Space-time & Gyroscopic Effect: Arthur's First Post

[Arthur95]

My first post (and from a mobile), so please pardon any impropriety...

If gravity bends spacetime, wouldn't we expect to see that effect on a rotating gyroscope? Using the Earth's axial tilt as an example: we have seasons through the year as we orbit, but shouldn't the curved spacetime created by the sun mean the Earth would maintain its tilt-orientation with respect to the sun all year (eg: northern hemisphere always inclined toward the sun for the 'endless summer')?

I imagine there is conservation of momentum / inertia or something coming into play here, or more likely I just don't understand this spacetime stuff!

Thanks for indulgence!
Arthur

 

[Simon Bridge]

Welcome to PF;

If gravity bends spacetime, wouldn't we expect to see that effect on a rotating gyroscope?

Yes - the curvature would affect everything.

Using the Earth's axial tilt as an example: we have seasons through the year as we orbit, but shouldn't the curved spacetime created by the sun mean the Earth would maintain its tilt-orientation with respect to the sun all year (eg: northern hemisphere always inclined toward the sun for the 'endless summer')?

No ... as you have seen, this does not happen.
The Earth is tilted wrt the line, drawn through curved space, from the Earth to the Sun.

Where the curvature is more extreme across the diameter of a planet, you do get one face always to the primary ... the effect is called "tidal locking". Which you probably already know ;)

 

[WannabeNewton]

If gravity bends spacetime, wouldn't we expect to see that effect on a rotating gyroscope? Using the Earth's axial tilt as an example: we have seasons through the year as we orbit, but shouldn't the curved spacetime created by the sun mean the Earth would maintain its tilt-orientation with respect to the sun all year (eg: northern hemisphere always inclined toward the sun for the 'endless summer')?

The Earth isn't exactly a gyroscope but it is to the extent that it doesn't matter for this discussion. What you're describing is possible in principle in GR but certainly not in practice in our solar system because the necessary general relativistic effects due to the Sun, that is, Thomas precession and geodetic precession, are far too weak; in fact Thomas precession would be entirely absent since the Earth is in free fall and hence doesn't accelerate relative to local inertial frames.

However let's consider a Schwarzschild black hole of mass $M$ and a gyroscope accelerating on a circular trajectory at a special radius ($r = 3M$) at which light can orbit. If the gyroscope axis is initially aligned in the radial direction, so that it points towards the black hole, then it will remain pointing towards the black hole during its entire trajectory around the black hole.

If you want I can point to some intuitive explanations of this effect.

 

[A.T.]

but shouldn't the curved spacetime created by the sun mean the Earth would maintain its tilt-orientation with respect to the sun all year

No, it just means that it won't exactly maintain its tilt-orientation with respect to the distant stars after one orbit. But as others said, this effect is tiny for the Sun Earth system.

 

[SpiderET]

Something distantly related but similar have been done experimentally in Gravity probe B experiment:
http://en.wikipedia.org/wiki/Gravity_Probe_B

They had almost perfect gyroscope rotating from pole to pole around Earth. They tried to measure tiny influence of frame dragging of Earth on the gyroscope.