[Dimensional (OP)]

usually spherical when in a rest frame?

Isn't this a coincidence since relativity says that structures like the moon also exist as disk-like shapes to sufficiently fast frames of reference?

In other words, why do large spherical objects seem to favor rest frames?

[Bored chemist]

I'm fairly sure that most of the big more -or -less round tings are rotating.
That means they are accelerating so I don't think they can be in a rest frame.

Many large objects are roughly spherical because that's the shape that gravity favours.

[Origin]

usually spherical when in a rest frame?

Large objects are spherical because all the matter in the object is being drawn towards the center of gravity.  So the natural shape would be a sphere since that shape has the entire surface closest to the center of gravity.
A rest frame is the frame you are in.  So that means that every celestial body in the universe except earth is not in a rest frame from your perspective.
 

Isn't this a coincidence since relativity says that structures like the moon also exist as disk-like shapes to sufficiently fast frames of reference?

It is not a coincidence.  The reason we do not see the moon or any other celestial body as a disk is simply because the velocity of earth compared to other bodies is very very slow when compared to c.  For instance we (the Earth and the Milky Way) are moving towards the 'great attractor' at about 1,340,000 mph or 372 miles/sec.  Imagine that somehow there was a planet moving at the same speed in the opposite direction so that it passed the earth at 742 miles/sec.  That speed is is 0.3% the speed of light, so we would see no discernable change in the body as it shot by us.
So in the grand scale of things, a planet moving past us at 3,000,000 mph is effectively at rest with us when compared to the speed of light.

[Dimensional (OP)]

I'm fairly sure that most of the big more -or -less round tings are rotating.
That means they are accelerating so I don't think they can be in a rest frame.

Many large objects are roughly spherical because that's the shape that gravity favours.

But general relativity says that these objects can be many other shapes, due to length contraction, and still function exactly the same way.

[Dimensional (OP)]

It is not a coincidence.  The reason we do not see the moon or any other celestial body as a disk is simply because the velocity of earth compared to other bodies is very very slow when compared to c.  For instance we (the Earth and the Milky Way) are moving towards the 'great attractor' at about 1,340,000 mph or 372 miles/sec.  Imagine that somehow there was a planet moving at the same speed in the opposite direction so that it passed the earth at 742 miles/sec.  That speed is is 0.3% the speed of light, so we would see no discernable change in the body as it shot by us.
So in the grand scale of things, a planet moving past us at 3,000,000 mph is effectively at rest with us when compared to the speed of light.

I understand that these large bodies are not contracting to any significant amount.  My curiosity is about why they are all spherical since we know that they can function just as easily as disks.  Why are they all spherical in a rest frame?  Shouldn't they all be random shapes since they can exist that way too?

[evan_au]

A thought experiment (or really do it): Take a glass of water, and drop in a pebble. It falls to the bottom of the glass.
- That is because if you imagine the more-dense pebble above some less-dense water, that is energetically unstable. It is more stable if the pebble moves beneath the water
- So denser things tend to fall towards the center of a body, and less-dense things rise to the top, farthest from the center.
- On long timeframes, even fairly solid-looking things like rock deform and flow like liquids
- So the structure of the Earth has dense metal at the center (mostly nickel & iron), then less-dense molten rock, then water, then air (and then a vacuum, which is less dense than air)

The structure is almost* spherically symmetric, in that the same force pulling dense things to the center of the Earth from United Kingdom also pulls things to the center of the Earth from New Zealand, on the opposite side of the Earth.

*The thing that provides a slight deviation from spherical symmetry is the rotation, making the planets (and the Sun) slightly disk-like. Centrifugal force makes them bulge outwards at the equator.
- The effect is fairly small. For Earth, rotating every 24 hours, the polar flattening is about 0.3%
Equatorial radius   6378 km (3963 mi)
Polar radius   6357 km (3950 mi)

- For Jupiter, rotating every 10 hours, it is 6% flattened.
Equatorial radius: 71,492 km (44,423 mi)
Polar radius: 66,854 km (41,541 mi)

So the planets are slightly flattened (disk-like), but it's due to their own rotation, rather than any relativistic effects.
- It is nothing like the disc-shaped world imagined by the science fiction/fantasy writer Terry Pratchett
https://en.wikipedia.org/wiki/Discworld

[Bored chemist]

I'm fairly sure that most of the big more -or -less round tings are rotating.
That means they are accelerating so I don't think they can be in a rest frame.

Many large objects are roughly spherical because that's the shape that gravity favours.

But general relativity says that these objects can be many other shapes, due to length contraction, and still function exactly the same way.

Anything that is close enough for us to judge what shape it is will be travelling sufficiently slowly that relativistic effects will be small.

[Dimensional (OP)]

A thought experiment (or really do it): Take a glass of water, and drop in a pebble. It falls to the bottom of the glass.
- That is because if you imagine the more-dense pebble above some less-dense water, that is energetically unstable. It is more stable if the pebble moves beneath the water
- So denser things tend to fall towards the center of a body, and less-dense things rise to the top, farthest from the center.
- On long timeframes, even fairly solid-looking things like rock deform and flow like liquids
- So the structure of the Earth has dense metal at the center (mostly nickel & iron), then less-dense molten rock, then water, then air (and then a vacuum, which is less dense than air)

The structure is almost* spherically symmetric, in that the same force pulling dense things to the center of the Earth from United Kingdom also pulls things to the center of the Earth from New Zealand, on the opposite side of the Earth.

*The thing that provides a slight deviation from spherical symmetry is the rotation, making the planets (and the Sun) slightly disk-like. Centrifugal force makes them bulge outwards at the equator.
- The effect is fairly small. For Earth, rotating every 24 hours, the polar flattening is about 0.3%
Equatorial radius   6378 km (3963 mi)
Polar radius   6357 km (3950 mi)

- For Jupiter, rotating every 10 hours, it is 6% flattened.
Equatorial radius: 71,492 km (44,423 mi)
Polar radius: 66,854 km (41,541 mi)

So the planets are slightly flattened (disk-like), but it's due to their own rotation, rather than any relativistic effects.
- It is nothing like the disc-shaped world imagined by the science fiction/fantasy writer Terry Pratchett
https://en.wikipedia.org/wiki/Discworld [nofollow]

But let's say an alien from another universe is traveling very fast past our own to the point that length contraction is very significant.  He wants to study our laws of physics.  He would notice that celestial bodies, like planets and stars, seem to prefer a disk shape.

Then he somehow realizes that there is a length contraction in his frame of reference.  He could then wonder why these bodies are all roughly the same shape, which is what I am doing.

So maybe a better question is why are all these objects roughly the same shape.  Why aren't some disk shaped and some spherical?

[Dimensional (OP)]

Anything that is close enough for us to judge what shape it is will be travelling sufficiently slowly that relativistic effects will be small.

But why aren't some of these relatively slow moving objects disk shaped?

[Bored chemist]

For a start some astronomical entities are disk shaped.
https://en.wikipedia.org/wiki/Milky_Way

So maybe a better question is why are all these objects roughly the same shape.

That question was already answered repeatedly.

Many large objects are roughly spherical because that's the shape that gravity favours.

Large objects are spherical because all the matter in the object is being drawn towards the center of gravity.  So the natural shape would be a sphere since that shape has the entire surface closest to the center of gravity.

A thought experiment (or really do it): Take a glass of water, and drop in a pebble. It falls to the bottom of the glass.
- That is because if you imagine the more-dense pebble above some less-dense water, that is energetically unstable. It is more stable if the pebble moves beneath the water
- So denser things tend to fall towards the center of a body, and less-dense things rise to the top, farthest from the center.

[Dimensional (OP)]

For a start some astronomical entities are disk shaped.
https://en.wikipedia.org/wiki/Milky_Way [nofollow]

So maybe a better question is why are all these objects roughly the same shape.

That question was already answered repeatedly.

Many large objects are roughly spherical because that's the shape that gravity favours.

Large objects are spherical because all the matter in the object is being drawn towards the center of gravity.  So the natural shape would be a sphere since that shape has the entire surface closest to the center of gravity.

A thought experiment (or really do it): Take a glass of water, and drop in a pebble. It falls to the bottom of the glass.
- That is because if you imagine the more-dense pebble above some less-dense water, that is energetically unstable. It is more stable if the pebble moves beneath the water
- So denser things tend to fall towards the center of a body, and less-dense things rise to the top, farthest from the center.

But according to general relativity, a disk shaped body works just as well as a sphere.  So why are there only spheres?

[Kryptid]

But according to general relativity, a disk shaped body works just as well as a sphere.

Only if the relative velocities involved are high.

[Dimensional (OP)]

But according to general relativity, a disk shaped body works just as well as a sphere.

Only if the relative velocities involved are high.

Well yes, of course. 

[Origin]

I understand that these large bodies are not contracting to any significant amount.  My curiosity is about why they are all spherical since we know that they can function just as easily as disks.

In the inertial frame of the objects they will always be spheres.  You will only see the flattening in another inertial frame moving at a relativistic speed to the object.  Since there are no bodies moving relative to earth at a large percentage of c we see no flattening.  Again let me emphasize if you are in the same inertial frame as a celestial body you will never see any flattening.  In other words in its own inertial frame a celestial body cannot 'function' as a disc or other shape.  I cannot think of a case where you would ever be in a situation where a celestial body was moving at relativistic speeds to earth.

[Dimensional (OP)]

In other words in its own inertial frame a celestial body cannot 'function' as a disc or other shape.  I cannot think of a case where you would ever be in a situation where a celestial body was moving at relativistic speeds to earth.

So what makes its rest frame unable to exist as a disc when it exists as a disk in, say, the frame of reference from a muon shooting to the ground from the Earth's upper atmosphere?

[Origin]

So what makes its rest frame unable to exist as a disc when it exists as a disk in, say, the frame of reference from a muon shooting to the ground from the Earth's upper atmosphere?

Because they are different frames!

[Dimensional (OP)]

So what makes its rest frame unable to exist as a disc when it exists as a disk in, say, the frame of reference from a muon shooting to the ground from the Earth's upper atmosphere?

Because they are different frames!

You are not answering the question.  Why can't, say, the Earth exist as a disc in its rest frame, when it can exist as a disc for a muon?

[Halc]

You are not answering the question.  Why can't, say, the Earth exist as a disc in its rest frame, when it can exist as a disc for a muon?

First of all, as has been pointed out, few objects form actual spheres since they're spinning and get fat in two dimensions in the middle like Earth is, or super-fat in the middle like our galaxy which has far too much angular momentum to form up into anything close to a sphere.
Secondly, all objects have the same proper shape (which means it isn't frame dependent). All events that comprise any object (like Earth) all exist as the same events in any frame. The only difference is that the different frame give different coordinates to each and every one of those events, and in frames where the (nearly spherical) object is moving fast, the set of events with any one given identical time coordinate  happen to not be very spatially separated along the line of motion. So it is the motion that changes the coordinates of the events (and the shape of it accordingly), and not the shape that determines the velocity.

As a side, there's no velocity at which a proper shape of a disk can be moved that contracts it back into a sphere in that frame. At best you might get a skinny rice grain shape. On the other hand, an object whose proper shape is already a skinny rice shape can indeed be contracted into a sphere in a frame where it is moving in the right direction.

[Dimensional (OP)]

You are not answering the question.  Why can't, say, the Earth exist as a disc in its rest frame, when it can exist as a disc for a muon?

First of all, as has been pointed out, few objects form actual spheres since they're spinning and get fat in two dimensions in the middle like Earth is, or super-fat in the middle like our galaxy which has far too much angular momentum to form up into anything close to a sphere.
Secondly, all objects have the same proper shape (which means it isn't frame dependent). All events that comprise any object (like Earth) all exist as the same events in any frame. The only difference is that the different frame give different coordinates to each and every one of those events, and in frames where the (nearly spherical) object is moving fast, the set of events with any one given identical time coordinate  happen to not be very spatially separated along the line of motion. So it is the motion that changes the coordinates of the events (and the shape of it accordingly), and not the shape that determines the velocity.

As a side, there's no velocity at which a proper shape of a disk can be moved that contracts it back into a sphere in that frame. At best you might get a skinny rice grain shape. On the other hand, an object whose proper shape is already a skinny rice shape can indeed be contracted into a sphere in a frame where it is moving in the right direction.

I don't understand how a proper shape can be the same shape in all frames.  I have heard of this, but I wonder how a disk can also be a sphere even with the time dimension?  This proper shape is not conceivable is it?

[Halc]

Going to answer the questions out of order.

I wonder how a disk can also be a sphere even with the time dimension?

If you add the time dimension to an object like a star, you have a 4D shape which is spherical in 3 dimensions and very extended in the time dimension. It isn't shaped like a hypersphere (a 4D ball) at all, but a cross section of this long thing will be spherical or some other shape depending on the angle at which it is sliced.

This proper shape is not conceivable is it?

It's actually pretty conceivable, especially using Euclidean geometry as an analogy. If you can't imagine 4D objects, try eliminating a spatial dimension. Now a star is a circle instead of sphere, and adding time makes it into this long garden-hose like shape that probably is close to but not completely straight. This is the worldline of the star. If you slice the hose/worldline perpendicular to the length of it, you get a circular cross section. That's the hose's proper shape: a circle (a ring actually since hoses are not solid). If you cut it at an angle, you get an ellipse whose eccentricity gets larger the more severe the angle at which the slice is taken. That's what it means for the shape of something to change given different proper frames. The proper shape is a slice taken perpendicular to the time dimension when said time dimension is chosen exactly parallel to the long extended dimension of the object in spacetime. The only difference is Minkowskian geometry in which angled cross sections form contracted flat disks instead of the extended ellipsoid that you get with an angled slice of 4D Euclidean worldline.

I don't understand how a proper shape can be the same shape in all frames.

The proper shape of an object is a function of the orientation of the object in 4D spacetime, and so corresponds only to a coordinate system in which the time dimension is similarly oriented. This is the frame in which the object (or at least its center of gravity) is stationary and its proper shape is defined. It will be the one frame in which the spatial dimensions of the object are all at their maximum value. Oddly, in Euclidean geometry, it would be the one frame in which the spatial dimensions of the object are all at their minimum value. Cross sections of Euclidean hoses get bigger if you cut them at an angle.