Project Orion (nuclear propulsion)

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.

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.