Does a Photon Carry Velocity of Its Source?

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vincent
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Earth is moving through space. If I throw a ball straight up, it falls down to me and is not left behind. This is obviously because it already carries the momentum of Earth's movement. But if I fire a photon straight up, does it also carry a velocity component in direction of Earth's movement?
If not, then it must be free of all the velocity components like movement of solar system through galaxy etc.
 
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It is just it’s speed that is independent of the source. It’s direction, wavelength, frequency, energy and momentum all depend on the source.
 
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