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@Article{GomesDeieMorb:2017:InPlSy,
               author = "Gomes, Rodney and Deienno, Rog{\'e}rio and Morbidelli, 
                         Alessandro",
          affiliation = "{Observat{\'o}rio Nacional} and {Instituto Nacional de Pesquisas 
                         Espaciais (INPE)} and {Universit{\'e} C{\^o}te dAzur}",
                title = "The inclination of the planetary system relative to the solar 
                         equator may be explained by the presence of planet 9",
              journal = "The Astronomical Journal",
                 year = "2017",
               volume = "153",
               number = "27",
             keywords = "celestial mechanics  planets and satellites: dynamical evolution 
                         and stability  Sun: general.",
             abstract = "We evaluate the effects of a distant planet, commonly known as 
                         planet 9, on the dynamics of the giant planets of the solar 
                         system. We find that the dynamics of the giant planets can be 
                         decomposed into a classic Lagrange Laplace dynamics relative to 
                         their own invariant plane and a slow precession of said plane 
                         relative to the total angular momentum vector of the solar system, 
                         including planet 9. Under specific configurations for planet 9, 
                         this precession can explain the current tilt of \∼6 
                         between the invariant plane of the giant planets and the solar 
                         equator. An analytical model is developed to map the evolution of 
                         the inclination of the inner giant planets invariant plane as a 
                         function of the planet 9\ʼs mass and orbital elements, and 
                         numerical simulations of the equations of motion are performed to 
                         validate our analytical approach. The longitude of the ascending 
                         node of planet 9 is found to be linked to the longitude of the 
                         ascending node of the giant planets invariant plane, which also 
                         constrains the longitude of the node of planet 9 on the ecliptic. 
                         Some of the planet 9 configurations that allow the explanation of 
                         the current solar tilt are compatible with those proposed to 
                         explain the orbital confinement of distant Kuiper Belt objects. 
                         This work gives an elegant explanation for the current tilt 
                         between the invariant plane of the inner giant planets and the 
                         solar equator and also adds new constraints to the orbital 
                         elements of planet 9.",
                  doi = "http://dx.doi.org/10.3847/1538-3881/153/1/27",
                  url = "http://dx.doi.org/http://dx.doi.org/10.3847/1538-3881/153/1/27",
                 issn = "0004-6256",
             language = "en",
           targetfile = "gomes_inclination.pdf",
        urlaccessdate = "24 nov. 2020"
}


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