@phdthesis{Spahn1994, author = {Spahn, Frank}, title = {Einfluß von Satelliten auf die Dynamik planetarer Ringe}, year = {1994}, language = {de} } @article{KrivovSremcevicSpahn2005, author = {Krivov, Alexander V. and Sremcevic, Miodrag and Spahn, Frank}, title = {Evolution of a Keplerian disk of colliding and fragmenting particles: a kinetic model with application to the Edgeworth-Kuiper belt}, issn = {0019-1035}, year = {2005}, abstract = {We present a kinetic model of a disk of solid particles, orbiting a primary and experiencing inelastic collisions. In distinction to other collisional models that use a 2D (mass-sernimajor axis) binning and perform a separate analysis of the velocity (eccentricity, inclination) evolution, we choose mass and orbital elements as independent variables of a phase space. The distribution function in this space contains full information on the combined mass, spatial, and velocity distributions of particles. A general kinetic equation for the distribution function is derived, valid for any set of orbital elements and for any collisional outcome, specified by a single kernel function. The first implementation of the model utilizes a 3D phase space (mass-semimajor axis-eccentricity) and involves averages over the inclination and all angular elements. We assume collisions to be destructive, simulate them with available material- and size-dependent scaling laws, and include collisional damping. A closed set of kinetic equations for a mass-semimajor axis-eccentricity distribution is written and transformation rules to usual mass and spatial distributions of the disk material are obtained. The kinetic "core" of our approach is generic. It is possible to add inclination as an additional phase space variable, to include cratering collisions and agglomeration, dynamical friction and viscous stirring, gravity of large perturbers, drag forces, and other effects into the model. As a specific application, we address the collisional evolution of the classical population in the Edgeworth-Kuiper belt (EKB). We run the model for different initial disk's masses and radial profiles and different impact strengths of objects. Our results for the size distribution, collisional timescales, and mass loss are in agreement with previous studies. In particular, collisional evolution is found to be most substantial in the inner part of the EKB, where the separation size between the survivors over EKB ' s age and fragments of earlier collisions lies between a few and several tens of km. The size distribution in the EKB is not a single Dohnanyi-type power law, reflecting the size dependence of the critical specific energy in both strength and gravity regimes. The net mass loss rate of an evolved disk is nearly constant and is dominated by disruption of larger objects. Finally, assuming an initially uniform distribution of orbital eccentricities, we show that an evolved disk contains more objects in orbits with intermediate eccentricities than in nearly circular or more eccentric orbits. This property holds for objects of any size and is explained in terms of collisional probabilities. The effect should modulate the eccentricity distribution shaped by dynamical mechanisms, such as resonances and truncation of perihelia by Neptune. (c) 2004 Elsevier Inc. All rights reserved}, language = {en} } @article{GraetzSeissSpahn2018, author = {Gr{\"a}tz, Fabio M. and Seiss, Martin and Spahn, Frank}, title = {Formation of moon-induced gaps in dense planetary rings}, series = {The astrophysical journal : an international review of spectroscopy and astronomical physics}, volume = {862}, journal = {The astrophysical journal : an international review of spectroscopy and astronomical physics}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0004-637X}, doi = {10.3847/1538-4357/aace00}, pages = {9}, year = {2018}, abstract = {We develop an axisymmetric diffusion model to describe radial density profiles in the vicinity of tiny moons embedded in planetary rings. Our diffusion model accounts for the gravitational scattering of the ring particles by an embedded moon and for the viscous diffusion of the ring matter back into the gap. With test particle simulations, we show that the scattering of the ring particles passing the moon is larger for small impact parameters than estimated by Goldreich \& Tremaine and Namouni. This is significant for modeling the Keeler gap. We apply our model to the gaps of the moons Pan and Daphnis embedded in the outer A ring of Saturn with the aim to estimate the shear viscosity of the ring in the vicinity of the Encke and Keeler gap. In addition, we analyze whether tiny icy moons whose dimensions lie below Cassini's resolution capabilities would be able to explain the gap structure of the C ring and the Cassini division.}, language = {en} } @article{SeilerSeissHoffmannetal.2019, author = {Seiler, Michael and Seiß, Martin and Hoffmann, Holger and Spahn, Frank}, title = {Hydrodynamic Simulations of Asymmetric Propeller Structures in Saturn's Rings}, series = {The astrophysical journal : an international review of spectroscopy and astronomical physics ; Supplement series}, volume = {243}, journal = {The astrophysical journal : an international review of spectroscopy and astronomical physics ; Supplement series}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0067-0049}, doi = {10.3847/1538-4365/ab26b0}, pages = {16}, year = {2019}, abstract = {The observation of the non-Keplerian behavior of propeller structures in Saturn's outer A ring raises the question: how does the propeller respond to the wandering of the central embedded moonlet? Here, we study numerically how the structural imprint of the propeller changes for a libration of the moonlet. It turns out that the libration induces an asymmetry in the propeller, which depends on the libration period and amplitude of the moonlet. Further, we study the dependence of the asymmetry on the libration period and amplitude for a moonlet with a 400 m Hill radius, which is located in the outer A ring. This allows us to apply our findings to the largest known propeller Bl{\´e}riot, which is expected to be of a similar size. For Bl{\´e}riot, we can conclude that, supposing the moonlet is librating with the largest observed period of 11.1 yr and an azimuthal amplitude of about 1845 km, a small asymmetry should be measurable but depends on the moonlet's libration phase at the observation time. The longitude residuals of other trans-Encke propellers (e.g., Earhart) show amplitudes similar to Bl{\´e}riot, which might allow us to observe larger asymmetries due to their smaller azimuthal extent, allowing us to scan the whole gap structure for asymmetries in one observation. Although the librational model of the moonlet is a simplification, our results are a first step toward the development of a consistent model for the description of the formation of asymmetric propellers caused by a freely moving moonlet.}, language = {en} } @article{SeissAlbersSremčevićetal.2019, author = {Seiß, Martin and Albers, Nicole and Sremčević, Miodrag and Schmidt, J{\"u}rgen and Salo, Heikki and Seiler, Michael and Hoffmann, Holger and Spahn, Frank}, title = {Hydrodynamic Simulations of Moonlet-induced Propellers in Saturn's Rings}, series = {The astronomical journal}, volume = {157}, journal = {The astronomical journal}, number = {1}, publisher = {IOP Publishing Ltd.}, address = {Bristol}, issn = {0004-6256}, doi = {10.3847/1538-3881/aaed44}, pages = {11}, year = {2019}, abstract = {One of the biggest successes of the Cassini mission is the detection of small moons (moonlets) embedded in Saturns rings that cause S-shaped density structures in their close vicinity, called propellers. Here, we present isothermal hydrodynamic simulations of moonlet-induced propellers in Saturn's A ring that denote a further development of the original model. We find excellent agreement between these new hydrodynamic and corresponding N-body simulations. Furthermore, the hydrodynamic simulations confirm the predicted scaling laws and the analytical solution for the density in the propeller gaps. Finally, this mean field approach allows us to simulate the pattern of the giant propeller Bl{\´e}riot, which is too large to be modeled by direct N-body simulations. Our results are compared to two stellar occultation observations by the Cassini Ultraviolet Imaging Spectrometer (UVIS), which intersect the propeller Bl{\´e}riot. Best fits to the UVIS optical depth profiles are achieved for a Hill radius of 590 m, which implies a moonlet diameter of about 860 m. Furthermore, the model favors a kinematic shear viscosity of the surrounding ring material of ν0 = 340 cm2 s-1, a dispersion velocity in the range of 0.3 cm s-1 < c0 < 1.5 cm s-1, and a fairly high bulk viscosity 7 < ξ0/ν0 < 17. These large transport values might be overestimated by our isothermal ring model and should be reviewed by an extended model including thermal fluctuations.}, language = {en} } @article{SeissSpahn2011, author = {Seiss, Martin and Spahn, Frank}, title = {Hydrodynamics of saturn's dense rings}, series = {Mathematical modelling of natural phenomena}, volume = {6}, journal = {Mathematical modelling of natural phenomena}, number = {4}, publisher = {EDP Sciences}, address = {Les Ulis}, issn = {0973-5348}, doi = {10.1051/mmnp/20116409}, pages = {191 -- 218}, year = {2011}, abstract = {The space missions Voyager and Cassini together with earthbound observations revealed a wealth of structures in Saturn's rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn's moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Furthermore, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed in the frame of hydrodynamical modeling of Saturn's dense rings. For this purpose we will characterize the physical properties of the ring particle ensemble by mean field quantities and point to the special behavior of the transport coefficients. We show that unperturbed rings can become unstable and how diffusion acts in the rings. Additionally, the alternative streamline formalism is introduced to describe perturbed regions of dense rings with applications to the wake damping and the dispersion relation of the density waves.}, language = {en} } @misc{SeissSpahn2011, author = {Seiß, Martin and Spahn, Frank}, title = {Hydrodynamics of Saturn's dense rings}, series = {Postprints der Universit{\"a}t Potsdam : Postprint Mathematisch Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Postprint Mathematisch Naturwissenschaftliche Reihe}, doi = {10.25932/publishup-41313}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-413139}, pages = {191 -- 218}, year = {2011}, abstract = {The space missions Voyager and Cassini together with earthbound observations re-vealed a wealth of structures in Saturn's rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn's moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Further-more, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed in the frame of hydrodynamical modeling of Saturn's dense rings. For this purpose we will characterize the physical properties of the ring particle ensemble by mean field quantities and point to the special behavior of the transport coefficients. We show that unperturbed rings can become unstable and how diffusion acts in the rings. Additionally, the alternative streamline formalism is introduced to describe perturbed regions of dense rings with applications to the wake damping and the dispersion relation of the density waves.}, language = {en} } @article{SremcevicKrivovKruegeretal.2005, author = {Sremcevic, Miodrag and Krivov, Alexander V. and Kr{\"u}ger, Harald and Spahn, Frank}, title = {Impact-generated dust clouds around planetary satellites : model versus Galileo}, issn = {0032-0633}, year = {2005}, abstract = {This paper focuses on tenuous dust clouds of Jupiter's Galilean moons Europa, Ganymede and Callisto. In a companion paper (Sremcevic et al., Planet. Space Sci. 51 (2003) 455-471) an analytical model of impact-generated ejecta dust clouds surrounding planetary satellites has been developed. The main aim of the model is to predict the asymmetries in the dust clouds which may arise from the orbital motion of the parent body through a field of impactors. The Galileo dust detector data from flybys at Europa, Ganymede and Callisto are compatible with the model, assuming projectiles to be interplanetary micrometeoroids. The analysis of the data suggests that two interplanetary impactor populations are most likely the source of the measured dust clouds: impactors with isotropically distributed velocities and micrometeoroids in retrograde orbits. Other impactor populations, namely those originating in the Jovian system, or interplanetary projectiles with low orbital eccentricities and inclinations, or interstellar stream particles, can be ruled out by the statistical analysis of the data. The data analysis also suggests that the mean ejecta velocity angle to the normal at the satellite surface is around 30°, which is in agreement with laboratory studies of the hypervelocity impacts. © 2004 Elsevier Ltd. All rights reserved}, language = {en} } @article{HsuSchmidtKempfetal.2018, author = {Hsu, Hsiang-Wen and Schmidt, J{\"u}rgen and Kempf, Sascha and Postberg, Frank and Moragas-Klostermeyer, Georg and Seiss, Martin and Hoffmann, Holger and Burton, Marcia and Ye, ShengYi and Kurth, William S. and Horanyi, Mihaly and Khawaja, Nozair and Spahn, Frank and Schirdewahn, Daniel and Moore, Luke and Cuzzi, Jeff and Jones, Geraint H. and Srama, Ralf}, title = {In situ collection of dust grains falling from Saturn's rings into its atmosphere}, series = {Science}, volume = {362}, journal = {Science}, number = {6410}, publisher = {American Assoc. for the Advancement of Science}, address = {Washington}, issn = {0036-8075}, doi = {10.1126/science.aat3185}, pages = {49 -- +}, year = {2018}, abstract = {Saturn's main rings are composed of >95\% water ice, and the nature of the remaining few percent has remained unclear. The Cassini spacecraft's traversals between Saturn and its innermost D ring allowed its cosmic dust analyzer (CDA) to collect material released from the main rings and to characterize the ring material infall into Saturn. We report the direct in situ detection of material from Saturn's dense rings by the CDA impact mass spectrometer. Most detected grains are a few tens of nanometers in size and dynamically associated with the previously inferred "ring rain." Silicate and water-ice grains were identified, in proportions that vary with latitude. Silicate grains constitute up to 30\% of infalling grains, a higher percentage than the bulk silicate content of the rings.}, language = {en} } @article{SramaKempfMoragasKlostermeyeretal.2006, author = {Srama, Ralf and Kempf, S. and Moragas-Klostermeyer, Georg and Helfert, S. and Ahrens, T. J. and Altobelli, N. and Auer, S. and Beckmann, U. and Bradley, J. G. and Burton, M. and Dikarev, V. V. and Economou, T. and Fechtig, H. and Green, S. F. and Grande, M. and Havnes, O. and Hillierf, J.K. and Horanyii, M. and Igenbergsj, E. and Jessberger, E. K. and Johnson, T. V. and Kr{\"u}ger, H. and Matt, G. and McBride, N. and Mocker, A. and Lamy, P. and Linkert, D. and Linkert, G. and Lura, F. and McDonnell, J.A.M. and M{\"o}hlmann, D. and Morfill, G. E. and Postberg, F. and Roy, M. and Schwehm, G.H. and Spahn, Frank and Svestka, J. and Tschernjawski, V. and Tuzzolino, A. J. and W{\"a}sch, R. and Gr{\"u}n, E.}, title = {In situ dust measurements in the inner Saturnian system}, series = {Planetary and space science}, volume = {54}, journal = {Planetary and space science}, number = {9-10}, publisher = {Elsevier}, address = {Oxford}, issn = {0032-0633}, doi = {10.1016/j.pss.2006.05.021}, pages = {967 -- 987}, year = {2006}, abstract = {In July 2004 the Cassini-Huygens mission reached the Saturnian system and started its orbital tour. A total of 75 orbits will be carried out during the primary mission until August 2008. In these four years Cassini crosses the ring plane 150 times and spends approx. 400 h within Titan's orbit. The Cosmic Dust Analyser (CDA) onboard Cassini characterises the dust environment with its extended E ring and embedded moons. Here, we focus on the CDA results of the first year and we present the Dust Analyser (DA) data within Titan's orbit. This paper does investigate High Rate Detector data and dust composition measurements. The authors focus on the analysis of impact rates, which were strongly variable primarily due to changes of the spacecraft pointing. An overview is given about the ring plane crossings and the DA counter measurements. The DA dust impact rates are compared with the DA boresight configuration around all ring plane crossings between June 2004 and July 2005. Dust impacts were registered at altitudes as high as 100 000 km above the ring plane at distances from Saturn between 4 and 10 Saturn radii. In those regions the dust density of particles bigger than 0.5 can reach values of 0.001m-3.}, language = {en} }