The arguments about why it wouldn't work to shoot a projectile into orbit sound convincing, so I suspect they're right. But what actually happens as you launch a projectile at a 45% angle with increasing velocities?
I couldn't find the simulator, but as I recall, from any point on the surface, whatever initial velocity you give a projectile will impact the surface at some time later, if it doesn't achieve escape velocity.
A good way to think of it is this way: if you were able to point the cannon tangential to the ground, ie horizontal, and you were to fire the projectile at exactly orbital speed for that elevation, then you would achieve orbit at ground level. If, however, you elevate the cannon at all from horizontal, you create an oblong orbit that intersects the surface at some point (even if the orbit extends thousands of miles up into space) That's because all orbits are elliptical to some degree. No matter what the angle or power, you're just creating an orbit with some degree of stretch that eventually comes back around to where you launched. A 45-degree launch from one place would just be the same as launching at 90-degrees from another place on the globe.
BTW, this makes for a nice hobby program to write over the weekend. I ended up adding angle, initial velocity, and projectile thrust. I also added scaling where you could either go very small, like a model rocket launch, or zoom out to include the moon. I was very surprised at the sizes of the earth and moon and the distances between them.
