Re: John Norman and other versions of 'Counter-Earth' plot trophe
- From: Stewart Robert Hinsley <{$news$}@meden.demon.co.uk>
- Date: Tue, 26 Jul 2005 23:29:33 +0100
In message <1122415299.25e54389983bd10f0a0c2d2c86ad686f@teranews>, Louann Miller <louann_m@xxxxxxxxx> writes
It's unstable. Consider a highly simplified system consisting of one star and two identical planets 180 degrees apart in the same circular orbit.Not asking about his knowledge of anatomy or psychology, but the basic idea of an Earthlike planet on the opposite side of our orbit.
Is there anything in orbital mechanics that would make this configuration impossible? Alternately, is there anything in orbital mechanics (similar to the Lagrange points) that would make this configuration likely, however slight the advantage?
Acceleration can be divided into radial and tangential components (in the coordinate frame of the center of mass aka the star). As above, the acceleration of the planets is purely radial.
Now let one of the planets be perturbed slightly ahead of its proper position. Now there is a tangential component to the acceleration of the planets. The planet which is slightly ahead is accelerated in the direction of its orbit, thus increasing its orbital velocity and radius. The other planet is accelerated against the direction of its orbit, thus decreasing its orbital velocity and radius. The deviation from the initial situation grows exponentially [1].
If this is possible, what about higher numbers of objects in the same orbit? Would they have to be evenly spaced?
If not evenly spaced (assuming equal masses) the situation isn't stable even in the absence of perturbations, because the tangential accelerations don't balance.
[1] Treat this usage as metaphorical. I don't know whether the actual growth is exponential, polynomial or something else, tho' I suspect exponential.
Would we, in fact, not be able to see a counter-earth? Yes, I know, elliptical orbit but I have the impression the ellipse is not that far off a circle.
Should my vague memory of the phrase "Kemplerer Rosette" from "Ringworld" be helping me out here?
--
Stewart Robert Hinsley
.
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