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:
“We must not suppose that, because a man is a rational animal, he will, therefore, always act rationally; or, because he has such or such a predominant passion, that he will act invariably and consequentially in pursuit of it. No, we are complicated machines; and though we have one main spring that gives motion to the whole, we have an infinity of little wheels, which, in their turns, retard, precipitate, and sometime stop that motion.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“... no one who has not been an integral part of a slaveholding community, can have any idea of its abominations.... even were slavery no curse to its victims, the exercise of arbitrary power works such fearful ruin upon the hearts of slaveholders, that I should feel impelled to labor and pray for its overthrow with my last energies and latest breath.”
—Angelina Grimké (1805–1879)
“From the way the grass bends, one can know the direction of the wind.”
—Chinese proverb.