An interdisciplinary course about Mars for teachers and science students is presented. The focus of the course is on planning for a journey with humans to the planet Mars. Issues in ethics, morality, rights and obligations, conflict management and human psychology as well as rocket orbits, fuel economy, radiation hazards and knowledge of the solar system are included. Examination of the teacher students include interpretation of the course material for future pedagogical usage.

Cultural astronomy is the study of the astronomy of ancient cultures and is sometimes called the anthropology of astronomy. The many ways that astronomy was used by ancient cultures are fascinating and this can be used to inspire interest in all astronomy, as well as astronomy in culture. Archaeoastronomy is interdisciplinary and among its practitioners are not only astronomers and astrophysicists, but also anthropologists, archaeologists, and Indigenous scholars. Much can be learned about ancient cultures though examination of how and why they used astronomy. This paper will highlight several examples that can capture public attention.

The growth of the Internet has facilitated the easy availability of resources for teaching astronomy and doing astronomy outreach. This overview concentrates on resources that are free or open access. Basic teaching materials like textbooks and lab activities can be found, along with higher level items such as concept inventories and interactive instructional tools. There is also a small but growing research literature on astronomy instruction to be found online. Astronomers engaged in outreach can have access to large image collections, tools for doing citizen science, and planetarium apps. These resources are of enormous value to both novice and seasoned instructors, and anyone conveying the excitement of astronomy to a public audience.

Intensive week-long Summer Schools in Statistics for Astronomers were initiated at Penn State in 2005 and have been continued annually. Due to their popularity and high demand, additional full summer schools have been organized in India, Brazil, Space Telescope Science Institute.

The Summer Schools seek to give a broad exposure to fundamental concepts and a wide range of resulting methods across many fields of statistics. The Summer Schools in statistics and data analysis for young astronomers present concepts and methodologies with hands on tutorials using the data from astronomical surveys.

Based on observations by Bailer-Jones et al. (2018) who propose a close fly-by of the K-type star Gliese 710 in approximately 1.36 Myr we investigate the immediate influence of the stellar passage on trajectories of Oort cloud objects. Using a newly developed GPU-based N-body code (Zimmermann (2021)) we study the motion of 3.6 million testparticles in the outer Solar system where the comets are distributed in three different “layers” around the Sun and the 4 giant planets. We study the immediate influence of Gliese 710 at three passage distances of 12000, 4300, and 1200 au. Additionally, different inclinations of the approaching star are considered. Depending on the passage distance a small number of comets (mainly from the disk and flared disk) is scattered into the observable region (< 5 au) around the Sun. In addition, a huge number of comets (mainly the ones directly in the path of the passing star) shows significant changes of their perihelia. But, they will enter the inner Solar system a long time after the stellar fly-by depending on their dynamical evolution.

Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using non-perturbative numerical analyses, making use of Poincaré sections but from a different perspective relative to previous implementations of this method. This perspective reveals fine structure of resonances which otherwise remains hidden in conventional approaches, including analytical, semi-analytical and numerical-averaging approaches based on the critical resonant angle. At low eccentricity, first order resonances do not have diverging widths but have two asymmetric branches leading away from the nominal resonance location. A sequence of structures called “low-eccentricity resonant bridges” connecting neighboring resonances is revealed. At planet-grazing eccentricity, the true resonance width is non-divergent. At higher eccentricities, the new results reveal hitherto unknown resonant structures and show that these parameter regions have a loss of some – though not necessarily entire – resonance libration zones to chaos. The chaos at high eccentricities was previously attributed to the overlap of neighboring resonances. The new results reveal the additional role of bifurcations and co-existence of phase-shifted resonance zones at higher eccentricities. By employing a geometric point of view, we relate the high eccentricity phase space structures and their transitions to the shapes of resonant orbits in the rotating frame. We outline some directions for future research to advance understanding of the dynamics of mean motion resonances.

We present a closed-form normalization method suitable for the study of the secular dynamics of small bodies inside the trajectory of Jupiter. The method is based on a convenient use of a book-keeping parameter introduced not only in the Lie series organization but also in the Poisson bracket structure employed in all perturbative steps. In particular, we show how the above scheme leads to a redefinition of the remainder of the normal form at every step of the formal solution of the homological equation. An application is given for the semi-analytical representation of the orbits of main belt asteroids.

In Karydis et al. (2021) we have introduced the method of shape continuation in order to obtain periodic orbits in the complex gravitational field of an irregularly-shaped asteroid starting from a symmetric simple model. What’s more, we map the families of periodic orbits of the simple model to families of the real asteroid model. The introduction of asymmetries in a gravitational potential may significantly affect the dynamical properties of the families. In this paper, we discuss the effect of the asymmetries in the neighborhood of vertically critical orbits, where, in the symmetric model, bifurcations of 3D periodic orbit families occur. When asymmetries are introduced, we demonstrate that two possible continuation schemes can take place in general. Numerical simulations, using an ellipsoid and a mascon model of 433-Eros, verify the existence of these schemes.

Empirically characterizing the spectral evolution of cool white dwarfs is a prerequisite to understanding the physical processes that shape the evolution of these old objects. However, the high photospheric densities of cool helium-rich atmospheres seriously complicate the study of those stars. We have recently developed an updated atmosphere code that is appropriate for high densities and that can model any cool white dwarf (including DZs and DQpecs). Here, we present recent advances in our understanding of the spectral evolution of cool white dwarfs that were made possible thanks to these improved models. We discuss in particular the evolution of the hydrogen-rich to helium-rich ratio at low effective temperatures as well as the DQ→ DQpec transition.

We revisit the problem of the secular dynamics in two-planet systems in which the planetary orbits exhibit a high value of the mutual inclination. We propose a ‘basic hamiltonian model’ for secular dynamics, parameterized in terms of the system’s Angular Momentum Deficit (AMD). The secular Hamiltonian can be obtained in closed form, using multipole expansions in powers of the distance ratio between the planets, or in the usual Laplace-Lagrange form. The main features of the phase space (number and stability of periodic orbits, bifurcations from the main apsidal corotation resonances, Kozai resonance etc.) can all be recovered by choosing the corresponding terms in the ‘basic Hamiltonian’. Applications include the semi-analytical determination of the actual orbital state of the system using Hamiltonian normalization techniques. An example is discussed referring to the system of two outermost planets of the ν-Andromedae system.

Recent GAIA observations revealed that the K-type star Gliese 710 will cross the Oort cloud in a distance between approximately 4000 and 12000 au in about 1.3 Myrs. This occurrence motivated us to study the influence of a stellar encounter on comets in the outer region of the solar system. Even if the Oort cloud extends to 100000 au from the sun, we restrict our study to the region between 30 and 25000 au where 25 million objects are distributed randomly. Comets at larger distances are not taken into account as they hardly enter the observable region after a single stellar fly-by. An overview of all objects that are scattered towards the sun for the different fly-by distances at 4000, 8000 and 12000 au shows that only a handful of objects are moving towards the sun immediately after the stellar encounter.

However, a subsequent long-term study of all objects that are moved into highly eccentric motion by the stellar fly-by shows a significant increase of comets crossing Jupiter’s orbit and entering into the observable region. In addition, our study shows the first comets crossing the orbit of Earth only about 2.5 Myrs after the stellar fly-by. Thus, the impact risk for the Earth increases only some million years after the stellar fly-by.

By means of numerical simulations we study the radial-orbit instability in anisotropic self-gravitating N–body systems under the effect of noise. We find that the presence of additive or multiplicative noise has a different effect on the onset of the instability, depending on the initial value of the orbital anisotropy.

Planetary material in the atmospheres of white dwarfs is thought to be scattered inwards from outer planetary systems. Dusty emission in the infrared traces the accretion. As the scattering of many small asteroids is a stochastic process, variability in the infrared emission is predicted. We report a 3 year near-infrared (J, H and K) monitoring campaign of 34 dusty, polluted white dwarfs which aims to search for dust emission variability. We find all white dwarfs have consistent near-infrared fluxes, implying the excess emission is stable. This suggests tidal disruption events which lead to large variabilities are rare and quick (<1 year) and become stable within a few years. For WD 0408–041, the system that shows both increases and decreases in dust emission over 11 years, our K band data suggest a potential colour change associated with the dust emission that needs further confirmation.

Many intermediate polars are hard X-ray sources. The theory of their hard X-ray radiation is well developed and allows us to determine white dwarf masse in this kind of cataclysmic variables. Here we present the results of determination the masses of 35 white dwarfs in the intermediate polars observed by observatories NuSTAR (10 sources) and Swift/BAT (25 sources). The corresponding mass accrerion rates and the luminosity function were also derived due to accurate distance to the sources well known now after Gaia DR2.

We consider four- and five-body problems with symmetrical masses (Caledonian problems). Families of periodic orbits originate from the collinear Schubart orbits. We present and discuss some of these periodic orbits.

We have shown that in the inner belt the loss of asteroids from the ν6 secular resonance and the 3:1 Jovian mean motion resonance accounts for the observation that the mean size of the asteroids increases with increasing orbital inclination. We have used that observation to constrain the Yarkovsky loss timescale and to show that the family asteroids are embedded in a background population of old ghost families. We argue that all the asteroids in the inner belt originated from a small number of asteroids and that the initial mass of the belt was similar to that of the present belt. We also show that the observed size frequency distribution of the Vesta asteroid family was determined by the action of Yarkovsky forces, and that the age of this family is comparable to the age of the solar system.

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.

The shape of the luminosity function of white dwarfs (WDLF) is sensitive to the characteristic cooling time and, therefore, it can be used to test the existence of additional sources or sinks of energy such as those predicted by alternative physical theories. However, because of the degeneracy between the physical properties of white dwarfs and the properties of the Galaxy, the star formation history (SFH) and the IMF, it is almost always possible to explain any anomaly as an artifact introduced by the star formation rate. To circumvent this problem there are at least two possibilities, the analysis of the WDLF in populations with different stories, like disc and halo, and the search of effects not correlated with the SFH. These procedures are illustrated with the case of axions.

Circumstellar discs are known to exist in great variety, from gas-rich discs around the youngest stars to evolved debris discs such as the solar system’s zodiacal cloud. Through gravitational interaction, exoplanets embedded in these discs can generate density variations, imposing potentially observable structural features on the disc such as rings or gaps. Here we report on a mirrored double crescent pattern arising in simulations of discs harbouring a small, moderately eccentric planet - such as Mars. We show that the structure is a result of a directed apsidal precession occurring in particles that migrate the planet’s orbital region under Poynting-Robertson drag. We further analyze the strength of this effect with respect to planet and particle parameters.

A powerful tool to investigate the stability of the orbits of natural and artificial bodies is represented by perturbation theory, which allows one to provide normal form estimates for nearly-integrable problems in Celestial Mechanics. In particular, we consider the orbital stability of point-mass satellites moving around the Earth. On the basis of the J 2 model, we investigate the stability of the semimajor axis. Using a secular Hamiltonian model including also lunisolar perturbations, the so-called geolunisolar model, we study the stability of the other orbital elements, namely the eccentricity and the inclination. We finally discuss the applicability of Nekhoroshev’s theorem on the exponential stability of the action variables. To this end, we investigate the non-degeneracy properties of the J 2 and geolunisolar models. We obtain that the J 2 model satisfies a “three-jet” non-degeneracy condition, while the geolunisolar model is quasi-convex non-degenerate.