Dynamical stability of an Earth Ring

From: AA Institute (abdul.ahad_at_ntlworld.com)
Date: 10/08/04 

Date: 8 Oct 2004 06:34:08 -0700

Suppose an asteroid by a distant future engineering achievement has
been captured into orbit around the Earth.
Now suppose we want to carve it out by detonating a series of missiles
that incrementally hollow their way into the body of such an asteroid.
The material excavated out of the body would create a thin ring system
around the Earth, as I try to illustrate here:-

http://uk.geocities.com/aa_spaceagent/restricted/earth-ring.html

My main concern with such a project is one of SAFETY. I'd like to know
what a *safe* perigee (minimum) altitude would be necessary to prevent
orbital decay of ring material. I don't want any material from my
hypothetical ring system coming down toward the Earth under any
circumstances. Would the ring material be contained in a narrow plane
of fixed orbital incline, or would it scatter over time?

QUESTION: I am under pressure to demonstrate by way of a mathematical
model the dynamical stability of such a ring system, composed of small
particles being gravitationally influenced by the Earth and the Moon
by way of "3 body problem".

What are the analytical equations necessary to help demonstrate
*theoretically* that such ring particles would indeed be stable in
their orbital paths around the Earth? Or if not, how would I be able
to show this?

I would sincerely appreciate all help, as this is quite *pivotal* to
my research on this article.

Thanks for any support.
Abdul Ahad

Relevant Pages

  • Dynamic stability of an Earth Ring
    ... been captured into orbit around the Earth. ... that incrementally hollow their way into the body of such an asteroid. ... The material excavated out of the body would create a thin ring system ... *theoretically* that such ring particles would indeed be stable in ...
    (sci.physics.research)
  • Re: Dynamical stability of an Earth Ring
    ... > been captured into orbit around the Earth. ... > that incrementally hollow their way into the body of such an asteroid. ... > The material excavated out of the body would create a thin ring system ...
    (sci.math.num-analysis)
  • Re: Dynamical stability of an Earth Ring
    ... > been captured into orbit around the Earth. ... > that incrementally hollow their way into the body of such an asteroid. ... > The material excavated out of the body would create a thin ring system ...
    (sci.math)
  • Dynamical stability of an Earth Ring
    ... been captured into orbit around the Earth. ... that incrementally hollow their way into the body of such an asteroid. ... The material excavated out of the body would create a thin ring system ... *theoretically* that such ring particles would indeed be stable in ...
    (sci.math.num-analysis)
  • Re: Dynamic stability of an Earth Ring
    ... > particles being gravitationally influenced by the Earth and the Moon ... I hereby report that a ring system that is not oriented along the ... from a non-circular orbit of an asteroid, will scatter its particles ... equatorial plane has a very short term ...
    (sci.physics.research)