Motion in An Arbitrary Direction
If, in the reference frame of the observer, the source is moving away with velocity at an angle relative to the direction from the observer to the source (at the time when the light is emitted), the frequency changes as
- (1)
In the particular case when and one obtains the transverse Doppler effect:
Due to the finite speed of light, the light ray (or photon, if you like) perceived by the observer as coming at angle, was, in the reference frame of the source, emitted at a different angle . and are tied to each other via the relativistic aberration formula:
Therefore, Eq. (1) can be rewritten as
- (2)
For example, a photon emitted at the right angle in the reference frame of the emitter would be seen blue-shifted by the observer:
In the non-relativistic limit, both formulæ (1) and (2) give
Read more about this topic: Relativistic Doppler Effect
Famous quotes containing the words motion, arbitrary and/or direction:
“All the phenomena which surround him are simple and grand, and there is something impressive, even majestic, in the very motion he causes, which will naturally be communicated to his own character, and he feels the slow, irresistible movement under him with pride, as if it were his own energy.”
—Henry David Thoreau (1817–1862)
“Pity on the person who has become accustomed to seeing in necessity something arbitrary, who ascribes to the arbitrary some sort of reason, and even claims that following that sort of reason has religious value.”
—Johann Wolfgang Von Goethe (1749–1832)
“When you know what men are capable of you marvel neither at their sublimity nor their baseness. There are no limits in either direction apparently.”
—Henry Miller (1891–1980)