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.

Didymos and Dimorphos are primary and secondary, respectively, asteroids who compose a binary system that make up the set of Near Earth Asteroids (NEAs). They are targets of the Double Asteroid Redirection Test (DART), the first test mission dedicated to study of planetary defense, for which the main goal is to measure the changes caused after the secondary body is hit by a kinect impactor. The present work intends to conduct a study, through numerical integrations, on the dynamics of massless particles distributed in the vicinity of the two bodies. An approximate shape for the primary body was considered as a model of mass concentrations (mascons) and the secondary was considered as a massive point. Our results show the location and size of stable regions, and also their lifetime.

Missions to asteroids have been the trend in space exploration for the last years. They provide information about the formation and evolution of the Solar System, contribute to direct planetary defense tasks, and could be potentially exploited for resource mining. Be their purpose as it may, the factor that all these mission types have in common is the challenging dynamical environment they have to deal with. The gravitational environment of a certain asteroid is most of the times not accurately known until very late mission phases when the spacecraft has already orbited the body for some time.

Shape models help to estimate the gravitational potential with a density distribution assumption (usually constant value) and some optical measurements of the body. These measurements, unlike the ones needed for harmonic coefficient estimation, can be taken from well before arriving at the asteroid’s sphere of influence, which allows to obtain a better approximation of the gravitational dynamics much sooner. The disadvantage they pose is that obtaining acceleration values from these models implies a heavy computational burden on the on-board processing unit, which is very often too time-consuming for the mission profile.

In this paper, the technique developed on [1] is used to create a validated Python-based tool that obtains spherical harmonic coefficients from the shape model of an asteroid or comet, given a certain density for the body. This validated software suite, called AstroHarm, is used to analyse the accuracy of the models obtained and the improvements in computational efficiency in a simulated spacecraft orbiting a small body.

The results obtained are shown offering a qualitative comparison between different order spherical harmonic models and the original shape model. Finally, the creation of a catalogue for harmonics is proposed together with some thoughts on complex modelling using this tool.

The averaged four-planetary motion theory is constructed up to the third order in planetary masses. The equations of motion in averaged elements are numerically integrated for the Solar system’s giant planets for different initial conditions. The comparison of obtained results with the direct numerical integration of Newtonian equations of motion shows an excellent agreement with them. It suggests that this motion theory is constructed correctly. So, we can use this theory to investigate the dynamical evolution of various extrasolar planetary systems with moderate orbital eccentricities and inclinations.

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.

We present an updated public version of EPM (Ephemerides of Planets and the Moon). Since the last public version, EPM2017, many improvements were made in both the observational database and the mathematical model. Latest lunar laser ranging observations have been added, as well as radio ranges of Juno spacecraft and more recent ranges of Odyssey and Mars Reconnaissance Orbiter. EPM2021 uses a new improved way to calculate radio signal delays in solar plasma and has a major update in the method of determination of asteroid masses. Also, a delay-capable multistep numerical integrator was implemented for EPM in order to properly account for tide delay in the equations of the motion of the Moon. The improved processing accuracy has allowed to refine existing estimates of the mass of the Sun and its change rate, parameters of the Earth–Moon system, masses of the Main asteroid belt and the Kuiper belt; and also to raise important questions about existing numerical models of solar wind.

We have randomly selected 20 close asteroid pairs (younger than 800 kyr) from known pairs, and by the application of backward numerical integration we have calculated their orbits. For the reason of speeding up the process of making the resonances visible, we have used a high value of Yarkowsky drift. The results of the calculation show that only two pairs appear to have a simple resonance with Earth and Jupiter while half of the tested pairs are visibly in the vicinity of three-body resonances.

We have found a 2-1J-1M resonance for the pair (56232) 1999 JM31 and (115978) 2003 WQ56. Following our study of the pair (10123) Fideoja and (117306) 2004 VF21, we discovered a different resonance than the 7-2J mean motion resonance previously published: we have proved that this pair is perturbed by 9-6J-4M three body resonance.

We address the question of identifying the long-term (secular) stability regions in the semi-major axis-eccentricity projected phase space of the Sun-Jupiter planar circular restricted three-body problem in the domains i) below the curve of apsis equal to the planet’s orbital radius (ensuring protection from collisions) and ii) above that curve. This last domain contains several Jupiter’s crossing trajectories. We discuss the structure of the numerical stability map in the (a,e) plane in relation to manifold dynamics. We also present a closed-form perturbation theory for particles with non-crossing highly eccentric trajectories exterior to the planet’s trajectory. Starting with a multipole expansion of the barycentric Hamiltonian, our method carries out a sequence of normalizations by Lie series in closed-form and without relegation. We discuss the applicability of the method as a criterion for estimating the boundary of the domain of regular motion.

We present the developed methods of digitization, image processing, reduction, and scientific data mining with the latest reference catalogs, which allowed us to obtain a good positional and photometric accuracy in B-band of 6,500 asteroids down to 17.5 m from the Ukrainian Virtual Observatory database of astroplates. The archive includes FON-Kyiv, FON-Kitab, FON-Dushanbe sky surveys (1981–1996) and astroplates of the Baldone and Tautenburg observatories. For some of asteroids, observations are either completely absent or not enough over the certain time interval to the moments of their official discoveries (about 300 such objects were found). Positional observations during these time scales are highly useful for a more detailed study of the dynamics and orbital parameters of asteroids as well as the obtained photometric parameters are very complementary with present-day data for studying changes in brightness and light curves.

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.

Tidal evolution of low-eccentric circumbinary planets is expected to drive the rotational evolution toward a pseudo-synchronous solution. In this work, we present a study of the oscillation amplitudes around this state by considering that the two central stars exert creep tides on the planet. These amplitudes are computed by direct numerical integrations of the creep equations and also by means of the calculation of the coefficients of the periodic terms in this stationary solution. As in the two-body-problem, the planetary spin and lag-angle are observed to have maximum oscillation amplitudes for stiff bodies and almost null oscillation for the gaseous regime, while the opposite behaviour is observed in the equatorial and polar flattenings. Our analytical approximation shows to be very accurate and specially necessary for very-low eccentric planets. However, the magnitudes of the oscillation amplitudes around the pseudo-synchronous solution in the circumbinary problem appears to be very small respect to the mean value. Thus, considering these oscillation in the computation of the tidal energy dissipation may not have a substantial contribution in the results, at least compared to the case in which only the mean values are taken into account.

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.

We have found three new members of the Rampo asteroids family: 2009HD95, 2010VO19, 2013JF69. We estimated the Yarkovsky semimajor axis drift rate. Based on the simulation results, estimates of the asteroid pairs’ age included in the family are obtained. In the scenario of the cascade disruption of the parent body of the asteroid (10321) Rampo, one can note the concentration of estimates of the pairs’ age to values of 900, 750, 500, and 250 kyr.

Currently, the Transiting Exoplanet Survey Satellite (TESS) searches for Earth-size planets around nearby dwarf stars. To identify specific weak variations in the light curves of stars, sophisticated data processing methods and analysis of the light curve shapes should be developed and applied. We report some preliminary results of our project to find and identify minima in the light curves of stars collected by TESS and stored in the MAST (Mikulski Archive for Space Telescopes) database. We developed Python code to process the short-cadence (2-min) TESS PDCSAP (Pre-search Data Conditioning Simple Aperture Photometry) light curves. Our code allows us to create test samples to apply machine learning methods to classify minima in the light curves taking into account their morphological signatures. Our approach will be used to find and analyze some sporadic events in the observed light curves originating from transits of comet-like bodies.