The rotating (or Angular) Doppler Effect.
Ball and Chair Analogy
Relative position of planets to us gives them an apparent red-shift or blue-shift due to them being on a geodesic that slices our rotating Earth frame near the equator (less shift) or far from it (more shift).
Imagine trying to catch a ball while spinning on an office chair. If someone throws it straight at your centre (normal to your spin direction, it has a very narrow chance of being well-timed.
Whereas if they throw it more to the side you are spinning away from them, then you and the ball end up with similar speeds and you have more time to catch it.
Hence, the path of least resistance from the thrower to you (the catcher) is not actually the shortest path in space. This is angular Newtonian relativity. From the perspective of the catcher, the path is actually curved, forming a good analogy for why mass curves space-time.For light, the curvature caused by
Implies spin has a gravity. Of course, because spin has energy and energy and mass are equivalent and inertial mass is equivalent to gravitational mass.
Light has an orbital angular momentum, and this was only discovered recently (last 20-25 years).
"A Doppler Effect for Distant Planets" - by Jon Cartwright, Scientific American 2013