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Can we still apply other SR transformations (length contraction, velocity transformation) to the sun and planets and their orbits, given that their enormous mass/momentum should produce very strong gravity? If so, then

[itex] u_{||} = \frac{u_{||}' + v}{1 + vu_{||}'/c^2} \Rightarrow u_{||} - v = \frac{u_{||}(1-\frac{v^2}{c^2})}{1 + vu_{||}'/c^2} \to 0[/itex]

[itex] u_{\perp} = \frac{u_{\perp}'}{\gamma(1 + vu_{||}'/c^2}) [/itex]

seem to imply that the observed orbital velocities of the planets relative to the sun will be less than their orbital velocities in the Sun's frame. How do we reconcile this with the much greater apparent mass of the sun, and the length contracted orbits on top of that? Shouldn't the planets spiral in towards the sun/each other?