thrown off

Dear Yousuf Khan:

On Friday, June 21, 2013 8:16:49 AM UTC-7, Yousuf Khan wrote:
....
Ummm, creme-filled chocolate Moon.

Good thing I am not that hungry...

David A. Smith

In article ,
"Mike Dworetsky" wrote:

snip

Thinking about it for a moment, the required speed would be the same as that
needed for reaching orbital velocity at altitude zero. If there were no
atmosphere that would work, so stuff would start "flying off", but only at
the equator.

Yes, once the linear speed of a point on the surface reaches sqrt(1/2)
times the escape velocity.

--
Odysseus

In sci.astro message , Fri, 21
Jun 2013 10:50:09, Mike Dworetsky
posted:

Mike Dworetsky wrote:
Yousuf Khan wrote:
On 20/06/2013 10:28 PM, wrote:
How fast would the earth have to spin, so that stuff
started flying off?


Thinking about it for a moment,

That is contrary to established custom; but Gandhi would have had
something to say about that.

the required speed would be the same as that needed for reaching
orbital velocity at altitude zero. If there were no atmosphere that
would work, so stuff would start "flying off", but only at the equator.


For a spherical symmetry, the period of a circular orbit depends only on
the mean density of the body within the sphere of which that circle is a
Great Circle, being given by
T^2 = (3 pi) / (G rho) .

http://www.merlyn.demon.co.uk/gravity2.htm#Gdy refers.

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set the following eddies spiralling through the
space-time continuum:

How fast would the earth have to spin, so that stuff
started flying off?

--
Rich

Assuming the earth did not change shape at its new spin rate (it inevitably
would) then if it were to spin at one revolution in 84 minutes, that would
be enough for centrifugal force at the equator to balance earth's gravity.

It's no coincidence that 84 minutes is the orbital period of satellites in
low earth orbit.

In reality the earth would not hold together at that sort of spin rate. It
would flatten even more, which would reduce the critical spin rate even
more - positive feedback leading to earth breaking up.
--
ξ: ) Proud to be curly

Interchange the alphabetic letter groups to reply

In article ,
Curlytop wrote:

snip

It's no coincidence that 84 minutes is the orbital period of satellites in
low earth orbit.

In reality the earth would not hold together at that sort of spin rate. It
would flatten even more, which would reduce the critical spin rate even
more - positive feedback leading to earth breaking up.

How much flatter would the Earth have been in the Palaeozoic, when the
length of a day was, say, 20 hours (i.e. its rotational speed was 20%
greater than that of today)? Is there a Hooke's-Law-like idealized
relation between angular speed and oblateness for an elastic ball?

--
Odysseus

In article ,
Odysseus writes:
Is there a Hooke's-Law-like idealized
relation between angular speed and oblateness for an elastic ball?

The relation for liquids was worked out in the 18th(!) century. See
http://farside.ph.utexas.edu/teachin...ml/node38.html

Looking up "Maclaurin spheroids" and "Jacobi ellipsoids" will provide
more information. I think these are all based on constant density,
but there must be similar solutions for any specified density law.
The tricky bit is that for fast enough rotations, the body tends to
become non-axisymmetric. I never took the course that studied all
this stuff, though, so don't ask me for details.

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