# Frames of reference

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So this isn't a homework question, but I felt like it was the most appropriate forum. My friend asked:

"Ok, so the earth is moving around the sun at 30 km per second. At the same time, the sun is moving around the galaxy at 250 km per second. But when the earth is moving around the sun in the same direction that the sun is moving around the galaxy, the earth is actually moving faster than the sun to get around and pass it. So the earth would speed up to 280km per second. The opposite is also true, in which case the earth going behind and around the sun would slow down to 220 km per second. that is a variance of + or - 60 km per second.....so why the hell don't we feel that, or at least see some effect of it in the tides or something?"

I know there's an error in how he is thinking. Something to do with frames of reference, maybe? I could be completely wrong. I was just wondering the answer to this question myself.

Thanks.

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If the motion were linear, it would have zero effect at all — inertial frames of reference are equivalent. It's just like being at rest. For accelerated motion, in this case rotational, the important terms is generally the angular speed, at least for the things we would notice. Even though the linear speed seems large, r is also, so the angular speed is small. Basically what tends to matter is the extent to which you can tell you are rotating and/or revolving.

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If the motion were linear, it would have zero effect at all — inertial frames of reference are equivalent. It's just like being at rest. For accelerated motion, in this case rotational, the important terms is generally the angular speed, at least for the things we would notice. Even though the linear speed seems large, r is also, so the angular speed is small. Basically what tends to matter is the extent to which you can tell you are rotating and/or revolving.

In short it is acceleration, not speed, that one can sense, and the centripetal acceleration for the roughly circular orbit of the earth around or the sun around the galactic center are rather small. Even the effect of the rotation of the earth is not ordinarily felt, but see "Foucault Pendulum"or Coriolis force for a concrete effect.

http://en.wikipedia.org/wiki/Foucault_pendulum

http://en.wikipedia.org/wiki/Coriolis_effect

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Ah. I see. Thanks to both of you. And thanks for the links DrRocket!

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