Apply math and the object flies in a parabolic arc (not accounting for air friction and wind)
Launch it high enough and the arc start looking elliptical. Gravitational force looks less like a constant rather is tempered by distance². If the acceleration closes the ellipse without hitting the (circular at this scale) ground, your object is now a satellite in orbit.
Keep accelerating and eventually (a whole lot of acceleration) and special relativity factors affect the trajectory…and mass…and time dilates between the object and observers.