Gyroscopic action on earth surface

[RandallB]

What will gyro alignment be if ?

Establish a free spinning spherical gyro similar to a GPB gyro; but designed to run on Earth surface at the equator supported by jets of air or something to minimize friction and not influence the spin once established.
Establish a spin axis Aligned with the Sun at high noon and the center of the earth.
Let run free for 6 hours.
Does spin axis it stay in line with the sun as it would were it in true orbital freefall?

Or does whatever we do to provide the required support (since it moves to slowly to be in orbit) cause the local influence of gravity to demand the gyroscope use the center of the Earth as a reference and keep the axis pointed there and turn it 90^o off of alignment with the sun?

 

[empirical]

Perhaps a gyrocompass might be relevant to your query.

 

[cesiumfrog]

The effect GPB aims to measure is neglegibly small; no matter how you support your gyro it should maintain it's orientation with respect to the distant stars. Over six hours it should stay aligned to the sun, not the earth. (Hence, like the stars themselves, it could be used for navigation.)

 

[Garth]

The gyroscope should experience the Geodetic Precession, which is a GR effect due to the curvature of space-time caused by the mass of the Earth, and Thomas Precession, which is a SR effect due to the Earth's surface supporting the gyro and therefore accelerating it relative to the freely falling inertial frame of reference.

There would also be a much smaller E-W Lense-Thirring or frame-dragging Precession, a GR effect caused by the spinning mass of the Earth dragging space-time and inertial compasses round with it.

Of course the gyro itself would have to be supported exactly through its centre of gravity otherwise it would suffer a much larger gyroscopic torque precession as the Earth's gravity tried to rotate it in the vertical direction.

The Thomas Precession named after Llewellyn Thomas, and discovered on Earth in 1988, is a correction to the spin-orbit interaction in Quantum Mechanics.

The GR effects can only be practically measured under the very sensitive conditions of the Gravity Probe B experiment in free fall and the results will be published April 2007. (we hope )

Garth

 

[HallsofIvy]

Sounds like it would behave very much like a Foucault pendulum.

 

[RandallB]

Sounds like it would behave very much like a Foucault pendulum.

It does ??
I read the responses as saying the gyro would turn losing its alignment with the Earth bound lab as the gyro in our 6 hour experiment remains inline with the Sun and Stars (continue the test for 6 months and it would lose alignment with the Sun to hold with the stars).

BUT a Foucault Pendulum at the equator shows no such turn or movement. At least not in my view of a Foucault Pendulum maybe someone has a reference that says different, but I doubt it.

 

[RandallB]

Garth
Although you did not say so directly, you are in agreement that the gyro would act as a three dimensional Gyrocompass and as long as my OP requirement that the support not influence the spin significantly it should easily show an ability to hold alignment with the sun. Sounds like a fun little demonstration to actually build (need to work in a trip to the equator somewhere, somehow, a grant maybe :-)

Of course this is a very coarse measurement between comparing a result between 0 and 90 would not call for a great deal of precision to confirm a 3D Gyrocompass working as expected.
But a few questions the other levels of measure you refer to:

Geodetic Precession,
Thomas Precession,
There would also be a much smaller E-W Lense-Thirring or frame-dragging Precession, a GR effect caused by the spinning mass of the Earth dragging space-time and inertial compasses round with it.

The Thomas Precession named after Llewellyn Thomas, and discovered on Earth in 1988, is a correction to the spin-orbit interaction in Quantum Mechanics.

Any Earth bound lab would not be able to insulate the experiment well enough and long enough to actually measure Geodetic Precession, or Lense-Thirring AKA frame-dragging Precession hence the need for the Gravity Probe B experiment.

But is Thomas Precession as “discovered on Earth in 1988” larger than the GR affects and actually measurable on Earth or is it a QM calculation discovery too small to be measured in our environment? (I’ll try to do some searches on it, but my guess is too small)

Also isn’t the “much smaller E-W Lense-Thirring” actually a West to East Precession in the same direction as Earth's rotation and the Geodetic Precession here?

And finally a question on the calculation of the expected Lense-Thirring being measure by GP-B; do you know if the GR formula for it requires taking into account the mass density distribution of the rotating mass (earth).
That is, would the expected Lense-Thirring on GP-B be different (smaller) if earth’s mass was concentrated in one-tenth the diameter or (larger) if Earth was hollow with all the mass located in a thick dense surface shell?