Christoph Lhotka - Academia.edu (original) (raw)

Papers by Christoph Lhotka

HAL (Le Centre pour la Communication Scientifique Directe), Sep 27, 2015

VizieR Online Data Catalog, Jul 1, 2013

Proceedings of the International Astronomical Union, Oct 1, 2019

The Laplace resonance is a configuration that involves the commensurability between the mean moti... more The Laplace resonance is a configuration that involves the commensurability between the mean motions of three small bodies revolving around a massive central one. This resonance was first observed in the case of the three inner Galilean satellites, Io, Europa, and Ganymede. In this work the Laplace resonance is generalised by considering a system of three satellites orbiting a planet that are involved in mean motion resonances. These Laplace-like resonances are classified in three categories: first-order (2:1&2:1, 3:2&3:2, 2:1&3:2), second-order (3:1&3:1) and mixed-order resonances (2:1&3:1). In order to study the dynamics of the system we implement a model that includes the gravitational interaction with the central body, the mutual gravitational interactions of the satellites, the effects due to the oblateness of the central body and the secular interaction of a fourth satellite and a distant star. Along with these contributions we include the tidal interaction between the central body and the innermost satellite. We study the survival of the Laplace-like resonances and the evolution of the orbital elements of the satellites under the tidal effects. Moreover, we study the possibility of capture into resonance of the fourth satellite.

EGU General Assembly Conference Abstracts, Apr 1, 2015

Journal Of Geophysical Research: Space Physics, May 1, 2020

With the successful launch of the satellite mission Gravity Recovery and Climate Experiment (GRAC... more With the successful launch of the satellite mission Gravity Recovery and Climate Experiment (GRACE) Follow-On in May 2018 the opportunity arises to resume the analysis of accelerometer data regarding space weather induced perturbations of the Earth's thermosphere. On 21 August 2018 a complex interplanetary coronal mass ejections occurred on the Sun, which subsequently triggered an unexpected large geomagnetic storm on 26 August. We present a detailed analysis of the interplanetary coronal mass ejection eruption and explore the occurred perturbation of the neutral mass density in the upper Earth's atmosphere. Due to the heating and the subsequent expansion of the thermosphere also the drag force acting on the spacecraft is enhanced. This leads to an additional storm-induced orbit decay, which we calculate by means of variations in the semimajor axis. The evaluation is based on the utilization of accelerometer measurements from GRACE Follow-On. For the reduction of disturbing nongravitational forces we implemented a physical shadow function, which incorporates the Earth's oblateness and the atmospheric refraction and extinction. Additionally, the estimation of Earth's reradiation is now based on hourly measurements by the Clouds and the Earth's Radiant Energy System. The resulting atmospheric densities and orbit decays are compared with predictions from our preliminary thermospheric forecasting tool, which is based on the study by Krauss et al. (2018, https://doi.org/10.1029/2018JA025778). The evaluation shows that the maximum estimated orbit decay triggered by the geomagnetic storm on 26 August is in the order of approximately 8.2 m and thus in good accordance with the forecasted value (9.5 m)-predicted with a lead time of about 60 min.

The gas giants Jupiter and Neptune are known to host Trojans, and also Mars has co-orbiting aster... more The gas giants Jupiter and Neptune are known to host Trojans, and also Mars has co-orbiting asteroids. Recently, in an extensive numerical investigation ([8]) the possibility of captures of asteroids by the terrestrial planets and even the Earth into the 1:1 mean motion resonance (MMR) was studied. The first Earth Trojan has been observed ([2]) and found to be in a so-called tadpole orbit closed to the Lagrange point L 4. We did a detailed study of the actual orbit of this Trojan 2010 TK7 including the study of clone orbits, derived an analytical mapping in a simplified dynamical system (Sun+Earth+massless asteroid) and studied the phase space structure of the Earth's Lagrange points with respect to the eccentricities and the inclinations of a large number of fictitious Trojans. The extension of stable zones around the Lagrange points is established with the aid of dynamical mappings; the known Trojan 2010 TK7 finds himself inside an unstable zone.

Astronomy and Astrophysics, Sep 1, 2018

Context. The dramatic event of the 2029 close encounter between the Earth and the asteroid Apophi... more Context. The dramatic event of the 2029 close encounter between the Earth and the asteroid Apophis on April 13 2029 at a minimum distance of 38 400 km constitutes an opportunity to make investigations about the modeling of the rotational changes of the asteroid during the event. Aims. In this paper we deepen a previous study of the rotational changes of Apophis caused by gravitational effects during the close encounter, using important constraints on initial conditions brought by new recent observational data. We also evaluate the effects of the triaxial form of the asteroid on the motion of its axis of rotation in space, as well as the modifications of the spin rate due to tidal deformation. Methods. First we used more drastic constraints for the physical and geometrical parameters of Apophis, deduced from recent observational campaigns. Second we evaluated the disturbing potential due to the Earth depending not only on the asteroid flattening, but also on the component due to its triaxiality, to deduce the equations of motion and investigate the displacement of the spin axis. Third we estimated what should be the zonal deformation of the asteroid due to the tide exerted by the Earth during the close encounter and we measured the consequences on variations of the spin rate. Results. We show that the variations of obliquity and precession in longitude of Apophis during the 2029 close encounter can reach very large values, at the level of of respectiveley 1-10 • and 10-40 • depending on geometrical parameters. On the contrary, effects on the spin rate should be relatively small, leading to variations of the sidereal angle of rotation not exceeding 30 s. Conclusions. The tribute of this paper is to give a constrained model of the important rotational variations of Apophis during its 2029 close encounter with the Earth.

EGU General Assembly Conference Abstracts, Apr 1, 2017

Physics of Plasmas, 2020

We investigate the interaction of dust with space plasmas and spacecraft with a special focus on ... more We investigate the interaction of dust with space plasmas and spacecraft with a special focus on the typical values of equilibrium charge and the typical time scales required to reach them. It is well known that objects in space become charged through the combination of a number of different processes: the photoelectric effect, the collection of free electrons and ions from the plasma, and by secondary electron emission due to the impact of highly energetic particles. In the equilibrium state, currents between the plasma and the charged object are balanced. However, perturbations on the orbit of the charged body and perturbations of the distribution of plasma particles may lead to time dependent deviations in charge. In this study, we are interested in order of magnitude estimates of these deviations as well as the time scales on which a charged body in space recovers to the equilibrium charge. Our study includes Maxwellian and Kappa plasma particle distribution functions and the ro...

Planetary and Space Science, 2012

Mercury is the target of the space missions MESSENGER and BepiColombo, that will in particular ob... more Mercury is the target of the space missions MESSENGER and BepiColombo, that will in particular observe its rotation to get information on its internal structure. This requires a rigorous modelization of this rotation. A difficulty comes from the obliquity of Mercury, that ...

Monthly Notices of the Royal Astronomical Society

Observations of dust in the Solar system have indicated the existence of structures at higher ecl... more Observations of dust in the Solar system have indicated the existence of structures at higher ecliptic latitudes, the origin of which is still an ongoing debate. In a previous study, we studied how the interplanetary magnetic field affects the orbital motion of charged dust particles that are moving in co-orbital motion with Jupiter. Our findings revealed that the Lorentz force causes oscillations in orbital inclinations that lead to electromagnetic transport of the dust particles to higher ecliptic latitudes. In this work, using numerical simulations, we investigate how this transportation depends on orbital lifetime, strength of the background magnetic field, planetary mass, and distance from the Sun. In addition, we study the dynamics also outside resonance. We present our findings using the saturation curve, which gives a relation between the maximum amplitude in inclination with respect to the particle size ranging from 1 to 501 mu\mumum. We further study the influence of the sol...

Physica D: Nonlinear Phenomena

arXiv (Cornell University), Dec 28, 2022

We study the breakdown of rotational invariant tori by implementing three different methods. Firs... more We study the breakdown of rotational invariant tori by implementing three different methods. First, we analyze the domains of analyticity of a torus with given frequency through the computation of the Lindstedt series expansions of the embedding of the torus and the drift term. The Padé and log-Padé approximants provide the shape of the analyticity domains by plotting the poles of the polynomial at the denominator of the Padé approximants. Then, we implement a Newton's method to construct the embedding of the torus; the breakdown threshold is then computed by looking at the blow-up of the Sobolev's norms of the embedding. Finally, according to Greene's method, we estimate the breakdown threshold of an invariant torus with irrational frequency by looking at the stability of the periodic orbits with periods approximating the frequency of the torus. We apply these methods to 2-dimensional and 4-dimensional standard maps. The 2-dimensional maps can either be conservative (symplectic) or dissipative (precisely, conformally symplectic, namely a dissipative map with the geometric property to transform the symplectic form into a multiple of itself). The 4-dimensional maps are obtained coupling (i) two symplectic standard maps, or (ii) two conformally symplectic standard maps, or (iii) a symplectic and a conformally symplectic standard map. The conformally symplectic maps depend on a dissipative parameter and a drift term, which is needed to get the existence of invariant attractors. While Padé and Newton's methods perform quite well and provide reliable results, when applying Greene's method, the computation of the periodic orbits in higher dimensional, dissipative maps is particularly complex.

EGU General Assembly Conference Abstracts, Apr 1, 2019

Astronomy & Astrophysics, 2021

The first three Galilean satellites of Jupiter, Io, Europa, and Ganymede, move in a dynamical con... more The first three Galilean satellites of Jupiter, Io, Europa, and Ganymede, move in a dynamical configuration known as the Laplace resonance, which is characterized by a 2:1 ratio of the rates of variation in the mean longitudes of Io-Europa and a 2:1 ratio of Europa-Ganymede. We refer to this configuration as a 2:1&2:1 resonance. We generalize the Laplace resonance among three satellites, S1, S2, and S3, by considering different ratios of the mean-longitude variations. These resonances, which we call Laplace-like, are classified as first order in the cases of the 2:1&2:1, 3:2&3:2, and 2:1&3:2 resonances, second order in the case of the 3:1&3:1 resonance, and mixed order in the case of the 2:1&3:1 resonance. We consider a model that includes the gravitational interaction with the central body together with the effect due to its oblateness, the mutual gravitational influence of the satellites S1, S2, and S3 and the secular gravitational effect of a fourth satellite S4, which plays the ...