DOI: 10.1126/science.1182583, 1367 (2010);327 Science, et al.Luciano IessGravity Field, Shape, and Moment of Inertia of Titan This copy is for your personal, non-commercial use only. clicking here.colleagues, clients, or customers by , you can order high-quality copies for yourIf you wish to distribute this article to others here.following the guidelines can be obtained byPermission to republish or repurpose articles or portions of articles ): January 31, 2011 www.sciencemag.org (this infomation is current as ofThe following resources related to this article are available online at http://www.sciencemag.org/content/327/5971/1367.full.htmlversion of this article at: including high-resolution figures, can be found in the onlineUpdated information and services, http://www.sciencemag.org/content/suppl/2010/03/09/327.5971.1367.DC1.htmlcan be found at: Supporting Online Material http://www.sciencemag.org/content/327/5971/1367.full.html#ref-list-1, 2 of which can be accessed free:cites 8 articlesThis article 2 article(s) on the ISI Web of Sciencecited by This article has been http://www.sciencemag.org/content/327/5971/1367.full.html#related-urls1 articles hosted by HighWire Press; see:cited by This article has been http://www.sciencemag.org/cgi/collection/planet_sciPlanetary Sciencesubject collections:This article appears in the following registered trademark of AAAS. is aScience2010 by the American Association for the Advancement of Science; all rights reserved. The title CopyrightAmerican Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by theScience on January 31, 2011www.sciencemag.orgDownloaded fromGravity Field, Shape, and Moment ofInertia of TitanLuciano Iess,1* Nicole J. Rappaport,2Robert A. Jacobson,2Paolo Racioppa,1David J. Stevenson,3Paolo Tortora,4John W. Armstrong,2Sami W. Asmar2Precise radio tracking of the spacecraft Cassini has provided a determination of Titan’s mass andgravity harmonics to degree 3. The quadrupole field is consistent with a hydrostatically relaxedbody shaped by tidal and rotational effects. The inferred moment of inertia factor is about0.34, implying incomplete differentiation, either in the sense of imperfect separation of rock fromice or a core in which a large amount of water remains chemically bound in silicates. Theequilibrium figure is a triaxial ellipsoid whose semi-axes a, b, and c differ by 410 meters (a – c)and 103 meters (b – c). The nonhydrostatic geoid height variations (up to 19 meters) are smallcompared to the observed topographic anomalies of hundreds of meters, suggesting a high degreeof compensation appropriate to a body that has warm ice at depth.Titan is Saturn’s largest moon and is secondin size only to Ganymede in the solar sys-tem. After being gravitationally capturedby Saturn on 1 July 2004, the spacecraft Cassinihas encountered Titan more than 50 times, car-rying out science observations and using themoon’s gravity field to change its orbit. Cassini’sobservations have unveiled a variety of featuresand phenomena not found on any other solarsystem satellite, such as hydrocarbon lakes, riverchannels, and dune fields (1). Although exogenicprocesses driven by the dense hydrocarbon-richatmosphere play a crucial role in shaping thecomplex topography observed by Cassini’s radar,contributions from endogenic processes are farless clear. Assessing the presence of active endo-genic processes and understanding the origin ofTitan’s complex topography require knowledgeof the moon’s interior structure, which can beindirectly inferred from gravity and rotation data.Here we present results about Titan’s gravity,shape, and moment of inertia (MoI) that con-strain models of the deep interior structure andprovide the appropriate reference to the large-scale topography.Of the more than 50 Titan flybys completedso far by the Cassini spacecraft, only 4 weredevoted to the determination of the gravity field.Titan’s gravity field is estimated from the space-craft’s range rate, measured to an accuracy upto 7.5 × 10−5m/s at 60-s integration times fromthe Doppler shift of the microwave carrier usedin the radio link to the ground. A detailed de-scription of the flyby characteristics, the observ-able quantities, and the estimation methods isgiven in the supporting online material (SOM).We processed the data using two different ap-proaches. In the first one, radio tracking dataacquired during each flyby were individuallyfitted for the spacecraft state vector (position andvelocity) at a reference epoch, and for the degree2 and 3 gravity coefficients. The four gravity fieldsolutions and the associated covariances werethen combined in a single multiarc solution(SOL1). In a second, more general approach(SOL2), all available radiometric tracking andoptical navigation imaging data from the Cassinimission, as well as data from the Pioneer andVoyager Saturn encounters and astronomicalobservations of Saturn and its satellites, werecombined in a global solution for the planetand satellite ephemerides and the gravitationalparameters of the bodies in the Saturnian sys-tem (2).In spite of the different approaches, thediscrepancy between the two solutions is statis-tically insignificant (Table 1). Although neithersolution was constrained a priori to the hydro-static ratio J2/C22= 10/3 between the degree 2harmonic coefficients the gravity field appears tobe dominated by a nearly hydrostatic quadrupole.The remaining degree 2 and 3 coefficients are atleast one order of magnitude smaller than J2, anindication that nonhydrostatic features, althoughsignificant, do not play a major role in shapingthe gravity body. The orientation of the principalaxes of inertia, determined by diagonalizing thequadrupole tensor, is consistent (to a 2s level)with the assumed rotation model (with the spinpole oriented along the normal to the orbitalplane, synchronous rotation, and the primemeridian toward Saturn at pericenter). The formalaccuracy in the principal axes orientation is about0.5° for the long axis (pointing to Saturn) and0.8° for the polar (short) axis.The ratio J2/C22is 3.186 T 0.042 for SOL1and 3.339 T 0.067 for SOL2, which are thereforeindistinguishable from each other (to a 2s level)and consistent with the value of 10/3 that is1Dipartimento di Ingegneria Aerospaziale ed Astronautica,Università La