Very interesting. Is it possible to make a trebuchet that can throw stuffs beyond escape velocity?
Orbital Velocity at grazing altitude is 8 km/s, and escape velocity is sqrt(2) times that, or about 11.3 km/s. Thing is, anything travelling that fast in the atmosphere tries to turn to plasma, so your launch arm would need to be a bit special. Or at very high altitude. Or have ablative heat shielding. But atmospheric drag would probably prevent you from getting anything like those speeds with this kind of mechanism.
>"In Project HARP, a 1960s joint United States and Canada defence project, a U.S. Navy 16 in (410 mm) 100 caliber gun was used to fire a 180 kg (400 lb) projectile at 3600 m/s or 12,960 km/h (8,050 mph), reaching an apogee of 180 km (110 mi), hence performing a suborbital spaceflight. However, a space gun has never been successfully used to launch an object into orbit or out of Earth's gravitational pull."