Single Close Encounters Do Not Make Eccentric Planetary Orbits

The recent discovery of a planet in an orbit with eccentricity $e = 0.63 \pm0.08$ around the Solar-type star 16 Cyg B, together with earlier discoveries ofother planets in orbits of significant eccentricity, raises the question of theorigin of these orbits, so unlike the nearly circular orbits of our Solarsystem. In this paper I consider close encounters between two planets, eachinitially in a nearly circular orbit (but with sufficient eccentricity topermit the encounter). Such encounters are described by a two-bodyapproximation, in which the effect of the attracting star is neglected, and bythe approximation that their separation vector follows a nearly parabolic path.A single encounter cannot produce the present state of these systems, in whichone planet is in an eccentric orbit and the other has apparently been lost.Even if the requirement that the second planet be lost is dropped, nearlycircular orbits cannot scatter into eccentric ones.Comment: 9 pp., 1 figure, te