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Sagnac' measure of Earth's Rotation

07/19/2007 9:26 PM

Since A Sagnac Ring can determine the Earth's rotation rate I was wondering if one placed on the equator of a large planet measuring 186,040,000 miles in diameter rotating 97,855 feet per second could accurately make this measurement?

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#1

Re: Sagnac' measure of Earth's Rotation

07/20/2007 7:30 AM

From the values that you gave, you are looking at 1 revolution per year, so you are effectively asking if a Sagnac ring can detect the Earth's movement around the Sun.

It can surely do it, but to what accuracy I do not know; surely it will be worse than for measuring Earth's 1 revolution per day.

Jorrie

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#2
In reply to #1

Re: Sagnac' measure of Earth's Rotation

07/20/2007 10:04 AM

Yes... That was the idea. It seems that the Sagnac Ring would show a sine wave as the earth rotated where the peak "high" would be 12 hours from the peak "low". Showing the "net" velocity. With the sensitivity claimed, I believe this pattern should present itself.

Thanks for your comments...

Jim

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#3
In reply to #2

Re: Sagnac' measure of Earth's Rotation

07/20/2007 10:47 AM

Hi again Jim.

You wrote: "It seems that the Sagnac Ring would show a sine wave as the earth rotated where the peak "high" would be 12 hours from the peak "low". Showing the "net" velocity."

No... There should not be any modulation, at least not due to velocity effects. The Sagnac ring measures absolute rotation rate only, not velocity.

There may be slight daily and monthly effects due to the Moon and tides that modulates the Earth's rotation rate mildly.

Jorrie

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#4
In reply to #3

Re: Sagnac' measure of Earth's Rotation

07/20/2007 3:43 PM

Ah!

So, the ring would see both earth's rotation and the earth's rotation around the sun, but the rotation around the sun would hardly register because of it's slow rotational rate. Sound close?

Thanks

Jim

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#5
In reply to #4

Re: Sagnac' measure of Earth's Rotation

07/21/2007 12:05 AM

Hi Jim.

Maybe not. Earth is not really rotating around the Sun, it's orbiting the Sun. Say Earth did not rotate relative to the Sun, i.e., every point on Earth was pointing at some fixed, distant star (no absolute Earth rotation). Then a day would have been about 365.25 present days long and there would be no Sagnac effect visible.

If the same spot on Earth pointed at the Sun, Earth would have an absolute rotation period of about 365.25 days and that would have been detectable in principle. This is same as your original question of a planet with the diameter of Earth's orbit and rotating once per 24 hours.

Hope this clears it.

Jorrie

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#6
In reply to #5

Re: Sagnac' measure of Earth's Rotation

07/21/2007 2:25 AM

Hello Again

Well... You may find it hard to believe, but your analogy sounds good, but my ability to comprehend has reached its limits.

Let me try one more time and then I suggest you give up on me...

Suppose I was on a Merry Go Round at the Fair. Suppose further, I was holding a portable Sagnac ring. When I got on, I would stand at the edge and I would "rotate myself" on my vertical axis and the Sagnac ring I'm holding would rotate with me. So, the Sagnac ring and I would be "absolutely" rotating. Then the Merry Go Round started up (rotating at twice my rotation "speed") and I kept on rotating but I walked (carefully because of my spinning) towards the center of the ride. Suppose the exact center of the ride was available for me to stand upon. So I approached (me still spinning), the center of the Merry Go Round and continued my spin and the Merry Go Round was spinning underneath me at twice the "speed". According to what you described (I think), the Sagnac ring would only register my absolute rotation with respect to it and the Sagnac ring would not "measure" the Merry Go Round spin presumably because it (the ring) is not rotating "absolutely" with respect to the Merry Go Round.

To help make it clear (probably to me), the Merry Go Round is the Earth "orbiting" the sun and me spinning is the Earth's rotation.

You now hopefully see where my level of intellect has prohibited me from understanding the difference between the Earth's spin and its rotation around the sun and my Merry Go Round "analogy".

I apologize if the difference is obvious.

During my attempt to describe my thoughts using the Merry Go Round analogy, the thought of what happens as I approached to center of the Merry Go Round intrigued me. You see, based upon my original thoughts (my first message), if the Sagnac ring somehow did register my spinning AND the Merry Go Round rotation, it would be interesting to observe the results as I approached the center of the Merry Go Round. In other words, how would the Sagnac ring measure both my spin and the Merry Go Round's rotation or would it?

Thanks again for trying to help me understand In the end, I may not be able to achieve understanding.

Thanks for trying

Jim

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#7
In reply to #6

Re: Sagnac' measure of Earth's Rotation

07/21/2007 4:05 AM

Hi Jim.

The Merry Go Round (MGR) analogy is actually quite good.

If you keep your rotation relative to the MGR platform constant, the Sagnac Ring (SR), correctly oriented in your hands, will measure the sum of your rotation and the MGR rotation. It does not matter where you are on the MGR, neter or perimeter, as long as the two absolute rotation rates remain the same.

Now imagine you standing on a frictionless platform (fp) that can freely rotate and fitted on top of the MGR platform. Put yourself into rotation before the MGR spins up. The SR will will measure your rotation only. Now spin up the MGR and the reading will not change, because you will keep the angular momentum around the axis of your fp. Your rotation rate relative to the distant stars remains the same.

Again, it will not make any difference if you and the platform slowly move towards the center of the MGR. All the above assumes that the rotation rates are relatively slow, so that centripetal forces are not affecting the apparatus.

The Earth around the Sun works more or less like you on top of the fp, on top of the MGR. The SR only measures the Earth's rotation relative to the distant stars.

Jorrie

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#8
In reply to #7

Re: Sagnac' measure of Earth's Rotation

07/21/2007 11:19 PM

Hello

My mind works quite slowly, but since you used the MGR and FP concept I think I have a chance of understanding. It may take me awhile... Give me a couple of days... I'll let you know...

Thanks for attaching your explanation to the MGR thought experiment. That has helped.

Jim

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#9

Re: Sagnac' measure of Earth's Rotation

08/04/2007 1:54 AM

Well, I have come to some conclusions.

1. A Sagnac device on Earth should "see" both rotations. The Earths and the Orbit (rotation around the sun). If it does not "see the rotation about the Sun, then I conclude that the Sun is rotating around the Earth.

2. If one places a pendulum (or a Sagnac ring) on the equator (presuming that this position is in a plane perpendicular to the Earth's axis of rotation) and sets it swinging in that plane, what happens over time? Does it precess 360 degrees in one year, or not? (Did the Sagnac ring detected the rotation around the Sun?) If it does, the Earth is rotating around the Sun; if it does not, the Sun is rotating around the Earth. Has someone tried this?

Quoting out of a Paper called "Sagnac effect: A century of Earth-rotated interferometers page 976. Michelson - "... he speculated on the likely size of an interferometer to detect the rotation of the Earth around the Sun. and came up with the answer of 100 square kilometers, ..."

Also referenced: "The ring laser gyro" by W. W. Chow and others. Pages 100 & 101.

Jim

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#10
In reply to #9

Re: Sagnac' measure of Earth's Rotation

08/04/2007 10:44 AM

Hi Jim.

I stand with my view: in principle, a Sagnag ring measures rotation relative to the distant stars and only that. Earth does not rotate around the Sun - it orbits it - and there is a big difference.

Consider a hypothetical situation where Earth has no rotation relative to the distant stars, but just orbits the Sun, so that a day and a year are of the same length. A Sagnag ring will measure no rotation, despite it orbiting the Sun.

I did not have time to read the papers that you mentioned, but a quick search revealed that at least the first one refers to the state of physics before the relativity 'revolution'. At that time, the movement through the 'aether' would presumably have been thought to affect a Sagnac ring's measurement.

A test that you can practically do: mount a good gyroscope or rate gyro or Sagnag ring on a frictionless platform near the edge of a MGR. Slowly spin the MGR around its axis and see if the gyro measures that rotation rate...

Jorrie

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