Talk:Three body problem

Level

This beautiful article would win if some terms were explicited.

If not, it will be an excellent resume between "connoisseurs".

May be, some extensions by annexed notes would give more audience : of course, it is depending mainly of the policy of Scholarpedia : is it for researchers or scholars ?

In any case , warm cheers for this new sort of "Pedia".

--Guerinsylvie 13:59, 25 August 2007 (EDT)

Reviewer B

Nice and complete "video clip" on the three-body problem, including most of the actual questions related to the problem and many historical remarks, with special emphasis on the huge french contributions to the problem.

The article will not be easy for the novel reader, in the same way that the excellent paper by A. Albouy - to which the reader is referred - is not (in my opinion) the best way to get a first idea about the two body problem. (I don't know if there is a Scholarpedia article about the Two Body Problem.)

In the section devoted to final motions, there is a reference to the work of E. Belbruno, in relation with the use of invariant manifolds for space mission design. I think that this has never been the approach used by Belbruno for the determination the so called "weak stability boundaries" which is something that, even in [Be], is not well defined. The low energy transfer trajectory used for the Hiten mission was computed by J. Miller and E. Belbruno using a "trial and error" method, close to the numerical definition given in [Be] for the WSB.

The references related to the questions addressed in the article, have been carefully selected. I should add to the list "D. Boccaletti and G. Pucacco: Theory of Orbits, Springer 2001" in which the reader will find (in just two volumes) the details of many of the topics included the article.

Answer from the author to Reviewer B

Thank you for your comments. To have produced at least once in my life a "video clip" makes me feel good !

I certainly agree that Albouy's paper, while very beautiful, is not the easiest introduction to the two-body problem. I added a very elementary reference to Wikipedia (which displays a nice animation) and referred also to [AKN] and [BP] (which I just added, following your suggestion). I refrained from adding reference to Goldstein and Arnold's books on mechanics, which are referred to in [AKN].

About Belbruno's reference, I would be grateful if you could propose a modification of my sentence

Answer from Reviewer B to author

Of the sentence "Closer to mission design, heteroclinic solutions in the restricted problem have been used to save fuel (and even a vessel: E. Belbruno, see [Be]) by C. Simó and cooauthors (see [Si]), W.S. Koon, M.W. Lo, J.E. Marsden and S.D. Ross (see [CelMech]),..." I should just remove the reference to Belbruno, and rewrite it as "Closer to mission design, heteroclinic solutions in the restricted problem have been used to save fuel by C. Simó and cooauthors (see [Si]), W.S. Koon, M.W. Lo, J.E. Marsden and S.D. Ross (see [CelMech]),..."

The kind of low energy transfers computed by Belbruno and Miller (using what is usually called "weak stability boundaries") correspond to motions not in a three-body problem, but in a four-body problem (Sun-Earth-Moon-spacecraft). These transfer orbits are close to some kind of heteroclinic connections between the invariant manifold structure of the Earth-Sun libration points with the invariant manifold structure of the Earth-Moon libration points (the boundary of the region of interaction should be the weak stability boundary) Nevertheless, this is not the approach used by Belbruno et al. (they use a non clear trial and error numerical procedure) but the one which is described by W.S. Koon, M.W. Lo, J.E. Marsden, and S.D. Ross in "Low Energy Transfer to the Moon" Celestial Mechanics and Dynamical Astronomy, 81, 63-73, 2001.

Answer from author to Reviewer B

I shall enter the modification and accept it.