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

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In summary: They found tiny deviation of the position of the North Pole from the real North Pole by about 2 meters.
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Arthur95
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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
 
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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 ;)
 
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  • #3
Arthur95 said:
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.
 
  • #4
Arthur95 said:
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.
 
  • #5
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.
 

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

1. What is space-time?

Space-time is a concept in physics that combines the three dimensions of space with the dimension of time into a single four-dimensional continuum. It is used to describe the physical universe and the relationships between objects in the universe.

2. What is the gyroscopic effect?

The gyroscopic effect, also known as gyroscopic precession, is a phenomenon where a spinning object experiences a force when its axis of rotation is tilted. This force is perpendicular to the direction of the tilt and causes the object to rotate around a different axis.

3. Who is Arthur and why is he mentioned in the title?

Arthur is a fictional character who serves as a metaphor in the explanation of the gyroscopic effect. He is used to demonstrate how an object's axis of rotation can change in response to external forces, similar to how a spinning top behaves.

4. How does the gyroscopic effect impact space-time?

The gyroscopic effect does not directly impact space-time. However, it is a fundamental principle in physics that helps us understand the behavior of objects in space-time. Understanding how the gyroscopic effect works is important in fields such as astrophysics and aerospace engineering.

5. What real-world applications does the gyroscopic effect have?

The gyroscopic effect has many practical applications, including navigation systems in airplanes, ships, and spacecraft. It is also used in gyroscopes, which are used in compasses, gyrocompasses, and other navigation devices. The gyroscopic effect is also utilized in various sports equipment, such as bicycles and motorcycles, to improve their stability and maneuverability.

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