# Earth's orbit around the Sun

Gday all,

I was just wondering if we would experience a (very small) centrifugal force due to the earth's rotation around the sun or not. I don't think there would be because the earth and everything on it is in a state of free fall around the sun, but I have been told there would be a centrifugal force (due to orbit, not rotation).

Who is correct?

Thanks

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tiny-tim
Homework Helper
Gday SprucerMoose!

Yes, it's the same tidal force that produces the tides.

(mostly, it's the Moon's tidal force, but the Sun's is also significant)

The centre of the Earth is in free-fall around the Sun, but the surface is generally going just a teeny bit too slow or too fast, and so the centripetal force is not exactly balanced by the gravity of the Sun (and Moon).

Andrew Mason
Homework Helper
I would say that SprucerMoose is correct in saying that there is no centrifugal force experienced by us in orbiting the sun. That is the fundamental difference between gravity and other forces.

I am not sure that tidal forces count as a centripetal force. It seems to me that they would be changing direction relative to the earth's rotation not relative to the earth-sun orbit. If by "we" you people who are gravitationally bound to the earth, there is a centrifugal effect experienced due to the spinning of the earth (it reduces our weight slightly) but that is all. (If the earth were to increase its rotational speed we would feel lighter).

AM

D H
Staff Emeritus
I was just wondering if we would experience a (very small) centrifugal force due to the earth's rotation around the sun or not. I don't think there would be because the earth and everything on it is in a state of free fall around the sun, but I have been told there would be a centrifugal force (due to orbit, not rotation).

Who is correct?
The answer depends on the frame of reference. You haven't specified it, so without that key info there is no saying who is correct.

Centrifugal forces are fictitious forces. They aren't quite "real". Fictitious forces such as the centrifugal force appear in some frames but not in others. From the perspective of an inertial frame, there is no centrifugal force due to the Earth's rotation about its axis nor from its orbit about the Sun. From the perspective of an inertial frame there are no fictitious forces whatsoever.

A centrifugal force due to the Earth's rotation does appear in a frame fixed with respect to the rotating Earth (this is our everyday perspective of things here on the surface of the Earth). Similarly, a centrifugal force appears in a frame rotating with the Earth's orbit about the Sun. In such a frame the Earth and the Sun are standing still. Newton's first law dictates that the net force on the Earth must be zero. Since the Sun attracts the Earth gravitationally, there must a force that counters this gravitational force.

AlephZero
Homework Helper
If the orbit was a circle, we would still feel a centrifugal force that is different from the sun's gravitational force at most places on the earth's surface, because the earth is a finite size. Tides are caused by the difference in the gravitational force between the points nearest and furthest from the sun (or moon). The centrifugal force is proportional to radius so is largest at the point on the earth's surface furthest away form the sun. The graviational force is proportional to 1/r^2 so it is largest at the point nearest to the sun.

Also, the orbit is an ellipse not a circle, which means that except at the nearest and furthest points from the sun, the gravitational and centrifugal forces act in different directions.

Compared with the earth's own gravitational field these effects are too small to notice without very accurate measurements, but they are big enough to cause the ocean tides. It is just a coincidence that the lunar and solar tides are of similar size. A small mass relatively close (the moon) gives the about same difference in gravitational force on opposite sides of the earth as a very large mass (the sun) much further away.

D H
Staff Emeritus
If the orbit was a circle, we would still feel a centrifugal force that is different from the sun's gravitational force at most places on the earth's surface, because the earth is a finite size. Tides are caused by the difference in the gravitational force between the points nearest and furthest from the sun (or moon).
Tidal forces are real and are the same in all frames. Centrifugal forces are not real and differ between frames.

Andrew Mason
Homework Helper
Tidal forces are real and are the same in all frames. Centrifugal forces are not real and differ between frames.
Tidal forces would be the same in all "intertial frames", of course. Centrifugal forces are not real forces but they are real effects experienced in non-inertial frames undergoing centripetal acceleration caused by something other than gravity.

The point the OP was making is that even in the non-inertial frame of the orbiting mass, no centrifugal effect is observed. The rollercoaster rider experiences centrifugal effect when experiencing centripetal acceleration. It is not a force but it is a real feeling. The orbiting astronaut experiencing centripetal acceleration due to gravity feels no centrifugal effect whatsoever.

AM

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Andrew Mason
Homework Helper
If the orbit was a circle, we would still feel a centrifugal force that is different from the sun's gravitational force at most places on the earth's surface, because the earth is a finite size.
Why is this a centrifugal 'force'? The tidal force on a mass m on the earth's surface is m x the difference between m x the gravitational acceleration vector of the earth's centre of mass relative to the sun and m x the gravitational acceleration vector of m relative to the sun. That is a vector pointing from m to the earth centre of mass. It does not depend on whether the earth is in a circular or elliptical orbit.

Tides are caused by the difference in the gravitational force between the points nearest and furthest from the sun (or moon). The centrifugal force is proportional to radius so is largest at the point on the earth's surface furthest away form the sun.
Are you referring to the tidal force? If so, is it not proportional to 1/r^3?

AM

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