The beta angle, an angle formed by the sunlight and a spacecraft orbital plane, is an important parameter for science orbit design of orbiter missions. This angle defines lighting conditions and eclipse occurrences, and is used for science observation planning. Not only is this parameter perturbed by the irregular gravity field of the primary body, it varies with the body’s motion around the Sun. Investigating

The nutations of Mars are about to be estimated to a few milliarcseconds accuracy with the radioscience experiments onboard InSight and ExoMars 2022. The contribution to the nutations due to the liquid core and tidal deformations will be detected, allowing to constrain the interior of Mars. To avoid introducing systematic errors in the determination of the core properties, an accurate precession and

To describe the rotation of a “rigid mantle + liquid core” system, the Poincaré–Hough–Zhukovsky equations are used. An analysis is made of the previously obtained (Ol’shanskii in Celest Mech Dyn Astron 131(12):Article number:57, 2019) conditions for regular precession of a system that does not have an axial symmetry. Upon receipt of the conditions, it is considered that the external torque can be neglected

The circular restricted three-body model is widely used for astrodynamical studies in systems where two major bodies are present. However, this model relies on many simplifications, such as point-mass gravity and planar, circular orbits of the bodies, and limiting its accuracy. In an effort to achieve higher-fidelity results while maintaining the autonomous simplicity of the classic model, we employ

Over the course of the last decade, observations of highly inclined (orbital inclination i > 60\(^\circ \)) trans-Neptunian objects (TNOs) have posed an important challenge to current models of solar system formation (Levison et al. in Icarus 196(1):258–273, 2008; Nesvorný in Astron J 150:73, 2015). These remarkable minor planets necessitate the presence of a distant reservoir of strongly out-of-plane

A previous study showed that a fingerprint of the initial shape of synthetic Oort clouds was detectable in the flux of “new” long-period comets. The present study aims to explain in detail how such a fingerprint is propagated by different classes of observable comets to improve the detection of fingerprints. It appears that three main long-term behaviors of observable comets are involved in this propagation:

This work introduces two Monte Carlo (MC)-based sampling methods, known as line sampling and subset simulation, to improve the performance of standard MC analyses in the context of asteroid impact risk assessment. Both techniques sample the initial uncertainty region in different ways, with the result of either providing a more accurate estimate of the impact probability or reducing the number of required

The stable distant retrograde orbits (DROs) around the Moon are considered as potential parking orbits for cislunar stations that are important facilities in cislunar space. Transfer orbits from DROs to lunar orbits will be fundamental and routine for operations of the cislunar stations. This paper studies transfer orbits from DROs to low lunar orbits with inclinations between 0° and 90°. Ten DROs

We deal with the orbit determination problem for a class of maps of the cylinder generalizing the Chirikov standard map. The problem consists of determining the initial conditions and other parameters of an orbit from some observations. A solution to this problem goes back to Gauss and leads to the least squares method. Since the observations admit errors, the solution comes with a confidence region

We prove the existence of periodic orbits of the two fixed centers problem bifurcating from the Kepler problem. We provide the analytical expressions of these periodic orbits when the mass parameter of the system is sufficiently small.

The set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equilateral restricted four-body problem admits certain simple homoclinic orbits which form the skeleton of the complete homoclinic intersection—or homoclinic web. In the present work, the planar restricted four-body problem is viewed as an invariant subsystem of the spatial problem, and the influence of this

In the first paragraph of the Introduction, the last sentence should read as “ Vinti.

Spacecraft and natural objects orbiting an active comet are perturbed by gas drag from the coma. These gases expand radially at about 0.5 km/s, much faster than orbital velocities that are on the order of meters per second. The coma has complex gas distributions and is difficult to model. Accelerations from gas drag can be on the same order of gravity and are currently poorly understood. Semi-analytical

Luna 3 (or Lunik 3 in Russian sources) was the first spacecraft to perform a flyby of the Moon. Launched in October 1959 on a translunar trajectory with large semimajor axis and eccentricity, it collided with the Earth in late March 1960. The short, 6-month dynamical lifetime has often been explained through an increase in eccentricity due to the Lidov–Kozai effect. However, the classical Lidov–Kozai

We study planar and three-dimensional retrograde periodic orbits, using the model of the restricted three-body problem (RTBP) with the Sun and Neptune as primaries and focusing on the dynamics of resonant trans-Neptunian objects (TNOs). The position and the stability character of the periodic orbits can provide important piece of information on the stability and long-term evolution of small TNOs in

We perform statistical wavelet analysis of the Main Belt asteroids, seeking statistically significant asteroid families. The goal is to test the new wavelet analysis algorithm and to compare its results with more traditional methods like the hierarchic clustering. We first consider several 1D distributions for various physical and orbital parameters of asteroids. Then, we consider three bivariate distributions

The current giant planet region is a transitional zone where transneptunian objects (TNOs) cross in their way to becoming Jupiter Family Comets. Their dynamical behavior is conditioned by the intrinsic dynamical features of TNOs and also by the encounters with the giant planets. We address the Giant Planet Crossing (GPC) population (those objects with 5.2 au \(< q < 30\,\hbox {au}\)) studying their

We consider, after Albouy–Moeckel, the inverse problem for collinear central configurations: Given a collinear configuration of n bodies, find positive masses which make it central. We give some new estimates concerning the positivity of Albouy–Moeckel Pfaffians: We show that for any homogeneity \(\alpha \) and \(n\le 6\) or \(n\le 10\) and \(\alpha =1\) (computer assisted) the Pfaffians are positive

Third-body perturbations have been extensively studied in recent years. Almost all previous works, however, assumed that the perturbations are caused by a third body that orbits the primary on a radius larger than the semimajor axis of the perturbed object. This assumption is justified as long as the primary is not accompanied by a third body in close orbit. In this work, we present an analytic model

The exploration of small bodies in the Solar system and the ability to perform remote or in situ science is tied to the understanding of the dynamical environment of such objects. As such, the evaluation of the gravity field arising from small bodies is key to this understanding. However, remote observations can only produce shape estimates, from which only uncertain gravity fields can be computed

Near rectilinear halo orbits (NRHOs), a subset of the \(L_1\) and \(L_2\) halo orbit families, are strong candidates for a future inhabited facility in line with the goals for NASA’s long-term cislunar transportation network. Higher-period dynamical structures that bifurcate from the NRHO region of the \(L_2\) halo family offer additional insight into motion departing from or arriving into the vicinity

We examine a 2-DOF Hamiltonian system modeling some previously unexplored dynamical effects in first-order mean motion resonances in the spatial circular restricted three-body problem “star-planet-asteroid.” In distinction from the well-known integrable model of Sessin and Ferraz-Mello (Celest Mech Dyn Astron 32:307–332, 1984) and Wisdom (Celest Mech Dyn Astron 38:175–180, 1986), in our analysis, we

The existence of Lagrange coefficients under two-body dynamics is well known, and the concept forms the basis of robust algorithms for solving a variety of fundamental astrodynamics problems. The Lagrange coefficients are generalized to Vinti theory in the present work, where the Vinti potential describes the dynamics of small objects like spacecraft orbiting an oblate body. Exact expressions for the

Having 50 years of unique observations, lunar laser ranging (LLR) is used to test central elements of Einstein’s theory of relativity, like a possible temporal variation of the gravitational constant or metric parameters. Here, we focused on a possible violation of the equivalence principle (EP) due to assumed dark matter in the galactic center. According to the EP, Earth and Moon experience the same

The Colombo top is a basic model in the rotation dynamics of a celestial body moving on a precessing orbit and perturbed by a gravitational torque. The paper presents a detailed study of analytical solution to this problem. By solving algebraic equations of degree 4, we provide the expressions for the extreme points of trajectories as functions of their energy. The location of stationary points (known

The increasing interest towards exploring small bodies in the Solar system has paved the way for the investigation of different gravity field models allowing robust orbit design and dynamical environment characterization. Among these, the spherical harmonics representation and the polyhedral gravity model are the most employed and studied—the former for historical reasons and the latter due to the

The Kepler potential \(\propto {-1/r}\) and the harmonic potential \(\propto r^2\) share the following remarkable property: In either of these potentials, a bound test particle orbits with a radial period that is independent of its angular momentum. For this reason, the Kepler and harmonic potentials are called isochrone. In this paper, we solve the following general problem: Are there any other isochrone

The purpose of this work is to determine the location and stability of the Cassini states of a celestial body with an inviscid fluid core surrounded by a perfectly rigid mantle. Both situations where the rotation speed is either non-resonant or trapped in a \(p\!:\!1\) spin–orbit resonance where p is a half integer are addressed. The rotation dynamics is described by the Poincaré–Hough model which

We propose an adaptation of the semilinear algorithm for the prediction of the impact corridor on ground of an Earth-impacting asteroid. The proposed algorithm provides an efficient tool, able to reliably predict the impact regions at fixed altitudes above ground with 5 orders of magnitudes less computations than Monte Carlo approaches. Efficiency is crucial when dealing with imminent impactors, which

This work focuses on the definition of satellite constellations whose secular relative distributions are invariant under the perturbation produced by the Earth gravitational potential. This is done by defining the satellite distribution directly in the Earth-Centered–Earth-Fixed frame of reference and using the along-track time distances between satellites to define the satellite constellation configuration

In this work, we consider the Kepler problem with a family of singular dissipations of the form \(-\frac{k}{|x|^\beta }\dot{x},\quad k>0, \beta >0.\) We present some results about the qualitative dynamics as \(\beta \) increases from zero (linear drag) to infinity. In particular, we detect some threshold values of \(\beta \), for which qualitative changes in the global dynamics occur. In the case \(\beta

Designing optimal spacecraft trajectories is a critical task for any mission design. In particular, mission designers seek to exploit from the combined effects of planetary gravity-assist maneuvers and electric propulsions systems to reduce both the flight time and propellant consumption. In order to obtain more realistic results, disturbances such as (1) gravitational force of secondary bodies, (2)

This paper presents a novel method to obtain the solution to the initial orbit determination problem for optical observations as a continuum of orbits—namely the orbit set—that fits the set of acquired observations within a prescribed accuracy. Differential algebra is exploited to analytically link the uncertainty in the observations to the state of the orbiting body with truncated power series, thus

Establishing long-term relative bounded motion between orbits in perturbed dynamics is a key challenge in astrodynamics to enable cluster flight with minimum propellant expenditure. In this work, we present an approach that allows for the design of long-term relative bounded motion considering a zonal gravitational model. Entire sets of orbits are obtained via high-order Taylor expansions of Poincarè

Based on Gauss’s variational equations (GVEs), the impulsive orbital-element corrections are investigated in orbit transfer problems. Both single impulse and multiple impulses are considered for the first-order and second-order GVEs. For the single impulse, a nonlinear least-squares iteration method for the minimum orbit error is provided to simultaneously solve for the impulse vector and the impulse

This article reviews the different mechanisms affecting the orbits of trans-Neptunian objects, ranging from internal perturbations (planetary scattering, mean-motion resonances, and secular effects) to external perturbations (galactic tides and passing stars). We outline the theoretical tools that can be used to model and study them, focussing on analytical approaches. We eventually compare these mechanisms

The bicircular model is a periodic time-dependent perturbation of the Earth–Moon restricted three-body problem that includes the direct gravitational effect of the Sun on the infinitesimal particle. In this paper, we focus on the dynamics in the neighbourhood of the \(L_1\) point of the Earth–Moon system. By means of a periodic time-dependent reduction to the centre manifold, we show the existence

We present a new method for computing orbits in the perturbed two-body problem: the position and velocity vectors of the propagated object in Cartesian coordinates are replaced by eight orbital elements, i.e. constants of the unperturbed motion. The proposed elements are uniformly valid for any value of the total energy. Their definition stems from the idea of applying Sundman’s time transformation

We propose a semianalytical method for the calculation of widths, libration centers and small-amplitude libration periods of the mean motion resonances \(k_p\):k in the framework of the circular restricted three-body problem valid for arbitrary eccentricities and inclinations. Applying the model to the trans-Neptunian region, we obtain several atlas of resonances between 30 and 100 au, showing their

In this paper, the feasibility of exploiting the Sun’s gravitational force to design the final phase (capture and orbit circularisation) to Mercury with a low propellant consumption has been investigated. The initial conditions, on the eccentricity and argument of pericentre, for the circularisation phase are obtained from a prime integral of motion, which takes place when the probe moves over a polar

Several dynamical systems of interest in Celestial Mechanics can be written in the form of a Newton equation with time-dependent damping, linear in the velocities. For instance, the modified Kepler problem, the spin–orbit model and the Lane–Emden equation all belong to such class. In this work, we start an investigation of these models from the point of view of contact geometry. In particular, we focus

We study the possible values of the nodal distance \(\delta _\mathrm{nod}\) between two non-coplanar Keplerian trajectories \(\mathcal{A}, \mathcal{A}'\) with a common focus. In particular, given \(\mathcal{A}'\) and assuming it is bounded, we compute optimal lower and upper bounds for \(\delta _\mathrm{nod}\) as functions of a selected pair of orbital elements of \(\mathcal{A}\), when the other elements

When building a space catalogue, it is necessary to acquire multiple observations of the same object for the estimated state to be considered meaningful. A first concern is then to establish whether different sets of observations belong to the same object, which is the association problem. Due to illumination constraints and adopted observation strategies, small objects may be detected on short arcs

This paper considers the energy required for collections of finite-density bodies to undergo escape under internal gravitational interactions alone. As the level of the system energy is increased, there are different combinations of components that can escape, until the total energy becomes positive, when the entire system can undergo mutual disruption. The results are also defined for bodies modeled

Massive gaseous nebula has been a key element to formation of large solid objects (planetesimals, giant planet cores) in the early phase of the Solar system evolution. Here, we focus on its effects during the stage when giant planets have already fully formed. Dynamical effects of the nebula on motion of planetesimals stirred by planets were twofold: (i) global gravitational acceleration, and (ii)

Cosmological N-body simulations are done on massively parallel computers. This necessitates the use of simple time integrators and, additionally, of mesh-grid approximations of the potentials. Recently, Adamek et al. (Nat Phys 12:346, 2016), Barrera-Hinojosa and Li (GRAMSES: a new route to general relativistic N-body simulations in cosmology—I. Methodology and code description, 2019) have developed

We revisit the problem of secular resonance sweeping during the dissipation of a protoplanetary disk and its possible role in exciting the orbits of primordial asteroids, in light of recent models of Solar system evolution. We develop an integrator that incorporates the gravitational effect of a uniformly (or not) depleting, axisymmetric disk with arbitrary surface density profile; its performance

The end-of-life disposal of Galileo satellites is needed to avoid collisions with operational spacecraft and to prevent the generation of space debris. Either disposal into stable graveyard orbits or disposal into the atmosphere exploiting eccentricity growth caused by lunisolar resonances is possible. However, there is a concern about the predictability of medium Earth orbits because of possible chaotic

The coupled attitude and orbit dynamics of solar sails is studied. The shape of the sail is a simplified quasi-rhombic pyramid that provides the structure helio-stability properties. After adimensionalization, the system is put in the form of a fast–slow dynamical system where the different timescales are explicitly related to the physical parameters of the system. The orientation of the body frame

Four expressions involving sums of position and velocity coordinates bounding the total angular momentum of particle systems, and by extension of any continuous or discontinuous material systems, are derived which are tighter for any particle configuration than similar inequalities derived by Sundman (Acta Math 36:105, 1913), Saari (Conference board of the mathematical sciences, No. 104, 2005. http://books

To describe the rotation of a rigid body with an ellipsoidal cavity filled with an ideal vorticated liquid, the Poincaré–Hough–Zhukovsky equations are used. It is obtained constraints (hereinafter referred to as configuration conditions) on the mass distribution and cavity dimensions of an asymmetric liquid-filled rigid body under which the rigid body can perform the regular precession. Two possible

This paper deals with the rotation and figure evolution of a planet near the 3/2 spin–orbit resonance and the exploration of a new formulation of the creep tide theory (Folonier et al. in Celest Mech Dyn Astron 130:78, 2018). This new formulation is composed by a system of differential equations for the figure and the rotation of the body simultaneously (which is the same system of equations used in

The increasing number of free-floating planets discovered in recent years confirms earlier theoretical predictions and leads us to believe that the possibility of such an object intruding an existing planetary system is not negligible, especially in dense clusters. We present a theoretical dynamical study on the interaction of a free-floating planet (hereafter FFP) with an initially bound star–planet

In our unitary description (Vivarelli in Meccanica 50:915–925, 2015) of the Kepler problem (obtained via the introduction of a simple structure, the primigenial sphere \(S_{p^{-1}}\)), we have shown that this sphere encompasses, in a sort of inbred order of its elements, several fundamental elements of the Kepler problem. In this paper, we show that also the mechanical energy of an elliptic Kepler

The first part of the present paper reveals interplays among invariant manifolds emanating from planar Lyapunov orbits around the three collinear Lagrange points \(L_1, L_2\), and \(L_3\) for high energies. Once the energetically forbidden region vanishes, the invariant manifolds together form closed separatrices bounding transit orbits in the phase space, deviating from the low-energy picture of invariant

We present a numerical study of the application of the Shannon entropy technique to the planar restricted three-body problem in the vicinity of first-order interior mean-motion resonances with the perturber. We estimate the diffusion coefficient for a series of initial conditions and compare the results with calculations obtained from the time evolution of the variance in the semimajor axis and eccentricity

A finite element method (FEM) for computing the gravitational interactions between two arbitrarily shaped celestial bodies is proposed. Expressions for the gravitational potential, attraction and torques are derived in terms of the finite element mesh division and mass density distribution. This method is implemented to a parallel-simulation package on a local cluster. Benchmarking tests are performed

Lambert’s problem is the two-point boundary value problem for Keplerian dynamics. The parameter and solution space is surveyed for both the zero- and multiple-revolution problems, including a detailed look at the stress cases that typically plague Lambert solvers. The problem domain, independent of formulation, is shown to be rectangular for each revolution case, making the elusive initial guess and

We investigate the dynamics of charged dust close to outer mean-motion resonances with planet Jupiter. The importance of the interplanetary magnetic field on the orbital evolution of dust is clearly demonstrated. New dynamical phenomena are found that do not exist in the classical problem of uncharged dust. We find changes in the orientation of the orbital planes of dust particles, an increased amount

Inspired by the original developments of recursive power series by means of Lagrange invariants for the classical two-body problem, a new analytic continuation algorithm is presented and studied. The method utilizes kinematic transformation scalar variables differentiated to arbitrary order to generate the required power series coefficients. The present formulation is extended to accommodate the spherical