I am envisioning a magnetic cannon to launch materials directly from Earth's surface to geosynchronous equatorial orbit. The parameters I have in mind are a near vacuum launch tube, about 10 km in length, running up and through the side of a mountain near the equator (there is a nice, 5700+ M volcano in Ecuador that is only 0.03 degrees north latitude, which seems promising if the earthquakes aren't too bad), launching at ~500 G's of acceleration for 2 seconds, before entering the atmosphere at relatively high altitude. A tube design that allows the projectile to essentially pack the air into the end of the tube as it fires could smooth the transition from tube to atmosphere, and at the trajectory you need (roughly 70 degrees from horizontal at tube exit), interaction with meaningful atmosphere will only occur for about 7 seconds. If the gun is stationary, then the projectile will consistently "land" in roughly the same place in orbit, with slight variation based on air conditions; so only slight course correction would be needed on-board to use the system to put mass on orbit to build and feed a space station complex.
The first question is: Can a projectile be designed with meaningful cargo space, self contained launch electronics, an engine system and a tiny bit of fuel for course correction once in orbit, which can withstand 2 seconds of 500 G acceleration, and then 7 seconds of atmospheric flight at orbital speed (starting with air pressure at 5700 M altitude, and getting less stressful from there)? What would you make such a projectile out of? How would you design it?
The second question is: Assuming a fairly large mass of cargo per launch (10-50 tons), can a magnetic launch system be built to achieve that 500 G acceleration along a 10 km track, without melting itself from its own power requirements? If so, how would you do it, and what would the power requirement actually be?
Third, how would you deal with the necessity of making the track curved? Is it better to use a shorter track with greater acceleration force, and fire straight? How important is the trade off between lower G-force at launch and longer, curved track?
Please note: This launch system is intended to be freight only. Humans would die from the G-forces of launch, and will still need to ride rockets, if this thing ever gets built.