Relative velocity=relative momentum?

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SUMMARY

The discussion centers on the momentum transfer of photons to a solar sail traveling at 0.866c, as analyzed through the lens of special relativity. It concludes that while photons always travel at the speed of light (c) in all reference frames, the momentum imparted to the sail is affected by the relativistic Doppler effect. Specifically, the momentum received by the sail moving at 0.866c is approximately one-fourth of that measured by an observer at rest relative to the radiation source. This demonstrates that relative velocity significantly influences momentum transfer in relativistic contexts.

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Assume a solar sail was traveling at a high speed (say .866c) away from the radiation source. The radiation hitting it is of course traveling at c. But according to the special theory of relativity it would appear on the sail that the radiation is hitting the sail at c speed (since the speed of light is constant in all reference frames). Thus would a photon supply the same momentum push when the sail is traveling away from the source at .866c as it would if the sail was merely at rest (or with a much lower speed) relative to the source?
 
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Thus would a photon supply the same momentum push when the sail is traveling away from the source at .866c as it would if the sail was merely at rest (or with a much lower speed) relative to the source?
No, momentum changes due to the relativistic Doppler effect. In your example, it would be ~1/4 of the momentum measured by an observer at rest wrt the source.
 

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