Re: Stable Orbit Formulae?

Greg Neill wrote:
"Timothy Partee" <tpartee@xxxxxxxxxxxxx> wrote in message
news:c7WdnY4sp7RM8uDanZ2dnUVZ_ramnZ2d@xxxxxxxxxxxxxxxx

Given two (planetesimal) orbital bodies whose Mass << Stellar Body,
what is the minimum permissible distance between the two bodies such
that they will not disrupt one another's orbital parameters?

There will always be perturbations due to mutual
interactions causing changes to the orbital
parameters. Whether or not these perturbations
can lead to disruptive changes (collisions or
ejections) can be difficult to determine because
it can depend upon resonances in the periods of
the bodies which can amplify, damp, or induce
cyclical changes.

You might want to try a search on orbital resonances
and peruse the topic.


Hmmm, interesting. However, it would seem that our own solar system's planets have a negligible effect upon each other in their (nearly) concentric orbits around Sol. There must be a threshold of distance/mass (Gravitational Force) at which effects of one orbital body become negligible to the other. In stellar formation modeling this equation, threshold, formula or what-have-you must exist and be defined somewhere, somehow. And considering that orbital velocity/period is a function of the difference of mass between the orbital body and it's stellar focus that is entirely predictable, unless there was a very specific orbital resonance between two randomly-defined bodies they would have negligible effect upon one another. In other words, I would think that vast majority of random incidence of two bodies placed in orbit around the same gravitational focal point with a sufficient distance from one another would not cause interference with each other's orbital parameters with regards to resonance. But resonance may indeed play a role in the "reasonal safe distance" between two objects...

I'm just looking for a general and believable "magic number" that says "orbital bodies A and B's semi-major axii should be at least X km distant from one another given A, B and stellar masses and assuming a perfectly circular, flat, non-eccentric orbits". To explain the problem better, I'm working on a simulation model where a galactic or semi-galactic body (galaxy, globular cluster, etc.) is populated with stars in random positions with probabilities for density accounted for using Gaussian algorithms and "minimum safe distance" maintained by measuring "F" at a reasonably low number. Stellar classes are only calculated right now based on the class probabilities given in the Main Sequence tables, which determines the star's radius, temperature and mass, as well as the upper and lower limit of planetary objects available to it. I'm at the point where when I generate a planetary object, I'm needing to verify that a new object being added to the stellar system is far enough away from existing objects to be clear of having an effect on their orbital parameters and vice-versa. This of course is assuming accretion disc development of planetary entities, and not including acquired or Kuiper objects.
Clearly there is a formula for this somewhere, since in our own system we can see that the asteroid belt is for the most part clear of the area of influence for Mars and Jupiter... Once again, the question is "where is object A (in a stable, perfect orbit) safe from object B's (also in a stable, perfect orbit) influence". And yes, I'm familiar with "Trojans and Greeks" in the case of Jupiter, but those were likely picked-up and gravitated toward L-points after Jupiter "cleared it's neighborhood" due to ejection caused by collisions with other belt objects or even foreign objects from the Kuiper belt...

It may be possible to achieve a reasonable "guesstimate" by assuming a non-orbital scenario taking the difference in semi-major axis between the two objects as the distance "r" in the gravitational force equation F = G((m1*m2)/r^2) where F is a reasonably low number, but that may be hugely ignorant on my part of some peculiarity of orbital physics... Which is the whole reason I'm asking the question here. =)

- Timothy Partee
.

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