The Grav Dampener is a device of the Trace Compression Block engine which is necessary for the pitch and yaw of a spaceship. It is likely powered by the Aft alternator, another engine component. During a heist, planned by Saffron, to steal Serenity it was sabotaged, by Saffron. She destroyed the filament in Serenity's Grav Dampener, as a result the ship was unable to change direction.