As far as I'm aware, a gun can't shoot a projectile into orbit - no matter how high it shoots a ballistic, the ballistic will eventually come back to earth (unless it gets captured by another body's gravitational field). In order to achieve orbit, you need to impart additional energy onto the object in order for it to get enough velocity to actually orbit.
Not from the Earth, no (not easily, anyway). Bull's plan involved using a gun to replace the heavy first stage of a multi-stage rocket.
The Iraqis didn't have the rocket technology (of course, that's why they hired Bull!), which would probably have looked like the US "Sprint" missile, and at the very raw edge of what was feasible at the time.
Interestingly, though, you can get from the Moon back to the Earth using only a gun-type launcher, IIRC. Some lunar mining concepts use this as a way for mined minerals to get back home without uneconomical use of rocket fuel -- typical schemes I've seen tossed around use various electromagnetic launchers with solar panels or nuclear reactors providing the juice. I've never run the numbers myself -- maybe some Kerbal Space Program junkie can figure it out though?
Probably the best use case for gun-type launchers is for orbital transfers of unmanned cargo. There were some neat ideas tossed around in the 80s of having a big satellite or space station with a nuclear reactor serve as a launch platform for small cargo pods, which would lack their own engines. As long as you balanced the number of "up" and "down" pods, you could keep the launch platform in an approximately stable orbit, supposedly. Very hard to do without a big honking nuclear reactor though.
The plan wasn't to get into orbit with the gun alone. They had designed shells that had rocket motors in them, to get them to orbital velocity. The gun was simply the first stage.
The critical problem with using a gun though, is the sheer amount of force applied when firing the gun. They couldn't even get dummy payloads to work correctly, the rockets motors warped due to the forces involved.
IIRC one solution is to use pressurized hydrogen gas pumped through a heat exchanger instead of explosive charges. That way, the pressures and temperatures involved can be controlled precisely.
> the ballistic will eventually come back to earth (unless it gets captured by another body's gravitational field)
Although ridiculously difficult and inefficient, it's possible to achieve orbit with just a gun, and another body's gravitational field. It doesn't need to be captured by said field, it can just be influenced enough to stabilise it's orbit.
> In a three-body or larger system, a gravity assist trajectory might be available such that a carefully aimed escape velocity projectile would have its trajectory modified by the gravitational fields of other bodies in the system such that the projectile would eventually return to orbit the initial planet using only the launch delta-v [1]
You are probably right, I just copied it from Wikipedia verbatim. I did have the "citation needed" label. My pedestrian take on this is if Iraq could afford to build a gun which shoots satellites into orbit, after all these years we'd have a few of those around by now. But it just highlighted the craziness and planned scale of the project. The assassination of course also adds to the intrigue.
