In article 02,
John Schutkeker wrote:

(Paul Schlyter) wrote in :

Another hypothetical case: if gravity would have varied as the inverse
*fifth* power of the distance, all orbits would have been spirals.

Are the orbits stable if gravity varies as the inverse 4th or 6th power of
the distance?

No.

If gravity varies as r^(-n) then circular orbits are stable only if n 3

For other shapes of the orbits the stability criterion get much more complex.
Even under normal r^(-2) gravity a very elongated elliptical orbit with
an eccentricity sufficiently close to one is unstable, since it can easily
be perturbed into a parabolic or hyperbolic orbit.

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Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
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