Re: 3 Planet Anomaly
- From: "AustinMN" <tacooper260@xxxxxxxxxxx>
- Date: 15 Feb 2007 13:31:09 -0800
On Feb 15, 2:40 am, "Martin Brown" <|||newspam...@xxxxxxxxxxxxxxxxxx>
wrote:
On Feb 14, 11:26 pm, Chris L Peterson <c...@xxxxxxxxxxxxxxxxxx> wrote:
On Wed, 14 Feb 2007 18:21:37 -0500, giannoni
<casagiann...@xxxxxxxxxxxxx> wrote:
If 3 planets of equal mass are positioned at rest in space, and
allowed to interact, then interesting transient behavior will follow
for a time, BUT eventually 2 of the 3 will will impart a combined
"escape velocity" to the 3rd. The 2 then orbit each other and drift
appart from the 3rd to infinity.
What if the three are equidistant (form the vertices of an equilateral
triangle), or if the three are collinear (equally spaced or otherwise)?
With the restriction of initially at rest this will not work they
would sit at the corners of a shrinking equilateral triangle until
they got really close together and then spontaneous symmetry breaking
would catapult one out.
The OP said "at rest" not "in orbit around a common point." I would
expect them to fall toward the center of gravity until they collided.
Of course, if there's just a slight offset somewhere, then one would
end up being forcibly ejected from the system.
However, I reckon you can break this claim as stated by placing two of
the planets adjacent to each other at the start of the experiment so
that they will merge to form a single body of mass 2M well before the
third planet which is started from a long way off arrives. You then
have a two body problem and a planet mass M in a very eccentric orbit.
ISTR that if you are allowed to set it up one body weakly bound
orbitting a long way out from two bodies in a tightly bound circular
orbit can be made effectively stable for all practical purposes.
That's what I would expect as well, as long as the more distant body
was far enough that the two more massive bodies appeared
(gravitationally) more-or-less equivalent to a single body of the same
total mass.
I believe the opposite is also possible; you can have a single small
body orbiting very close to one of two large bodies that are orbiting
very far apart. All of the stable orbit moons of the solar system
could be taken as examples of this.
Austin
.
- References:
- 3 Planet Anomaly
- From: giannoni
- Re: 3 Planet Anomaly
- From: Chris L Peterson
- Re: 3 Planet Anomaly
- From: Martin Brown
- 3 Planet Anomaly
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