Talk:Space Manifold dynamics

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    This note is very well written, and it summarizes in few pages a huge amount of work that has been done in the field of Space Manifold Dynamics.

    I have only few minor comment which I list below.

    1. In the "Introduction" (second line), I have changed the word "Hohmann" into "patched-conics" because I think this is the most general case. Apollo, Voyager, etc. have been designed using patched-conics, and they are not -strictly speaking - Hohmann transfers. (An Hohmann transfer to the Moon takes about 5 days, the Apollo transfer was 3 days long).

    2. I think that the average reader is not familiar with the dynamical system nomenclature of 'center' and 'saddle' type of equilibrium. I suggest to insert a reference to a standard book of dynamical system theory (e.g., Wiggins) the first time these words are introduced (in 'The phase space around the collinear equilibrium points ...' section).

    3. Please review grammar of this sentence: "At L1 the two bounded components joint and after it appears, there is a bottleneck that connects the regions around both primaries".

    4. I think that when the halo orbit is mentioned for the first time, it is necessary to reference a sample work by R. Farquhar of late '60s (as far as I know, he is the inventor of the word 'halo' orbit, therefore he deserves a citation).

    5. In the section 'Transfers to libration point orbits' it would be desirable (at the end of the section) to mention what happens in the Earth--Moon frame where there is no intersection. I know the case of empty intersection (between stable manifold and departure orbit) is mentioned, but I think it is interesting explicitly saying that this happens when going to the L1 and L2 halo orbits of the Earth--Moon system.

    6. In the section 'Transfers in a 4-body problem' I would mention also application to interplanetary transfers (between outer planets), moon-to-moon transfers (about a giant planet), and also interplanetary transfers between inner planets (where there is, again, no intersection).

    7. There are recent works that combine stable/unstable manifolds with low-thrust propulsion. In these works the "Shoot the Moon" concept is reviewed under the perspective of low-thrust, as well as the strategy to transfers to equilibrium point orbits when the stable manifold does not intersect the departure orbit (for instance see G. Mingotti, F. Topputo, and F. Bernelli-Zazzera, “Low-Energy, Low-Thrust Transfers to the Moon”, Celestial Mechanics and Dynamical Astronomy, Vol. 105, pp. 61-74, 2009). Few words on these applications may be spent in the section 'Other applications' or 'Further applications'.

    In accordance with the mixed-mode review, I have corrected few typos directly in the text.

    Best regards.


    We thank the referee for all the comments and suggestions. We have included all of them. The particular responses to each question are:

    1.- We agree.

    2.- A reference has been added.

    3.- The sentence has been rewritten.

    4.- A reference of R.W.Farquhar has been added.

    5.- A paragraph and a reference has been added.

    6.- Two examples of missions have been added.

    7.- The idea and works exposed by the referee have been included in a paragraph at the end of the section.

    In addition to the comments of the referee, we have added two comments/paragraphs:

    • at the end of the Section Transfers to libration points, two figures and a comment have been added in order to illustrate another usage of the invariant manifolds via the heteroclinic connections
    • at the end of the Station Keeping Section we have added a sentence explaining the differences between SOHO and ISEE3.

    Best regards,

    Gerard Gómez and Esther Barrabés


    This is an excellent article that succinctly introduces the main ideas behind 'space manifold dynamics', the techniques used to implement them, and major applications. The article is very well written, but I did notice that both the UK and American spellings are used for some words ('centre' and 'center', 'manoeuvre' and 'maneuver'). I have no objection to this, but the authors may wish to stick to just one version!

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