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:
“The motion picture made in Hollywood, if it is to create art at all, must do so within such strangling limitations of subject and treatment that it is a blind wonder it ever achieves any distinction beyond the purely mechanical slickness of a glass and chromium bathroom.”
—Raymond Chandler (1888–1959)
“It is not an arbitrary “decree of God,” but in the nature of man, that a veil shuts down on the facts of to-morrow; for the soul will not have us read any other cipher than that of cause and effect. By this veil, which curtains events, it instructs the children of men to live in to-day.”
—Ralph Waldo Emerson (1803–1882)
“Each man has his own vocation. The talent is the call. There is one direction in which all space is open to him. He has faculties silently inviting him thither to endless exertion. He is like a ship in the river; he runs against obstructions on every side but one; on that side all obstruction is taken away, and he sweeps serenely over a deepening channel into an infinite sea.”
—Ralph Waldo Emerson (1803–1882)