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Date: Wed, 18 Jun 1997 11:01:14 -0500

To: "Anthony C. Zuppero" , zuppero@srv.net, zca@inel.gov

From: "John J. Matese"

Subject: Re: comet hole, lunar ice rocket

Cc: pgwhitman@usl.edu

Hello Tony,

I found a few hours to think about your comet hole problem. As I understand it, the question essentially can be phrased as

"Is the hole due to (1)dynamics unrelated to the inner planets, (2)disappearance due to devolitization or breakup, (3)dynamics related to the inner planets?"

Of the three options listed my gut feeling is that they rank in importance in that order, with all contributing to some extent. Brian Marsden's comments might in part be paraphrased in the following way.

Jupiter family SP comets are often discussed in terms of their Tisserand parameter, essentially the Jacobi constant of a restricted three body problem. Scaling distances to Jupiter's semimajor axis, a comet of semimajor axis a(scaled), eccentricity e, inclination i has a Tisserand parameter

T = 1/a +2 sqrt[a(1-e^2)] cosine(i)

One can show that if T>3 Jupiter crossing is impossible. Most comets have 2.5 An illustration: a comet transfered from Saturn (Q ~ 2) to Jupiter (q ~ 1) with i ~ 0 has T = 2.976 and, within the approximation that T is strictly conserved, the minimum q that can ever be obtained would be .56 ~ 2.9AU.

So, in this view, the clustering of T near 3 (which causes a deficiency of comets with small q) could be due to the dynamical mechanism by which JF comets are assumed to be produced - from the Kuiper belt via transfer between the giant planets.

Of course one must always keep an open mind that the reverse could be true, i.e., mechanisms (2) and (3) above create a deficiency of small q JF comets -> T clustering near 3 -> we are fooled into thinking that the Kuiper belt is the source. That is very ad hoc and would be difficult to defend.

I hope this helps.

Best regards

 John J. Matese                Professor of Physics
 matese@usl.edu                The University of Southwestern Louisiana
                               Lafayette, Louisiana  (USA)