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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?

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Are you talking about tidal forces? – Mark Eichenlaub Jan 10 '11 at 0:01
Centrifugal acceleration is $v^2 / r$. I suggest you plug in the relevant numbers. Short story: galactic distances are far too huge for that acceleration to be anything but negligible. – Marek Jan 10 '11 at 0:16
Mark: that didn't occur to me, but it sounds like an effect that could be measured. The Arabs built entire buildings to measure the tides precisely (by connecting vast tanks to the sea by tunnels, then marking a column that ran through the middle), and perhaps the fact of galactic orbit could be evidenced if the tidal levels coincided with predictions made by theory and astronomical observations. Of course, now I'm wondering if you could measure the effect by the moon's distance to Earth, too. – C. Lawrence Wenham Jan 10 '11 at 0:33
@Mark, not exactly, but ties are the only uncompensated term left after you realize that all the bodies involved are freely falling. Of course they go by $d\frac{m_1 m_2}{r^3}$ (where $d$ is the separation from the free-falling center), so that effect is even more trivial than Marek suggests. – dmckee Jan 10 '11 at 1:25

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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:

  1. 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.

  2. 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.

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