Relative velocity=relative momentum?

[h1a8]

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?

 

[Ich]

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.