Shape of a spinning "planet"

[Allen Windhorn]

Is there a simple way to describe the shape of a spinning object
constrained only by gravity and centrifugal force? I would think some
kind of calculus of variations would be required, which I don't
understand very well, and the gravitational attraction would involve
some messy integrals.

Mesklin comes to mind, but what I was actually wondering is whether
you could melt a comet and spin it to make a lens. Yes, I know it
would boil off, I'll deal with that later.

TIA,
Allen

[N:dlzc D:aol T:com (dlzc)]

Post by Allen Windhorn
Is there a simple way to describe the shape of a spinning object
constrained only by gravity and centrifugal force? I would think some
kind of calculus of variations would be required, which I don't
understand very well, and the gravitational attraction would involve
some messy integrals.

Oblate spheroid.

Post by Allen Windhorn
Mesklin comes to mind, but what I was actually wondering is whether
you could melt a comet and spin it to make a lens. Yes, I know it
would boil off, I'll deal with that later.

Not only would it boil off...
The curvature would be wrong, and
"moons" would spin off.

David A. Smith

[Allen Windhorn]

Post by N:dlzc D:aol T:com (dlzc)

Post by Allen Windhorn
Is there a simple way to describe the shape of a spinning object
constrained only by gravity and centrifugal force? I would think some
kind of calculus of variations would be required, which I don't
understand very well, and the gravitational attraction would involve
some messy integrals.

Oblate spheroid.

That was the obvious answer, but I couldn't prove it. Thanks.

Post by N:dlzc D:aol T:com (dlzc)

Post by Allen Windhorn
Mesklin comes to mind, but what I was actually wondering is whether
you could melt a comet and spin it to make a lens. Yes, I know it
would boil off, I'll deal with that later.

Not only would it boil off...
The curvature would be wrong, and
"moons" would spin off.

Oh well, I guess I'll abandon that idea.

Thanks again

Allen

[Jonathan Silverlight]

Post by Allen Windhorn

Post by N:dlzc D:aol T:com (dlzc)

Post by Allen Windhorn
Is there a simple way to describe the shape of a spinning object
constrained only by gravity and centrifugal force? I would think some
kind of calculus of variations would be required, which I don't
understand very well, and the gravitational attraction would involve
some messy integrals.

Oblate spheroid.

That was the obvious answer, but I couldn't prove it. Thanks.

In the "Addendum to Whirligig World" which Hal Clement added after his
novella "Under" (Analog January 2000), Hal notes that an oblate spheroid
is not the right answer! (John Campbell apparently said something about
Euler spinning in his grave, which I don't pretend to follow).
Apparently the real shape is like a discus, with a curve at the poles, a
fairly sharp edge at the equator, and flattened mid-latitudes.

Post by Allen Windhorn

Post by N:dlzc D:aol T:com (dlzc)

Post by Allen Windhorn
Mesklin comes to mind, but what I was actually wondering is whether
you could melt a comet and spin it to make a lens. Yes, I know it
would boil off, I'll deal with that later.

[Allen Windhorn]

Post by Jonathan Silverlight
In the "Addendum to Whirligig World" which Hal Clement added after his
novella "Under" (Analog January 2000), Hal notes that an oblate
spheroid is not the right answer! (John Campbell apparently said
something about Euler spinning in his grave, which I don't pretend to
follow).
Apparently the real shape is like a discus, with a curve at the poles,
a fairly sharp edge at the equator, and flattened mid-latitudes.

He didn't happen to give a mathematical description or process, did
he? I suppose the simplest thing would be some sort of finite element
analysis.

Thanks for the interesting note.

Regards,
Allen

[Mr. 4X]

Post by Allen Windhorn
Is there a simple way to describe the shape of a spinning object
constrained only by gravity and centrifugal force?

I think that's called an 'ellipsoid'.

Post by Allen Windhorn
I would think some
kind of calculus of variations would be required, which I don't
understand very well, and the gravitational attraction would involve
some messy integrals.

Maybe someone in a math group can help.

Post by Allen Windhorn
Mesklin comes to mind, but what I was actually wondering is whether
you could melt a comet and spin it to make a lens. Yes, I know it
would boil off, I'll deal with that later.
TIA,
Allen

[Kathy Rages]

Post by Allen Windhorn
Is there a simple way to describe the shape of a spinning object
constrained only by gravity and centrifugal force? I would think some
kind of calculus of variations would be required, which I don't
understand very well, and the gravitational attraction would involve
some messy integrals.

Google on "rotation" "Maclaurin spheroid". It's not exactly simple, but
there is a closed analytic expression.

[Jonathan Silverlight]

Post by Kathy Rages

Post by Allen Windhorn
Is there a simple way to describe the shape of a spinning object
constrained only by gravity and centrifugal force? I would think some
kind of calculus of variations would be required, which I don't
understand very well, and the gravitational attraction would involve
some messy integrals.

Google on "rotation" "Maclaurin spheroid". It's not exactly simple, but
there is a closed analytic expression.

I gather that a Maclaurin spheroid is homogeneous. That might be true
for a comet, but it certainly wouldn't be true for anything much larger.

[Allen Windhorn]

Post by Jonathan Silverlight

Post by Kathy Rages

Post by Allen Windhorn
Is there a simple way to describe the shape of a spinning object
constrained only by gravity and centrifugal force? I would think some
kind of calculus of variations would be required, which I don't
understand very well, and the gravitational attraction would involve
some messy integrals.

Google on "rotation" "Maclaurin spheroid". It's not exactly simple, but
there is a closed analytic expression.

I gather that a Maclaurin spheroid is homogeneous. That might be true
for a comet, but it certainly wouldn't be true for anything much larger.

I would expect a lot of rocks and stuff would fall to the center,
where they might need to be fished out. Gases would evaporate.

Now I think of it, wasn't there a SF novel recently where somebody
lived in a big sphere of water?

Regards,
Allen

[Allen Windhorn]

Post by Kathy Rages

Post by Allen Windhorn
Is there a simple way to describe the shape of a spinning object
constrained only by gravity and centrifugal force? I would think some
kind of calculus of variations would be required, which I don't
understand very well, and the gravitational attraction would involve
some messy integrals.

Google on "rotation" "Maclaurin spheroid". It's not exactly simple, but
there is a closed analytic expression.

Thanks much, I will.

Regards,
Allen

[Steve Willner]

Post by Allen Windhorn
Is there a simple way to describe the shape of a spinning object
constrained only by gravity and centrifugal force?

No, it's not simple. It depends on the equation of state, just for
starters. James Jeans and probably others of his era spent a lot of
time on this question. You might try putting 'liquid star' in an ADS
title search. I found a few articles by Jeans but not any very
extensive work, but I didn't look very hard.

If the rotation is small, an oblate spheroid is a reasonable
approximation.