Existing ship mounted railguns already shoot projectiles around 3km/s.
It is generally thought that they could be scaled up to 8 km/s and larger size.
The main problem is that if you fire human sized objects that fast at sea level you end up with a plasma ball due to air friction. This isn't an issue with chemical rockets because they start at 0 and accelerate to Vmax, whereas the railgun projectiles start at Vmax and decelerate.
Higher altitude would remove much of the friction problem.
The biggest advantage of very high altitude reducing the friction problem isn't just that it stops your projectile from turning into plasma, it is that the size of the minimum viable projectile is reduced. People keep focusing on getting people or vehicles into orbit, but the main advantage of a gun-to-orbit system is that the packet size can be made very small. Think machine gun instead of cannon. This means a smaller gun and thus smaller capital investment.
Instead of the balloon-supported long gun that mikewarot suggested, imagine a balloon at 30 km altitude supporting a 5 meter long gun and a few tons of both propellant and <1 gram pellets. A target satellite is shot in a long continuous burst, leaving the satellite with a lot more mass and a slightly disturbed orbit. Later shots from a different location and direction can be used to compensate for the added impulse to the satellite's orbit.
This could be a cheap way to get a bunch of metal into orbit, or possibly even fuel and oxidizer.
While that's not my intention, if you actually wanted to damage satellites and cause a Kessler Syndrome scenario, it's hard to find a system that would have a bigger bang-for-your-buck.
I was rather envisioning a target satellite that is designed to absorb the pellet as an inelastic collision. It would probably resemble something like this: https://en.wikipedia.org/wiki/Black_body#/media/File:Black_b... . Of course, if it didn't work as designed, then it could be a problem.
The point was that a high altitude low-mass-per-shot gun system could get mass into orbit with a similar energy cost as a space elevator with significantly less upfront capital cost and no need for miracle materials.
> Existing ship mounted railguns already shoot projectiles around 3km/s.
Projectiles of what mass? And with what acceleration? As I understand it, with feasible railgun lengths the acceleration is well above the limit of human tolerance, and the projectile mass is significantly smaller than a typical payload put into LEO by conventional rockets.
Existing ship mounted railguns already shoot projectiles around 3km/s. It is generally thought that they could be scaled up to 8 km/s and larger size. The main problem is that if you fire human sized objects that fast at sea level you end up with a plasma ball due to air friction. This isn't an issue with chemical rockets because they start at 0 and accelerate to Vmax, whereas the railgun projectiles start at Vmax and decelerate.
Higher altitude would remove much of the friction problem.