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
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“subways, rivered under streets
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the overtone of motion
underground, the monotone
of motion is the sound
of other faces, also underground—”
—Hart Crane (1899–1932)
“Me, what’s that after all? An arbitrary limitation of being bounded by the people before and after and on either side. Where they leave off, I begin, and vice versa.”
—Russell Hoban (b. 1925)
“The young ... look into visages dull-eyed, long-toothed, wattle-necked, and chop-fallen, something they have never been and which they cannot imagine ever being.... If it occurs to a young person, looking at us, that this is the direction in which he himself travels, how can he forgive, let alone bear the sight of, us, who constantly bring him the bad news of our own faces, bitter signposts pointing to his own destination?”
—Jessamyn West (1902–1984)