I have long daydreamed about building a electro-magnetic catapault in the Ecuadorian Andes. Went off to do the math this morning and realized that it would need to accelerate its payload to Mach 34 to achieve escape velocity. I can't think of ANY way to break the sound barrier 34 times over on rail system--which pretty much kills the concept.
(Maybe if the railway were airless and a REALLY BIG laser blasted the atmosphere out of the way at the upper end?)
No. I think the giant slingshot approach is dead.