site), but as a high thrust, high efficiency propulsion system in space.
A: I know very little about the subject but i do have this to offer.
Nuclear reactors make heat energy not kinetic energy. The conversion from one to the other would introduce many problems, weight being the main one.
People don't like the idea of sending something up that's radioactive and may come back down and "mess up" the ground with its radiation.
BUT!!!! there may be a way to use the power of a nuke to get stuff in space without any of the above worries!  And humans have "accidentally" almost done it.
You will need to read this here
But the short of it is, you could put a nuke in a hole and then place the rocket on top. The force of the nuke will then push the rocket into space (its not that simple but its a basic concept) The rocket would still need some propellant for getting into orbit and general maneuvering. BUT it is possible to get an object to escape velocity using a nuke.
A: I would say there are two main problems to consider. One is that heat is not the same as thrust, and the mechanisms we have to convert reactor heat to thrust would add such weight to the rocket that would never get off the ground.
Another problem is that the rate of energy generation required (power) would probably melt any reactor that we now have.
I expected that more quantitative explanations are available.
A: It takes a tremendous amount of thrust to propel something from launch to orbit. A nuclear powered propulsion device doesn't lend itself well to this task, not to mention the risk of an accident, which for fission systems in particular, poses a large health and safety risk.
Once the craft has made it beyond the Earth's atmosphere however, both fission and fusion propulsion systems begin to look attractive when you consider their specific impulses.
http://www.dtic.mil/dtic/tr/fulltext/u2/a283968.pdf
