Superluminal motion

In astronomy, superluminal motion is the apparently faster-than-light motion seen in some radio galaxies, BL Lac objects, quasars, blazars and recently also in some galactic sources called microquasars. Bursts of energy moving out along the relativistic jets emitted from these objects can have a proper motion that appears greater than the speed of light. All of these sources are thought to contain a black hole, responsible for the ejection of mass at high velocities. Light echoes can also produce apparent superluminal motion. Superluminal motion occurs as a special case of a more general phenomenon arising from the difference between the apparent speed of distant objects moving across the sky and their actual speed as measured at the source. In tracking the movement of such objects across the sky, a naive calculation of their speed can be derived by a simple distance divided by time calculation. If the distance of the object from the Earth is known, the angular speed of the object can be measured, and the speed can be naively calculated via: apparent speed = distance to object angular speed. This calculation does not yield the actual speed of the object, as it fails to account for the fact that the speed of light is finite. When measuring the movement of distant objects across the sky, there is a large time delay between what has been observed and what has occurred, due to the large distance the light from the distant object has to travel to reach us. The error in the above naive calculation comes from the fact that when an object has a component of velocity directed towards the Earth, as the object moves closer to the Earth that time delay becomes smaller. This means that the apparent speed as calculated above is greater than the actual speed. Correspondingly, if the object is moving away from the Earth, the above calculation underestimates the actual speed. This effect in itself does not generally lead to superluminal motion being observed.