Dynamics of an Earth Ring

Herb Schaltegger wrote in message ...
In article ,
(AA Institute) wrote:

If the perigee of the asteroid's orbit is 40,000 km and say the apogee
is 200,000 km then that may be a safe option. If the apogee goes much
above 250,000 km then there's the Moon's perturbing influence to worry
about, since it orbits at around 380,000 km.

There's ALWAYS the Moon's perturbing influence to worry about. Have you
ever done any three-body problems? There's a reason they can't be done
analytically, you know. Especially when one of the objects is massive
enough to cause tides on the other object from 225,000 miles away, as
well as influence menstrual, mating, spawning and behavioral patterns of
a good deal of the life on it.

I'm serious that a ring will be created around the Earth at some point
in the future and I need some equations to simulate the event. I want
to be able to analytically demonstrate the long term stability of such
a ring system and all I get is joke after joke on this thread...

I will try more analytical groups like sci.math and physics.

Abdul

In article ,
(AA Institute) wrote:

Herb Schaltegger wrote in message
...
In article ,
(AA Institute) wrote:

If the perigee of the asteroid's orbit is 40,000 km and say the apogee
is 200,000 km then that may be a safe option. If the apogee goes much
above 250,000 km then there's the Moon's perturbing influence to worry
about, since it orbits at around 380,000 km.

There's ALWAYS the Moon's perturbing influence to worry about. Have you
ever done any three-body problems? There's a reason they can't be done
analytically, you know. Especially when one of the objects is massive
enough to cause tides on the other object from 225,000 miles away, as
well as influence menstrual, mating, spawning and behavioral patterns of
a good deal of the life on it.

I'm serious that a ring will be created around the Earth at some point
in the future and I need some equations to simulate the event. I want
to be able to analytically demonstrate the long term stability of such
a ring system and all I get is joke after joke on this thread...

I will try more analytical groups like sci.math and physics.

Abdul

What I wrote isn't a joke.

Do you understand ANYTHING about gravity and the three-body problem?
You CAN'T solve it analytically; you have to do it computationally. You
might start by doing a literature search on the Saturn ring system to
get an idea of the complexity involved. You seen to be thinking like a
science fiction writer or futurist; try thinking like an engineer or
scientist instead. Stop talking grand generalities and start talking
equations and numerical methods for analyzing complex (e.g., chaotic)
systems.

--
Herb Schaltegger, B.S., J.D.
"Never underestimate the power of human stupidity."
~ Robert A. Heinlein
http://www.angryherb.net

"AA Institute" wrote in message
om...
Alan LeHun wrote in message
.. .
In article ,
says...
You didn't spot the three dots I put after I wrote the word
"heartless"; that means I was joking.

Not to most people. That's a new usage for an ellipsis.

New to you perhaps.



we could have just used an ellipsis...

What is an ellipsis? I've heard of an ellipse but never an ellipsis.


You didn't even try to look the word up before posting. No one takes you
seriously because you don't do your own homework. They post joke responses
to you because they can tell you're not yet worthy of anything substantive.

"AA Institute" wrote in message
om...
Herb Schaltegger wrote in message
...
In article ,
(AA Institute) wrote:

If the perigee of the asteroid's orbit is 40,000 km and say the apogee
is 200,000 km then that may be a safe option. If the apogee goes much
above 250,000 km then there's the Moon's perturbing influence to worry
about, since it orbits at around 380,000 km.

There's ALWAYS the Moon's perturbing influence to worry about. Have you
ever done any three-body problems? There's a reason they can't be done
analytically, you know. Especially when one of the objects is massive
enough to cause tides on the other object from 225,000 miles away, as
well as influence menstrual, mating, spawning and behavioral patterns of
a good deal of the life on it.

I'm serious that a ring will be created around the Earth at some point
in the future and I need some equations to simulate the event. I want
to be able to analytically demonstrate the long term stability of such
a ring system and all I get is joke after joke on this thread...

I will try more analytical groups like sci.math and physics.

If you're talking about a solid ring, I believe a quick and simple analysis
should prove it to be unstable. Try looking at it from the opposite
perspective. Even a solid spherical surface is only metastable, in the sense
that there is no net gravitational field inside it to stabilise the position
of a centrally located body. I would expect a ring (I can do the math if you
insist, but you should be able to do it yourself) to pull objects away from
the centre radially. Newton's third law then tells you that a centrally (but
not perfectly centrally) located body would pull a ring away from a stable
position.
Grim

"Grimble Gromble" wrote in message
...


I'm serious that a ring will be created around the Earth at some point
in the future and I need some equations to simulate the event. I want
to be able to analytically demonstrate the long term stability of such
a ring system and all I get is joke after joke on this thread...

I will try more analytical groups like sci.math and physics.

If you're talking about a solid ring, I believe a quick and simple
analysis
should prove it to be unstable. Try looking at it from the opposite
perspective. Even a solid spherical surface is only metastable, in the
sense
that there is no net gravitational field inside it to stabilise the
position
of a centrally located body. I would expect a ring (I can do the math if
you
insist, but you should be able to do it yourself) to pull objects away
from
the centre radially. Newton's third law then tells you that a centrally
(but
not perfectly centrally) located body would pull a ring away from a stable
position.
Grim


It's been done. Google for references to an analysis that a math class did
for Larry Niven's ringworld. The math works regardless of the scale of the
system. It's not stable. Our large moon makes it damned near impossible.

AA: If you even think about responding to this posting, do it with some
serious mathematics. If you can't do that, you're wasting my time.


MK

T wrote in message . com...
My initial question is "Why not do the same thing on the Moon itself?";
lots of room to tunnel underground, etc.

I have since highlighted some of the attractions like surface
minerals, easy reach from Earth, artificial gravity, robotic
excavation, etc.

http://uk.geocities.com/aa_spaceagen...arth-ring.html

otoh, I like the general idea of a ring around the planet but it sounds
unstable with the Earth/Moon binary setup; other ringed planets have a
much greater difference in the Moon to Planet ratio.

Again, I have done some thinking around the precession rates for
non-polar orbits and it appears the *safest* option is to stick the
whole ring system in the Earth's equatorial plane. I think that is one
of the easiest lessons from all the outer planetary rings.

The only shame with this arrangement is we will not experience the
thrills of 'ring rise' and 'ring set', the dream view will be slightly
weakened...

AAI

"Bootstrap Bill" wrote:

"Derek Lyons" wrote in message
...

B2 didn't work because far more attention was paid to ecological
mysticism than to science and engineering. I'd not use it as 'proof'
of anything one way or another.

Is there any chance that another similar project will be attempted in the
near future?

I don't know one way or another. I'd have to say that the spectacular
failure of B2 mitigates against someone getting the gumption and cash
together for another try.

D.
--
Touch-twice life. Eat. Drink. Laugh.

-Resolved: To be more temperate in my postings.
Oct 5th, 2004 JDL

(George William Herbert) wrote in message news:416642fb$0

There are plenty of studies of Controlled Ecological
Life Support Systems (CELSS) done by NASA, including some
"locked the researcher in the sealed habitat with the
plants for several months" tests done back in the early
90s (and since then, on and off). No, not referring to
Biosphere-2, these were smaller scale high efficiency
NASA projects.

Were the studies done under sunlight or using artificial lighting?
Were they successful?

Thanks
Abdul

AA: If you even think about responding to this posting, do it with some
serious mathematics. If you can't do that, you're wasting my time.

In light of your very dangerous fore-warning... I am being a bit brave
here!

Are you familiar with this equation (quoted by Henry Spencer on
sci.space.tech a while back):-

An Earth circling satellite orbit will precess along the equator over
time according to the equation:-

-3/2 * J2 * (R^2 / p^2) * n * cos (i)

[Where J2 is a constant related to Earth's flattening, R is the
Earth's eq. Radius, p = a*(1-e^2) (in which a is the orbit's
semi-major axis and e is its eccentricity), n is the mean motion and i
is the orbit's inclination.]

???

AAI

"AA Institute" wrote in message
om...
AA: If you even think about responding to this posting, do it with some
serious mathematics. If you can't do that, you're wasting my time.
In light of your very dangerous fore-warning... I am being a bit brave
here!
What's brave about wasting someone else's time?

Are you familiar with this equation (quoted by Henry Spencer on
sci.space.tech a while back):-
An Earth circling satellite orbit will precess along the equator over
time according to the equation:-
-3/2 * J2 * (R^2 / p^2) * n * cos (i)
[Where J2 is a constant related to Earth's flattening, R is the
Earth's eq. Radius, p = a*(1-e^2) (in which a is the orbit's
semi-major axis and e is its eccentricity), n is the mean motion and i
is the orbit's inclination.]
Being familiar with an equation is not the same as understanding it. That
the earth's flattening is involved suggests that this precession is caused
by tidal influences experienced by the satellite as it orbits above and
below the earth's equatorial plane. That there is no term relating to the
lunar and stellar masses, suggests that this is a very simplified analysis
in which all other influences have been ignored. Is there any reason you
introduce this (idealised particulate) satellite into a discussion on earth
rings? Perhaps you are comparing the effect on an orbiting satellite of the
earth's equatorial bulge to that of an independently orbiting ring? You do
realise that there are significant electromagnetic forces operating between
the 'equatorial' bulge and the 'spherical' earth?
Grim