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)
“We do the same thing to parents that we do to children. We insist that they are some kind of categorical abstraction because they produced a child. They were people before that, and they’re still people in all other areas of their lives. But when it comes to the state of parenthood they are abruptly heir to a whole collection of virtues and feelings that are assigned to them with a fine arbitrary disregard for individuality.”
—Leontine Young (20th century)
“From the way the grass bends, one can know the direction of the wind.”
—Chinese proverb.