References: Griffiths, David J. (2007), Introduction to Electrodynamics, 3rd Edition; Pearson Education – Chapter 12, Post 6.
Although no object can travel faster than light, it is possible for the apparent speed of an object to be greater than . A common example is that of the apparent motion of a star across the sky. Suppose a star is a distance from Earth at time and that its velocity is towards Earth at an angle to the line of sight. At time it arrives at a point whose distance from Earth is
The times of arrival at Earth of the light emitted at distances and are
During this time, the star moves a distance perpendicular to the line of sight of , so the apparent speed as seen from Earth is
This speed has a maximum at an angle which can be found by setting the derivative to zero:
At this angle, the apparent speed is
Since as , can be much larger than even though the actual speed of the star is less than . This again illustrates the importance of correctly interpreting the raw data that we see, and of allowing for the travel time of the light.