My friends and I were reminiscing about our intro physics classes and decided to revisit an old problem were we were required to calculate the orbital velocity of a cannonball fired from 1 meter above an airless earth.
We extended this problem to a debate about whether this same hypervelocity cannon on Earth can launch an object into a stable orbit above the atmosphere without any additional propellant in the object itself. So far, we haven't found a solution, but we are looking at the possibility of atmospheric skipping or using the gravitational influence of the moon to adjust our object's trajectory.
Is it possible for our hypothetical cannon to launch something into a stable orbit around the Earth from Earth's surface without any additional thrust?