Can we measure the "Tilt-A-Whirl" effect of the Earth+Sun orbiting the galactic hub? You've probably ridden on the fairground ride called the "Tilt-A-Whirl", or--as Disneyland calls it--the "Spinning Teacups", as well as other fairground rides that employ epicycles. You can really feel the centrifugal force strongly when your car spins complementary to the spin of the main rotor. 
Now, can that extra force be measured on Earth as our orbit around the Sun complements the Sun's orbit around the galactic hub? Has anyone done it?
 A: The force that you feel in a Tilt-A-Whirl is not possible in a galaxy and does not correspond to anything in our solar system.
In a Tilt-A-Whirl, you are subject to two additional constraints that are not present in the solar system galaxy interaction:


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*The base of the Tilt-A-Whirl platform is not flat so there are times when the Earth's gravity slows the spinning of the cars as you go uphill and times when the Earth's gravity speeds up the spinning of the cars as you go downhill as the overall platform rotates changing the plane of the individual cars as it goes around. There is no corresponding accelerating/decelerating force in the galaxy that affects the solar system.

*There is a physical constraint that keeps the individual cars in a Tilt-A-Whirl fixed to the larger rotating platform so the riders in the cars are kept at a fixed radius from the point of the car's rotation. In the galaxy, the Earth is free to move outward when the velocity increases so that it always follows an elliptical geodesic orbit which is a straight unaccelerated line through spacetime. Likewise, the variations in speed of the entire solar system as it revolves around the galaxy are not reflected in additional force because the system is not attached so it too follows an elliptical geodesic orbit rather than a circular one.
