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The thing that surprised me when reading about NERVA is that - according to Wiki article - space race partially died out because the US Government explicitly decided they're tired with it and there are better ways of spending money than going to Mars.
One interesting bit that was in George Dyson's book but not the Wikipedia article (that I saw) was that for sustained thrust the idea is to keep the pusher plate in resonance with the atomic bomb detonations. You use a half sized bomb to get things going then detonate full sized bombs when the plate is heading away from the main compartment.

The real problem with an Orion drive is launching the thing. Simple atomic bombs don't generate that much fallout (relatively speaking) by themselves. There wasn't any noticeable fallout in Japan after the explosions at Hiroshima and Nagasaki. The big source of dangerous fallout is when neutrons from an atomic explosion are captured by nearby materials and transmute them into radioactive ones. For an explosion high up the surrounding hydrogen, oxygen, carbon, and nitrogen don't turn into anything nasty. But if the explosion is near the ground there are all sorts of horrible things that can easily be produced.

If you wanted to launch an Orion into space with relatively little fallout you would need to either have boosters that lift it a kilometer up before it engages it's main drive or launch it a large area you've covered completely with graphite (see again carbon-14 not being dangerous).

The reason that the bombs the US and USSR have stockpiled produce so much fallout is their third stages. First you have a regular atomic bomb that sets of a fusion explosion. But surrounding these is the bomb's shell made out of the Uranium-238 that was left over after the process of separating out the uranium-235. You can't create a chain reaction with U238 but it does fission and produce a lot of energy (but no neutrons) when you hit it with a neutron and about half the energy of a bomb can come from the case. You can easily make the case out of lead instead and have a relatively clean nuclear bomb but the military considered the fallout a feature rather than a bug.

In the end project Orion was a cool idea and not so crazy as you might think at first. But I'd much rather people use conventional nuclear thermal rockets where you use a normal reactor to heat a bunch of propellant. It doesn't offer the same combination of power and efficiency as Orion but if you switch your reactor to generate power and run a VASIMR then you can have at least one or the other and you don't have to deal with any fallout.

EDIT: Oh, there's also the problem of EMP as Orion passes through the ionosphere. The bombs it uses are much smaller than an H bomb so they probably won't cause problems but nobody knows for sure.

You could always construct it in orbit too? That might be the safest option?
Yes you certainly could. But once you're in orbit you don't really need high thrust anymore, you might as well connect a normal nuclear reactor to an electric drive of some sort. I suppose there are still other places in the solar system you might want to land. Venus and hypothetical floating platforms on Saturn, Uranus, or Neptune might make Orion worthwhile. Orion might also be required to take off from the surface of Jupiter (which has much stronger gravity than the other gas giants). But for other bodies the gravity is light enough that I'd just use nuclear thermal and leave the pusher plate at home. For most space travel the journey is going to take a long time so it doesn't matter if you get up to cruising speed in 15 minutes with your Orion drive or a week with your nuclear electric.
Id think if the US was to look into nuclear based engines we should restart the NERVA program. But of course with anything nuclear politics and environmental activists would be all over it.

My propulsion professor (former deputy director, AFRL Propulsion Directorate) said the way they get around the buzzwords "nucler" and "atomic" was to call it "general purpose"

People forget that Kennedy's actual request was: First - "before this decade is out, is landing a man on the moon and returning him safely to earth"

Second - "acceleate development of the Rover nuclear rocket"

Third - "accelerate the use of satellites for world wide communications"

Fourth - "a satellite system for world wide weather observation"

Too bad we only got 3 out of 4 and are still stuck with cans of flammable mud.