<p>A perforating gun gravitational orientation system includes a perforating gun (12) and a swivel device (22) connected to the perforating gun to permit rotation of the perforating gun within casing, and the perforating gun spaced apart from the casing by the swivel device. Another perforating gun gravitational orientation system includes the swivel device having an axis of rotation which is spaced apart from a center of gravity of the perforating gun. Yet another perforating gun gravitational orientation system includes the swivel device having an axis of rotation which is spaced apart from a center axis of the perforating gun.</p>