A sling would be much better for this: it's much smaller than a huge gun and also more flexible since the direction and elevation can be changed by altering the

A sling would be much better for this: it's much smaller than a huge gun and also more flexible since the direction and elevation can be changed by altering the release point and axis. Centripetal acceleration is a = v^2 / r so for 300 m/s (about mach 1) speeds, for 1 gee centripetal acceleration you'd need 9 km radius.