@software{pyodide,
  author       = {Michael Droettboom and
                  Roman Yurchak and
                  Hood Chatham and
                  Dexter Chua and
                  Marc Abramowitz and
                  casatir and
                  Jason Stafford and
                  Madhur Tandon and
                  Will Lachance and
                  Jan Max Meyer and
                  Michael Greminger and
                  Chris Trevino and
                  Joe Marshall and
                  Adam Seering and
                  Nicolas Ollinger and
                  Ondřej Staněk and
                  Sergio and
                  Teon L Brooks and
                  Wei Ouyang and
                  Jay Harris and
                  chigozienri},
  title        = {pyodide/pyodide:},
  month        = aug,
  year         = 2021,
  publisher    = {Zenodo},
  version      = {0.18.0},
  doi          = {10.5281/zenodo.5156931},
  url          = {https://doi.org/10.5281/zenodo.5156931}
}

@software{ReboundZenodo2025,
  author       = {{Rein}, H. and
      {Tamayo}, D. and
      {Liu}, S.-F. and
      {Winkler}, L. and
      {Bartram}, P. and
      {Silburt}, A. and
      {Brown}, G. and
      {Baronett}, S. A.  and
      {Lu}, T. and
                  Robert Melikyan and
                  Rosemary Dorsey and
                  Luke Wriglesworth and
                  Dave Spiegel and
                  Steven Rieder and
                  Francesco Biscani and
                  Albert Zhang and
                  Dang Pham and
                  Thomas Rometsch and
                  katvolk and
                  Jose Antonio Castro and
                  Kyle Conroy and
                  Meldonization and
                  Rejean LeBlanc and
                  Ruth-Huang6012 and
                  Ryan Janish and
                  Sam Hadden and
                  dongsubo and
                  Uilian Ries and
                  Daniel Kastinen},
  title        = {hannorein/rebound: 4.4.10},
  month        = jul,
  year         = 2025,
  publisher    = {Zenodo},
  version      = {4.4.10},
  doi          = {10.5281/zenodo.15784767},
  url          = {https://doi.org/10.5281/zenodo.15784767},
  swhid        = {swh:1:dir:f5d07a50017aa1de0c2db27cbbb646e872002525
                   ;origin=https://doi.org/10.5281/zenodo.7808755;vis
                   it=swh:1:snp:e74f9be830de1dfa0a7ebc9199a6d4f159365
                   efb;anchor=swh:1:rel:0c30df97535cf044b381fcc96be39
                   e2cff8e6c49;path=hannorein-rebound-3a1cbcb
                  },
}

@ARTICLE{Williams2022,
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}


@article{KaplanMeier1958,
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@Misc{Williams2013,
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@ARTICLE{BrownRein2023,
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}


@ARTICLE{Krauss2003,
author = {{Krauss}, Lawrence M. and {Chaboyer}, Brian},
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adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{Batygin2019,
archivePrefix = {arXiv},
arxivId = {1902.10103v1},
author = {Batygin, Konstantin and Adams, Fred C. and Brown, Michael E. and Becker, Juliette C.},
doi = {10.1016/j.physrep.2019.01.009},
eprint = {1902.10103v1},
issn = {03701573},
journal = {Physics Reports},
month = {may},
pages = {1--53},
title = {{The planet nine hypothesis}},
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@ARTICLE{2020RNAAS...4..221B,
       author = {{Brown}, Garett and {Rein}, Hanno},
        title = "{A Repository of Vanilla Long-term Integrations of the Solar System}",
      journal = {Research Notes of the American Astronomical Society},
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}

@ARTICLE{BrownRein2022,
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}

@ARTICLE{Salpeter1955,
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@ARTICLE{Abbot2022,
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}



@ARTICLE{2021arXiv210514976M,
       author = {{Mogavero}, Federico and {Laskar}, Jacques},
        title = "{Long-term dynamics of the solar system inner planets}",
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}

@ARTICLE{Grimm2022,
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}



@ARTICLE{Mogavero2021,
       author = {{Mogavero}, Federico and {Laskar}, Jacques},
        title = "{Long-term dynamics of the inner planets in the Solar System}",
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archivePrefix = {arXiv},
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}

@ARTICLE{Mogavero2022,
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}


@ARTICLE{Zeebe2015,
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@ARTICLE{2012arXiv1209.5996L,
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@article{Laskar2000,
author = {Laskar, Jacques},
doi = {10.1103/PhysRevLett.84.3240},
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number = {15},
pages = {3240--3243},
pmid = {11019060},
title = {{On the Spacing of Planetary Systems}},
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year = {2000}
}

@article{Zakamska2004,
author = {Zakamska, Nadia L. and Tremaine, Scott},
doi = {10.1086/422023},
issn = {0004-6256},
journal = {The Astronomical Journal},
keywords = {formation,general,planetary systems,planets and satellites},
month = {aug},
number = {2},
pages = {869--877},
title = {{Excitation and Propagation of Eccentricity Disturbances in Planetary Systems}},
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year = {2004}
}

@article{Nascimbeni2012,
author = {Nascimbeni, V. and Bedin, L. R. and Piotto, G. and {De Marchi}, F. and Rich, R. M.},
doi = {10.1051/0004-6361/201118655},
issn = {00046361},
journal = {Astronomy and Astrophysics},
keywords = {Globular clusters: individual: NGC 6397,Planetary systems,Techniques: photometric},
pages = {1--10},
title = {{An HST search for planets in the lower main sequence of the globular cluster NGC 6397}},
volume = {541},
year = {2012}
}

@article{Spurzem2009,
archivePrefix = {arXiv},
arxivId = {astro-ph/0612757},
author = {Spurzem, R. and Giersz, M. and Heggie, D. C. and Lin, D. N.C.},
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eprint = {0612757},
issn = {15384357},
journal = {Astrophysical Journal},
keywords = {Globular clusters: general,Planetary systems,Solar system: formation},
number = {1},
pages = {458--482},
primaryClass = {astro-ph},
title = {{Dynamics of planetary systems in star clusters}},
volume = {697},
year = {2009}
}

@article{Dotti2019,
archivePrefix = {arXiv},
arxivId = {1908.07747},
author = {Dotti, Francesco Flammini and Kouwenhoven, M. B.N. and Cai, Maxwell Xu and Spurzem, Rainer},
doi = {10.1093/mnras/stz2346},
eprint = {1908.07747},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Galaxy: Stellar content,Planetary systems,Stars: Solar-type,Stars: Statistics},
number = {2},
pages = {2280--2297},
publisher = {Oxford University Press},
title = {{Planetary systems in a star cluster I: The Solar system scenario}},
volume = {489},
year = {2019}
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@article{Zheng2015,
archivePrefix = {arXiv},
arxivId = {1508.01593},
author = {Zheng, Xiaochen and Kouwenhoven, M. B.N. and Wang, Long},
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eprint = {1508.01593},
issn = {13652966},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Methods: numerical,Open clusters and associations: general,Planetary systems,Planets and satellites: dynamical evolution and stability,Solar neighbourhood,Stars: kinematics and dynamics},
number = {3},
pages = {2759--2770},
title = {{The dynamical fate of planetary systems in young star clusters}},
volume = {453},
year = {2015}
}


@article{Bovy2017,
archivePrefix = {arXiv},
arxivId = {1704.05063},
author = {Bovy, Jo},
doi = {10.1093/mnras/stx1277},
eprint = {1704.05063},
issn = {0035-8711},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Galaxy: disc,Galaxy: fundamental parameters,Galaxy: stellar content,Galaxy: structure,Solar neighbourhood,Stars: statistics},
month = {sep},
number = {2},
pages = {1360--1387},
title = {{Stellar inventory of the solar neighbourhood using Gaia DR1}},
url = {https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/stx1277},
volume = {470},
year = {2017}
}


@article{Laughlin2000,
author = {Laughlin, Gregory and Adams, Fred C.},
doi = {10.1006/icar.2000.6355},
issn = {00191035},
journal = {Icarus},
keywords = {Stars and planetary systems,Stellar dynamics},
number = {2},
pages = {614--627},
title = {{The Frozen Earth: Binary Scattering Events and the Fate of the Solar System}},
volume = {145},
year = {2000}
}

@article{Malmberg2007a,
archivePrefix = {arXiv},
arxivId = {astro-ph/0702524},
author = {Malmberg, Daniel and {De Angeli}, Francesca and Davies, Melvyn B. and Church, Ross P. and Mackey, Dougal and Wilkinson, Mark I.},
doi = {10.1111/j.1365-2966.2007.11885.x},
eprint = {0702524},
issn = {0035-8711},
journal = {Monthly Notices of the Royal Astronomical Society},
keywords = {Binaries: general,Celestial mechanics,Open clusters and associations: general,Planetary systems,Stellar dynamics},
month = {jul},
number = {3},
pages = {1207--1216},
primaryClass = {astro-ph},
title = {{Close encounters in young stellar clusters: implications for planetary systems in the solar neighbourhood}},
url = {https://academic.oup.com/mnras/article-lookup/doi/10.1111/j.1365-2966.2007.11885.x},
volume = {378},
year = {2007}
}

@ARTICLE{2012A&A...548A..43B,
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        title = "{A simple model of the chaotic eccentricity of Mercury}",
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         year = 2012,
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archivePrefix = {arXiv},
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 primaryClass = {astro-ph.EP},
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      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{Laskar1997,
author = {Laskar, Jacques},
journal = {Astronomy and Astrophysics},
keywords = {Solar system: formation,celestial mechanics,chaotic phenomena,diffusion,instabilities,planet formation},
pages = {75--78},
title = {{Large scale chaos and the spacing of the inner planets.}},
volume = {317},
year = {1997}
}


@article{Laskar1992,
author = {Laskar, Jacques and Quinn, Thomas and Tremaine, Scott},
doi = {10.1016/0019-1035(92)90196-E},
issn = {10902643},
journal = {Icarus},
keywords = {secular},
mendeley-tags = {secular},
number = {1},
pages = {148--152},
title = {{Confirmation of resonant structure in the solar system}},
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archivePrefix = {arXiv},
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pages = {8},
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url = {https://www.aanda.org/10.1051/0004-6361/201832905},
volume = {616},
year = {2018}
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@article{Valenti2016,
archivePrefix = {arXiv},
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keywords = {Galaxy: bulge,Galaxy: structure},
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pages = {L6},
title = {{Stellar density profile and mass of the Milky Way bulge from VVV data}},
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@ARTICLE{SyerTremaine1995,
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archivePrefix = {arXiv},
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eprint = {2005.00026},
issn = {0035-8711},
journal = {Monthly Notices of the Royal Astronomical Society},
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title = {{8 in 10 Stars in the Milky Way Bulge Experience Stellar Encounters Within 1000 AU in a Gigayear}},
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year = {2020}
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@article{PortegiesZwart2015,
archivePrefix = {arXiv},
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@article{Chabrier2003,
archivePrefix = {arXiv},
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@article{Mann2019,
archivePrefix = {arXiv},
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publisher = {IOP Publishing},
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@article{Bailer-Jones2018,
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year = {2018}
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@ARTICLE{Adams2010,
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@ARTICLE{PfalznerVincke2020,
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@ARTICLE{Hernandez2022,
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}



@article{Hernandez2020,
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@article{Batygin2008,
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@article{Cai2017,
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@ARTICLE{Zink2020,
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@inproceedings{Ponce2019,
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@misc{gnuparallel,
      author       = {Tange, Ole},
      title        = {GNU Parallel 20221022 (`Nord Stream')},
      month        = Oct,
      year         = 2022,
      note         = {{GNU Parallel is a general parallelizer to run multiple serial command line programs in parallel without changing them.}},
      publisher    = {Zenodo},
      doi          = {10.5281/zenodo.7239559},
      url          = {https://doi.org/10.5281/zenodo.7239559}
}

@article{Tamayo2020,
archivePrefix = {arXiv},
arxivId = {1908.05634},
author = {Tamayo, Daniel and Rein, Hanno and Shi, Pengshuai and Hernandez, David M.},
doi = {10.1093/mnras/stz2870},
eprint = {1908.05634},
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keywords = {Gravitation,Methods: numerical,Planets and satellites: dynamical evolution and stability},
month = {jan},
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pages = {2885--2901},
publisher = {Oxford University Press},
title = {{REBOUNDx: a library for adding conservative and dissipative forces to otherwise symplectic N-body integrations}},
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@ARTICLE{ReinTamayoBrown2019,
archivePrefix = {arXiv},
arxivId = {1907.11335},
author = {Rein, Hanno and Tamayo, Daniel and Brown, Garett},
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@article{ReinBrownTamayo2019,
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@ARTICLE{Abbot2023,
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}


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@ARTICLE{Zeipel1910,
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@ARTICLE{Wisdom2018,
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@article{januszenodo2017, 
    title={Bit-wise reversible integrations of the Solar System with JANUS}, 
    DOI={10.5281/zenodo.546258}, 
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    abstractNote={<p>This dataset contains 24 integrations of the Solar System. The integrator is JANUS, a bit-wise reversible algorithm that uses a mix of integer and floating-point arithmetic. The files are Simulation Archives, which can be opened with the REBOUND code.  </p>}, 
    publisher={Zenodo}, 
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	Author = {{Rein}, H. and {Tamayo}, D.},
    year={2017}, month={Apr}}


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@misc{matplotlib2,
author       = {Michael Droettboom and
John Hunter and
Thomas A Caswell and
Eric Firing and
Jens Hedegaard Nielsen and
Phil Elson and
Benjamin Root and
Darren Dale and
Jae-Joon Lee and
Jouni K. Seppänen and
Damon McDougall and
Andrew Straw and
Ryan May and
Nelle Varoquaux and
Tony S Yu and
Eric Ma and
Charlie Moad and
Steven Silvester and
Christoph Gohlke and
Peter Würtz and
Thomas Hisch and
Federico Ariza and
Cimarron and
Ian Thomas and
James Evans and
Paul Ivanov and
Jeff Whitaker and
Paul Hobson and
mdehoon and
Matt Giuca},
title        = {matplotlib: matplotlib v1.5.1},
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@Article{matplotlib,
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Pages     = {90--95},
abstract  = {Matplotlib is a 2D graphics package used for Python
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publisher = {IEEE COMPUTER SOC},
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@ARTICLE{Laskar1989,
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    title = "{A numerical experiment on the chaotic behaviour of the solar system}",
  journal = {\nat},
 keywords = {Chaos, Planetary Evolution, Solar System, Laplace Equation, Liapunov Functions, SOLAR SYSTEM, NUMERICAL METHODS, STABILITY, PLANETS, COMPUTER METHODS, ORBITS, PARAMETERS, MASS, ECCENTRICITY, INCLINATION, TIME SCALE, MOTION, CELESTIAL MECHANICS, TERRESTRIAL PLANETS, PERTURBATIONS, RESONANCE},
     year = 1989,
    month = mar,
   volume = 338,
    pages = {237},
      doi = {10.1038/338237a0},
   adsurl = {http://adsabs.harvard.edu/abs/1989Natur.338..237L},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{EvansTremaine1999,
   author = {{Evans}, N.~W. and {Tremaine}, S.},
    title = "{Linear Multistep Methods for Integrating Reversible Differential Equations}",
  journal = {\aj},
   eprint = {astro-ph/9906376},
 keywords = {CELESTIAL MECHANICS, STELLAR DYNAMICS, METHODS: NUMERICAL},
     year = 1999,
    month = oct,
   volume = 118,
    pages = {1888-1899},
      doi = {10.1086/301057},
   adsurl = {http://adsabs.harvard.edu/abs/1999AJ....118.1888E},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{Landauer1961,
  title={Irreversibility and heat generation in the computing process},
  author={Landauer, Rolf},
  journal={IBM journal of research and development},
  volume={5},
  number={3},
  pages={183--191},
  year={1961},
  publisher={IBM}
}

@article{Pihajoki2015,
  title={Explicit methods in extended phase space for inseparable Hamiltonian problems},
  author={Pihajoki, Pauli},
  journal={Celestial Mechanics and Dynamical Astronomy},
  volume={121},
  number={3},
  pages={211--231},
  year={2015},
  publisher={Springer}
}


@article{Kahan1997,
  title={Composition constants for raising the orders of unconventional schemes for ordinary differential equations},
  author={Kahan, William and Li, Ren-Cang},
  journal={Mathematics of Computation of the American Mathematical Society},
  volume={66},
  number={219},
  pages={1089--1099},
  year={1997}
}

@book{Hairer2006,
  title={Geometric numerical integration: structure-preserving algorithms for ordinary differential equations},
  author={Hairer, Ernst and Lubich, Christian and Wanner, Gerhard},
  volume={31},
  year={2006},
  publisher={Springer Science \& Business Media}
}

@Article{LevesqueVerlet1993,
    author="Levesque, D.
    and Verlet, L.",
    title="Molecular dynamics and time reversibility",
    journal="Journal of Statistical Physics",
    year="1993",
    volume="72",
    number="3",
    pages="519--537",
    abstract="We present a time-symmetrical integer arithmetic algorithm for numerical (molecular dynamics) simulations of classical fluids. This algorithm is used to illustrate, through concrete examples, that time-asymmetric evolutions are typical for systems of many particles evolving according to reversible microscopic dynamics and to calculate the asymptotic behavior of the velocity autocorrelation function with an improved accuracy. The equivalence between equilibrium time averages and microcanonical ensemble averages is checked via two new sampling methods for computing microcanonical averages of classical systems.",
    issn="1572-9613",
    doi="10.1007/BF01048022",
    url="http://dx.doi.org/10.1007/BF01048022"
}
@Book{Kendall1994,
 author = {Kendall, Maurice},
 title = {Kendall's advanced theory of statistics},
 publisher = {Edward Arnold Halsted Press},
 year = {1994},
 address = {London New York},
 isbn = {0340807520}
 }
@ARTICLE{Caratheodory1919,
    author = {{Caratheodory}, {C}},
    title = "{Über den Wiederkehrsatz von Poincaré}",
        journal = {Preuss. Akad. Wiss.},
    volume = 34,
    year = 1919,
   pages =  {580-584},
}

@ARTICLE{Cai2015,
   author = {{Cai}, M.~X. and {Meiron}, Y. and {Kouwenhoven}, M.~B.~N. and 
	{Assmann}, P. and {Spurzem}, R.},
    title = "{Block Time Step Storage Scheme for Astrophysical N-body Simulations}",
  journal = {\apjs},
archivePrefix = "arXiv",
   eprint = {1506.07591},
 primaryClass = "astro-ph.IM",
 keywords = {globular clusters: general, methods: data analysis, methods: numerical, virtual observatory tools},
     year = 2015,
    month = aug,
   volume = 219,
      eid = {31},
    pages = {31},
      doi = {10.1088/0067-0049/219/2/31},
   adsurl = {http://adsabs.harvard.edu/abs/2015ApJS..219...31C},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{Rein2019,
   author = {{Rein}, H. and {Hernandez}, D.~M. and {Tamayo}, D. and {Brown}, G. and 
	{Eckels}, E. and {Holmes}, E. and {Lau}, M. and {Leblanc}, R. and 
	{Silburt}, A.},
    title = "{Hybrid symplectic integrators for planetary dynamics}",
  journal = {Monthly Notices of the Royal Astronomical Society},
archivePrefix = "arXiv",
   eprint = {1903.04972},
 primaryClass = "astro-ph.EP",
 keywords = {gravitation, methods: numerical, planets and satellites: dynamical evolution and stability},
     year = 2019,
    month = jun,
   volume = 485,
    pages = {5490-5497},
      doi = {10.1093/mnras/stz769},
   adsurl = {https://ui.adsabs.harvard.edu/abs/2019MNRAS.485.5490R},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Hernandez2016,
   author = {{Hernandez}, D.~M.},
    title = "{Fast and reliable symplectic integration for planetary system N-body problems}",
  journal = {Monthly Notices of the Royal Astronomical Society},
archivePrefix = "arXiv",
   eprint = {1511.07476},
 primaryClass = "astro-ph.EP",
 keywords = {methods: numerical, celestial mechanics, planets and satellites: dynamical evolution and stability},
     year = 2016,
    month = jun,
   volume = 458,
    pages = {4285-4296},
      doi = {10.1093/mnras/stw569},
   adsurl = {http://adsabs.harvard.edu/abs/2016MNRAS.458.4285H},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{HernandezDehnen2016,
   author = {{Hernandez}, D.~M. and {Dehnen}, W.},
    title = "{A study of symplectic integrators for planetary system problems: error analysis and comparisons}",
  journal = {Monthly Notices of the Royal Astronomical Society},
archivePrefix = "arXiv",
   eprint = {1612.05329},
 primaryClass = "astro-ph.EP",
 keywords = {gravitation, methods: analytical, methods: numerical, celestial mechanics, planets and satellites: dynamical evolution and stability},
     year = 2017,
    month = jul,
   volume = 468,
    pages = {2614-2636},
      doi = {10.1093/mnras/stx547},
   adsurl = {http://adsabs.harvard.edu/abs/2017MNRAS.468.2614H},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}



@ARTICLE{Faber2010,
   author = {{Faber}, N.~T. and {Stibbe}, D. and {Portegies Zwart}, S. and 
	{McMillan}, S.~L.~W. and {Boily}, C.~M.},
    title = "{Particle-based sampling of N-body simulations}",
  journal = {Monthly Notices of the Royal Astronomical Society},
 keywords = {methods: N-body simulations, methods: numerical, stars: kinematics},
     year = 2010,
    month = jan,
   volume = 401,
    pages = {1898-1903},
      doi = {10.1111/j.1365-2966.2009.15775.x},
   adsurl = {http://adsabs.harvard.edu/abs/2010MNRAS.401.1898F},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{WangSpurzem2015,
       author = {{Wang}, Long and {Spurzem}, Rainer and {Aarseth}, Sverre and {Nitadori}, Keigo and {Berczik}, Peter and {Kouwenhoven}, M.~B.~N. and {Naab}, Thorsten},
        title = "{NBODY6++GPU: ready for the gravitational million-body problem}",
      journal = {\mnras},
     keywords = {methods: numerical, globular clusters: general, Astrophysics - Instrumentation and Methods for Astrophysics, Astrophysics - Solar and Stellar Astrophysics},
         year = 2015,
        month = jul,
       volume = {450},
       number = {4},
        pages = {4070-4080},
          doi = {10.1093/mnras/stv817},
archivePrefix = {arXiv},
       eprint = {1504.03687},
 primaryClass = {astro-ph.IM},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2015MNRAS.450.4070W},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}



@ARTICLE{NitadoriAarseth2012,
       author = {{Nitadori}, Keigo and {Aarseth}, Sverre J.},
        title = "{Accelerating NBODY6 with graphics processing units}",
      journal = {\mnras},
     keywords = {methods: numerical, globular clusters: general, Astrophysics - Instrumentation and Methods for Astrophysics, Physics - Computational Physics},
         year = 2012,
        month = jul,
       volume = {424},
       number = {1},
        pages = {545-552},
          doi = {10.1111/j.1365-2966.2012.21227.x},
archivePrefix = {arXiv},
       eprint = {1205.1222},
 primaryClass = {astro-ph.IM},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2012MNRAS.424..545N},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}



@ARTICLE{Farr2012,
   author = {{Farr}, W.~M. and {Ames}, J. and {Hut}, P. and {Makino}, J. and 
	{McMillan}, S. and {Muranushi}, T. and {Nakamura}, K. and {Nitadori}, K. and 
	{Portegies Zwart}, S.},
    title = "{PSDF: Particle Stream Data Format for N-body simulations}",
  journal = {\na},
archivePrefix = "arXiv",
   eprint = {1201.1694},
 primaryClass = "astro-ph.IM",
     year = 2012,
    month = jul,
   volume = 17,
    pages = {520-523},
      doi = {10.1016/j.newast.2012.01.003},
   adsurl = {http://adsabs.harvard.edu/abs/2012NewA...17..520F},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{Tamayo2015,
   author = {{Tamayo}, D. and {Triaud}, A.~H.~M.~J. and {Menou}, K. and {Rein}, H.
	},
    title = "{Dynamical Stability of Imaged Planetary Systems in Formation: Application to HL Tau}",
  journal = {\apj},
archivePrefix = "arXiv",
   eprint = {1502.05099},
 primaryClass = "astro-ph.EP",
 keywords = {celestial mechanics, planet{\ndash}disk interactions, planetary systems, planets and satellites: dynamical evolution and stability, planets and satellites: formation, submillimeter: planetary systems},
     year = 2015,
    month = jun,
   volume = 805,
      eid = {100},
    pages = {100},
      doi = {10.1088/0004-637X/805/2/100},
   adsurl = {http://adsabs.harvard.edu/abs/2015ApJ...805..100T},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@INPROCEEDINGS{Nobili1986,
   author = {{Nobili}, A. and {Roxburgh}, I.~W.},
   title = "{Simulation of general relativistic corrections in long term numerical integrations of planetary orbits}",
   keywords = {Celestial Mechanics, Computational Astrophysics, Numerical Integration, Orbital Mechanics, Planetary Orbits, Relativistic Effects, Gravitational Effects, Newton Theory, Orbit Perturbation, Planet Ephemerides},
   booktitle = {Relativity in Celestial Mechanics and Astrometry.  High Precision Dynamical Theories and Observational Verifications},
   year = 1986,
   series = {IAU Symposium},
   volume = 114,
   editor = {{Kovalevsky}, J. and {Brumberg}, V.~A.},
   pages = {105-110},
   adsurl = {http://adsabs.harvard.edu/abs/1986IAUS..114..105N},
   adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Saha1997,
   author = {{Saha}, P. and {Stadel}, J. and {Tremaine}, S.},
    title = "{A Parallel Integration Method for Solar System Dynamics}",
  journal = {\aj},
   eprint = {astro-ph/9605016},
 keywords = {METHODS: NUMERICAL, CELESTIAL MECHANICS},
     year = 1997,
    month = jul,
   volume = 114,
    pages = {409},
      doi = {10.1086/118485},
   adsurl = {http://adsabs.harvard.edu/abs/1997AJ....114..409S},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@article{Brogan2015,
  title={THE 2014 ALMA LONG BASELINE CAMPAIGN: FIRST RESULTS FROM HIGH ANGULAR RESOLUTION OBSERVATIONS TOWARD THE HL TAU REGIONThis article is part of the ALMA Long Baseline Campaign collection. An introduction and the full list of articles can be found at http://iopscience. iop. org/2041-8205/page/Focus\_on\_the\_ALMA\_Long\_Baseline\_Campaign.},
  author={Brogan, CL and P{\'e}rez, LM and Hunter, TR and Dent, WRF and Hales, AS and Hills, RE and Corder, S and Fomalont, EB and Vlahakis, C and Asaki, Y and others},
  journal={The Astrophysical Journal Letters},
  volume={808},
  number={1},
  pages={L3},
  year={2015},
  publisher={IOP Publishing}
}

@Article{Sidlichovsky1996,
author="{\v{S}}idlichovsk{\'y}, Milo{\v{s}}
and Nesvorn{\'y}, David",
title="Frequency modified fourier transform and its application to asteroids",
journal="Celestial Mechanics and Dynamical Astronomy",
year="1996",
month="Mar",
day="01",
volume="65",
number="1",
pages="137--148",
abstract="Recently a method has been suggested to analyze the chaotic behaviour of a conservative dynamical system by numerical analysis of the fundamental frequencies. Frequencies and amplitudes are determined step by step. As the frequencies are not generally orthogonal, a Gramm-Schmidt orthogonalization is made and for each new frequency the old amplitudes of previously determined frequencies are corrected. For a chaotic trajectory variations of the frequencies and amplitudes determined over different time periods are expected. The change of frequencies in such a calculation is a measure of the chaoticity of the trajectory. While amplitudes are corrected, the frequencies (once determined) are constant. We suggest here simple linear corrections of frequencies for the effect of other close frequencies. The improvement of frequency determination is demonstrated on a model case. This method is applied to the first fifty numbered asteroids.",
issn="1572-9478",
doi="10.1007/BF00048443",
url="https://doi.org/10.1007/BF00048443"
}


@article{Nesvorny2012,
  title={Statistical study of the early solar system's instability with four, five, and six giant planets},
  author={Nesvorn{\`y}, David and Morbidelli, Alessandro},
  journal={The Astronomical Journal},
  volume={144},
  number={4},
  pages={117},
  year={2012},
  publisher={IOP Publishing}
}

@ARTICLE{Rauch1999,
  title={Dynamical chaos in the Wisdom-Holman integrator: Origins and solutions},
  author={Rauch, Kevin P and Holman, Matthew},
  journal={The Astronomical Journal},
  volume={117},
  number={2},
  pages={1087},
  year={1999},
  publisher={IOP Publishing}
}

@article{Laskar2011,
author = {Laskar, Jacques and Fienga, A and Gastineau, M. and Manche, H},
doi = {10.1051/0004-6361/201116836},
issn = {0004-6361},
journal = {Astronomy \& Astrophysics},
keywords = {celestial mechanics,chaos,dynamical evolution and,ephemerides,methods,numerical,planets and satellites,secular},
mendeley-tags = {secular},
month = {aug},
pages = {A89},
title = {{La2010: a new orbital solution for the long-term motion of the Earth}},
url = {http://www.aanda.org/10.1051/0004-6361/201116836},
volume = {532},
year = {2011}
}



@ARTICLE{Fienga2011,
   author = {{Fienga}, A. and {Laskar}, J. and {Kuchynka}, P. and {Manche}, H. and 
	{Desvignes}, G. and {Gastineau}, M. and {Cognard}, I. and {Theureau}, G.
	},
    title = "{The INPOP10a planetary ephemeris and its applications in fundamental physics}",
  journal = {Celestial Mechanics and Dynamical Astronomy},
archivePrefix = "arXiv",
   eprint = {1108.5546},
 primaryClass = "astro-ph.EP",
 keywords = {Planetary ephemerides, Celestial Mechanics, Fundamental physics, Asteroid masses},
     year = 2011,
    month = nov,
   volume = 111,
    pages = {363-385},
      doi = {10.1007/s10569-011-9377-8},
   adsurl = {http://adsabs.harvard.edu/abs/2011CeMDA.111..363F},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{Conway1986,
  title={An improved algorithm due to Laguerre for the solution of Kepler's equation},
  author={Conway, Bruce A},
  journal={Celestial mechanics},
  volume={39},
  number={2},
  pages={199--211},
  year={1986},
  publisher={Springer}
}

@ARTICLE{Danby1983,
  title={The solution of Kepler's equation, I},
  author={Danby, JMA and Burkardt, TM},
  journal={Celestial Mechanics},
  volume={31},
  number={2},
  pages={95--107},
  year={1983},
  publisher={Springer}
}

@ARTICLE{Danby1987,
   author = {{Danby}, J.~M.~A.},
    title = "{The Solution of Kepler's Equations - Part Three}",
  journal = {Celestial Mechanics},
     year = 1987,
    month = sep,
   volume = 40,
    pages = {303-312},
      doi = {10.1007/BF01235847},
   adsurl = {http://adsabs.harvard.edu/abs/1987CeMec..40..303D},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@INPROCEEDINGS{Hedman2012,
   author = {{Hedman}, M.~M. and {Nicholson}, P.~D. and {Salo}, H.},
    title = "{Probing Periodic Patterns In Saturn's Inner A Ring With Cassini-VIMS}",
booktitle = {AAS/Division for Planetary Sciences Meeting Abstracts},
     year = 2012,
   series = {AAS/Division for Planetary Sciences Meeting Abstracts},
   volume = 44,
    month = oct,
    pages = {414.05},
   adsurl = {http://adsabs.harvard.edu/abs/2012DPS....4441405H},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{Tancredi2001,
   author = {{Tancredi}, G. and {S{\'a}nchez}, A. and {Roig}, F.},
    title = "{a Comparison Between Methods to Compute Lyapunov Exponents}",
  journal = {\aj},
 keywords = {Methods: Numerical, Solar System: General},
     year = 2001,
    month = feb,
   volume = 121,
    pages = {1171-1179},
      doi = {10.1086/318732},
   adsurl = {http://adsabs.harvard.edu/abs/2001AJ....121.1171T},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{MikkolaPalmer2000,
   author = {{Mikkola}, S. and {Palmer}, P.},
    title = "{Simple derivation of Symplectic Integrators with First Order Correctors}",
  journal = {Celestial Mechanics and Dynamical Astronomy},
 keywords = {PERTURBED TWO-BODY PROBLEM, SYMPLECTIC INTEGRATION, SYMPLECTIC CORRECTORS, perturbed two-body problem, symplectic integration, symplectic correctors},
     year = 2000,
    month = aug,
   volume = 77,
    pages = {305-317},
      doi = {10.1023/A:1011165912381},
   adsurl = {http://adsabs.harvard.edu/abs/2000CeMDA..77..305M},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{TittemoreWisdom1989,
   author = {{Tittemore}, W.~C. and {Wisdom}, J.},
    title = "{Tidal evolution of the Uranian satellites. II - an explanation of the anomalously high orbital inclination of Miranda}",
  journal = {\icarus},
 keywords = {Evolution (Development), Miranda, Orbital Mechanics, Orbital Resonances (Celestial Mechanics), Hamiltonian Functions, Libration, Perturbation Theory, Trajectory Analysis, Umbriel},
     year = 1989,
    month = mar,
   volume = 78,
    pages = {63-89},
      doi = {10.1016/0019-1035(89)90070-5},
   adsurl = {http://adsabs.harvard.edu/abs/1989Icar...78...63T},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Wisdom1996,
   author = {{Wisdom}, J. and {Holman}, M. and {Touma}, J.},
    title = "{Symplectic Correctors}",
  journal = {Fields Institute Communications, Vol.~10, p.~217},
 keywords = {HAMILTONIAN, SYMPLECTIC, INTEGRATOR},
     year = 1996,
   volume = 10,
    pages = {217},
   adsurl = {http://adsabs.harvard.edu/abs/1996FIC....10..217W},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@PHDTHESIS{Wisdom1981,
   author = {{Wisdom}, J.~L.},
    title = "{The origin of the Kirkwood gaps: A mapping for asteroidal motion near the 3/1 commensurability 1. The resonance overlap criterion and the onset of stochastic behavior in the restricted three-body problem 2.}",
 keywords = {Asteroids, Celestial Mechanics, Gaps, Stochastic Processes, Three Body Problem, Entropy, Mapping, Orbit Perturbation, Planetary Orbits, Scaling Laws},
   school = {California Institute of Technology, Pasadena.},
     year = 1981,
   adsurl = {http://adsabs.harvard.edu/abs/1981PhDT.........5W},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{MikkolaInnanen1999,
   author = {{Mikkola}, S. and {Innanen}, K.},
    title = "{Symplectic Tangent Map for Planetary Motions}",
  journal = {Celestial Mechanics and Dynamical Astronomy},
 keywords = {PLANETARY SYSTEMS, LIAPUNOV EXPONENTS, CHAOS, SYMPLECTIC INTEGRATION, planetary systems, Liapunov exponents, chaos, symplectic integration},
     year = 1999,
    month = may,
   volume = 74,
    pages = {59-67},
      doi = {10.1023/A:1008312912468},
   adsurl = {http://adsabs.harvard.edu/abs/1999CeMDA..74...59M},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{Cincotta2003,
  title={Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbits},
  author={Cincotta, PM and Giordano, CM and Sim{\'o}, C},
  journal={Physica D: Nonlinear Phenomena},
  volume={182},
  number={3},
  pages={151--178},
  year={2003},
  publisher={Elsevier}
}

@inProceedings{Grazier2005,
author = "K. R. Grazier and W. I. Newman and James M. Hyman and Philip W. Sharp and David J. Goldstein",
title = "Achieving Brouwer's law with high-order St\unhbox \voidb@x \bgroup \let \unhbox \voidb@x \setbox \@tempboxa \hbox {o\global \mathchardef \accent@spacefactor \spacefactor }\accent 127 o\egroup \spacefactor \accent@spacefactor rmer multistep methods",
journal = "ANZIAM J.",
volume = "46",
pages = "C786--C804",
year = 2005,
booktitle = "Proc. of 12th Computational Techniques and Applications Conference CTAC-2004",
editor = "Rob May and A. J. Roberts",
month = aug,
note = "\protect \url {http://anziamj.austms.org.au/V46/CTAC2004/Graz} [August 23, 2005]",
keywords = "Brouwer's law, multistep integrators, high order accuracy",
}
@ARTICLE{Mikkola1997,
   author = {{Mikkola}, S.},
    title = "{Practical Symplectic Methods with Time Transformation for the Few-Body Problem}",
  journal = {Celestial Mechanics and Dynamical Astronomy},
 keywords = {symplectic integration, few-body problem, few-body problem.},
     year = 1997,
    month = feb,
   volume = 67,
    pages = {145-165},
      doi = {10.1023/A:1008217427749},
   adsurl = {http://adsabs.harvard.edu/abs/1997CeMDA..67..145M},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{Pebay2008,
  title={Formulas for robust, one-pass parallel computation of covariances and arbitrary-order statistical moments},
  author={P{\'e}bay, Philippe},
  journal={Sandia Report SAND2008-6212, Sandia National Laboratories},
  year={2008}
}

@BOOK{StiefelScheifele1971,
   author = {{Stiefel}, E.~L. and {Scheifele}, G.},
    title = "{Linear and Regular Celestial Mechanics. (Die Grundlehren d. math. Wissenschaften, Band 174)}",
  publisher = "{Springer}",
  address = "{Berlin/Heidelberg/New York}",
     year = 1971,
}

@article{Park2017,
	doi = {10.3847/1538-3881/aa5be2},
	year = 2017,
	month = {feb},
	publisher = {American Astronomical Society},
	volume = {153},
	number = {3},
	pages = {121},
	author = {Ryan S. Park and William M. Folkner and Alexander S. Konopliv and James G. Williams and David E. Smith and Maria T. Zuber},
	title = {Precession of Mercury's Perihelion from Ranging to {theMESSENGERSpacecraft}},
	journal = {The Astronomical Journal},
}

@INPROCEEDINGS{Stumpff1962,
   author = {{Stumpff}, K.},
    title = "{Himmelsmechanik, Band I}",
    booktitle = "{Himmelsmechanik, Band I}",
  publisher = "{VEB Deutscher Verlag der Wissenschaften}",
  address = "{Berlin}",
     year = 1962
}
@Article{LaskarRobutel2001,
author="Laskar, Jacques
and Robutel, Philippe",
title="High order symplectic integrators for perturbed Hamiltonian systems",
journal="Celestial Mechanics and Dynamical Astronomy",
year="2001",
volume="80",
number="1",
pages="39--62",
issn="1572-9478",
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@book{Vogelaere1956,
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@Article{Fousse2007,
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@ARTICLE{KimKim2009,
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@ARTICLE{Kim2010,
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@article{Kim2001,
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@article{Levrard2009,
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@article{ReinTamayo2019,
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@proceedings{Reipurth07,
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@article{Gammie96,
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@article{Kalas2008,
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@article{LecoanetAdams2008,
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      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}



@ARTICLE{Spalding2018,
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archivePrefix = {arXiv},
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       adsurl = {https://ui.adsabs.harvard.edu/abs/2018ApJ...869L..19S},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


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@article{Rivera2005,
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}


@article{Toomre1964,
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@misc{planetdef,
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@misc{exoplanet,
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@article{BodenheimerPollack86,
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@book{fehlberg69,
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@book{nr,
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@book{StoerBulirsch02,
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@article{SandorKley06,
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@article{oishi2007,
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@article{MarcyButler01,
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@ARTICLE{Kinoshita1991,
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author = {Laskar, Jacques},
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primaryClass = {math},
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@ARTICLE{HoangMogaveroLaskar2022,
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       number = {1},
        pages = {1342-1350},
          doi = {10.1093/mnras/stac1299},
archivePrefix = {arXiv},
       eprint = {2205.04170},
 primaryClass = {astro-ph.EP},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2022MNRAS.514.1342H},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{ChanLee2023,
       author = {{Chan}, Man Ho and {Lee}, Chak Man},
        title = "{The Solar system test for the general modified gravity theories}",
      journal = {\mnras},
     keywords = {Planets and satellites: general, General Relativity and Quantum Cosmology, Astrophysics - Earth and Planetary Astrophysics},
         year = 2023,
        month = feb,
       volume = {518},
       number = {4},
        pages = {6238-6242},
          doi = {10.1093/mnras/stac3509},
archivePrefix = {arXiv},
       eprint = {2212.01019},
 primaryClass = {gr-qc},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2023MNRAS.518.6238C},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Milgrom1983,
       author = {{Milgrom}, M.},
        title = "{A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis.}",
      journal = {\apj},
     keywords = {Cosmology, Galactic Structure, Nonrelativistic Mechanics, Stellar Motions, Particle Acceleration, Solar System, Astrophysics},
         year = 1983,
        month = jul,
       volume = {270},
        pages = {365-370},
          doi = {10.1086/161130},
       adsurl = {https://ui.adsabs.harvard.edu/abs/1983ApJ...270..365M},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{MoffatToth2008,
       author = {{Moffat}, J.~W. and {Toth}, V.~T.},
        title = "{Testing Modified Gravity with Globular Cluster Velocity Dispersions}",
      journal = {\apj},
     keywords = {dark matter, globular clusters: general, gravitation, Astrophysics, General Relativity and Quantum Cosmology},
         year = 2008,
        month = jun,
       volume = {680},
       number = {2},
        pages = {1158-1161},
          doi = {10.1086/587926},
archivePrefix = {arXiv},
       eprint = {0708.1935},
 primaryClass = {astro-ph},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2008ApJ...680.1158M},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{Verlinde2017,
       author = {{Verlinde}, Erik},
        title = "{Emergent Gravity and the Dark Universe}",
      journal = {SciPost Physics},
     keywords = {High Energy Physics - Theory, General Relativity and Quantum Cosmology},
         year = 2017,
        month = may,
       volume = {2},
       number = {3},
          eid = {016},
        pages = {016},
          doi = {10.21468/SciPostPhys.2.3.016},
archivePrefix = {arXiv},
       eprint = {1611.02269},
 primaryClass = {hep-th},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2017ScPP....2...16V},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@book{Newton1687,
    year = {1687},
    publisher = {Societatis Regiae},
    author = {Isaac Newton},
    title = {Philosophiae Naturalis Principia Mathematica},
}


@ARTICLE{Einstein1915,
    author = {{Einstein}, Albert},
    title = "{Die Feldgleichungen der Gravitation}",
    journal = {Sitzungsberichte der K{\"o}niglich Preu{\ss}ischen Akademie der Wissenschaften},
    year = 1915,
    month = jan,
    pages = {844-847},
    adsurl = {https://ui.adsabs.harvard.edu/abs/1915SPAW.......844E},
    adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% After failed attempts by Euler and Lagrange, Laplace finds that the mean motion of Jupiter and Saturn does not contribute to their secular motion.
@article{Laplace1776,
  title={Sur le principe de la gravitation universelle et sur les in{\'e}galit{\'e}s s{\'e}culaires des plan{\`e}tes qui en d{\'e}pendent},
  author={Laplace, Pierre Simon},
  journal={M{\'e}moire de l’Acad{\'e}mie royale des sciences de Paris},
  volume={8},
  pages={199--275},
  year={1776}
}

%% In this 1776 publication (completed in 1774) Lagrange introduces the first linear differential equations for the inclinations and nodes of the planets. 
@misc{Lagrange1776,
  title={Sur l’alt{\'e}ration des moyens mouvements des plan{\`e}tes},
  author={Lagrange, JL},
  year={1776},
  journal={M{\'e}moires de la Acad{\'e}mie de Berlin}
}

@book{Lagrange1778,
  title={Recherches sur les \'equations s\'eculaires des mouvemens des noeuds, et des inclinaisons des orbites des plan\`etes},
  author={Lagrange, Joseph Louis},
  year={1778},
  publisher={de l'Imprimerie Royale}
}

%% Laplace quickly publishes results for the eccentricities and aphelions of planetary orbits.
@article{Laplace1775,
  title={M\'emoire sur les solutions particuli\`eres des \'equations diff\'erentielles et sur les in\'egalit\'es s\'eculaires des plan\`etes},
  author={Laplace, Pierre Simon},
  journal={M{\'e}moire de l’Acad{\'e}mie royale des sciences de Paris},
  year={1775}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Publications Lagrange 1781 through 1784 are where Lagrange gives the first complete solution of the six main planets of the solar system (see Laskar 2013).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book{Lagrange1781,
  title={Th\'eorie des variations s\'eculaires des  \'el\'ements des plan\`etes, Premi\`ere partie},
  author={Lagrange, Joseph Louis},
  publisher={Nouveaux M\'emoires de l'Acad\'emie des Sciences et Belles-Lettres de Berlin},
  year={1781}
}
@book{Lagrange1782,
  title={Th\'eorie des variations s\'eculaires des \'el\'ements des plan\`etes, Seconde partie contenant la d\'etermination de ces variations pour chacune des pla\`etes principales},
  author={Lagrange, Joseph Louis},
  publisher={Nouveaux M\'emoires de l'Acad\'emie des Sciences et Belles-Lettres de Berlin},
  year={1782}
}

@book{Lagrange1783a,
  title={Th\'eorie des variations p\'eriodiques des mouvements des plan\`etes, Premi\`ere partie},
  author={Lagrange, Joseph Louis},
  publisher={Nouveaux M\'emoires de l'Acad\'emie des Sciences et Belles-Lettres de Berlin},
  year={1783}
}

@book{Lagrange1783b,
  title={Sur les variations s\'eculaires des mouvements moyens des plan\`etes},
  author={Lagrange, Joseph Louis},
  publisher={Nouveaux M\'emoires de l'Acad\'emie des Sciences et Belles-Lettres de Berlin},
  year={1783}
}

@book{Lagrange1784,
  title={Th\'eorie des variations p\'eriodiques des mouvements des plan\`etes, Seconde partie},
  author={Lagrange, Joseph Louis},
  publisher={Nouveaux M\'emoires de l'Acad\'emie des Sciences et Belles-Lettres de Berlin},
  year={1784}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Laplace carried on the work and derived a theory for Jupiter and Saturn which matched observations from 240 BC to 1715 AD. Previous work had not even managed to match observations for more than a few decades.
@article{Laplace1785,
  title={Th\'eorie de Jupiter et Saturne},
  author={Laplace, Pierre Simon},
  journal={M{\'e}moire de l’Acad{\'e}mie royale des sciences de Paris},
  year={1785}
}

%% Le Verrier extends the expansion to higher order.
@article{LeVerrier1840,
  title={Sur les variations s{\'e}culaires des {\'e}l{\'e}ments elliptiques des sept plan\`etes principales: Mercure, V{\'e}nus, La Terre, Mars, Jupiter, Saturne et Uranus},
  author={Le Verrier, UJJ},
  journal={J. Math. Pures Appli},
  volume={4},
  number={1840},
  pages={220--254},
  year={1840}
}

@article{LeVerrier1841,
  title={M\'emoire sur les in\'egalit\'es s\'eculaires des plan\`etes},
  author={Le Verrier, UJJ},
  journal={J. Math. Pures Appli},
  pages={28--110},
  year={1841}
}

%% Poincare discusses how the soluitons of Laplace, Lagrange, and Poisson seem to imply a proof of stability, but on closer inspection such a claim cannot be made.
@article{Poincare1898,
  title={Sur la Stabilit{\'e} du Syst{\`e}me Solaire (1898)},
  author={Poincar{\'e}, Henri},
  journal={Annuaire du Bureau des Longitudes pour l’an 1898},
  year={1898},
}

%% Poincare also showed that the 3-body problem is non-integrable.
@book{Poincare1899,
  title={Les m{\'e}thodes nouvelles de la m{\'e}canique c{\'e}leste},
  author={Poincar{\'e}, Henri},
  volume={3},
  year={1899},
  publisher={Gauthier-Villars et fils, imprimeurs-libraires}
}

%% The development of KAM Theory
@inproceedings{Kolmogorov1954,
  title={On conservation of conditionally periodic motions for a small change in Hamilton's function},
  author={Kolmogorov, Andrey Nikolaevich},
  booktitle={Dokl. Akad. Nauk SSSR},
  volume={98},
  pages={527--530},
  year={1954}
}

@ARTICLE{Arnold1963,
       author = {{Arnol'd}, V.~I.},
        title = "{Proof of a Theorem of A. N. KOLMOGOROV on the Invariance of Quasi-Periodic Motions Under Small Perturbations of the Hamiltonian}",
      journal = {Russian Mathematical Surveys},
         year = 1963,
        month = oct,
       volume = {18},
       number = {5},
        pages = {9-36},
          doi = {10.1070/RM1963v018n05ABEH004130},
       adsurl = {https://ui.adsabs.harvard.edu/abs/1963RuMaS..18....9A},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{Moser1962,
  title={On invariant curves of area-preserving mappings of an annulus},
  author={M{\"o}ser, J},
  journal={Nachr. Akad. Wiss. G{\"o}ttingen, II},
  pages={1--20},
  year={1962}
}

%% The high order secular expansion of Laskar
@ARTICLE{Laskar1985,
    author = {{Laskar}, J.},
    title = "{Accurate methods in general planetary theory}",
    journal = {\aap},
     year = 1985,
    month = mar,
    volume = {144},
    number = {1},
    pages = {133-146},
    adsurl = {https://ui.adsabs.harvard.edu/abs/1985A&A...144..133L},
    adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{Laskar1986,
       author = {{Laskar}, J.},
        title = "{Secular terms of classical planetary theories using the results of general theory}",
      journal = {\aap},
     keywords = {Celestial Mechanics, Computational Astrophysics, Numerical Integration, Orbital Elements, Planetology, Secular Variations, Eccentric Orbits, Lunar Effects, Orbit Perturbation, Planetary Mass, Planetary Orbits, Precession, Relativistic Effects, Taylor Series, Lunar and Planetary Exploration},
         year = 1986,
        month = mar,
       volume = {157},
       number = {1},
        pages = {59-70},
       adsurl = {https://ui.adsabs.harvard.edu/abs/1986A&A...157...59L},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

