Brian Marsden, Smithsonian Observatory

Date: Mon, 02 Jun 1997 15:29:56 MST
From: Brian Marsden, Smithsonian Astrophysics Observatory
Reply-To: brian%cfaps1.span@noao.edu
To: zuppero@srv.net

On the general shape of the distribution

It seems to me that the effect is partly dynamics, partly selection. The bulk of the comets are Jupiter-family, with their aphelia near Jupiter, where they spend most of the time. Hence the peak there. Inside Jupiter's orbit the distribution should steadily drop, for this is simply a sign of increasing eccentricity, higher eccentricities being progressively less probable than nearly circular orbits. But low-eccentricity orbits with aphelia near Jupiter have perihelion distances that are quite large, so the comets are always faint and not so likely to be discovered. So the reduction is too precipitious, in reality, as one comes in from 5 to, say, 2.5 AU. At lower perihelion distances than this, comets are more likely to be discovered. However, as the perihelion distance decreases below 1.5 AU the eccentricity increases to more improbable levels. At their aphelia, high-eccentriciity orbits would be less well matched to Jupiter's velocity, so they are not so likely to be produced from an origin in the Jupiter-Saturn- and-out-to-the-Kuiper Belt region. As the perihelion distance diminishes toward 1 AU and less there are also further problems, again partly physical, partly selection: physical from the disintegration of the objects from ice vaporization near the sun, selection because of the reduced opportunities to observe a faint comet near perihelion at 1 AU and less.

So I would say your distribution is essentially what I would expect.

on the abruptness at Mars orbit

Date: Tue, 03 Jun 1997 07:03:01 MST

Perhaps, indeed, the "abruptness" at 1.5 AU is intriguing. Water-ice vaporization tends to set in closer to 2.5-3.0 AU, however, something that is more likely to be involved in explaining the recovery in this range from the dip in the distribution at 3-4 AU. I don't know that the 1.5 AU is related to Mars. On the other hand, I don't know that anyone has really considered whether Mars (or the earth, for that matter) has some special influence on the distribution of the short-period comets. I think my qualitative analysis yesterday has some significance, but maybe some other dynamical effect sharpens the details.

Regards

Brian G. Marsden