Lunar frozen orbits revisited

An impulsive feedback control is developed to establish specie c relative orbits for spacecraft formation e ying. The relative orbit tracking errors are expressed in terms of mean orbit elements. The feedback control, based on Gauss’ s variational equations of motion, allows specie c orbit elements or orbit element sets to be controlled with minimal impact on the remaining osculating orbit elements. This is advantageous when J2-invariant orbits are to be controlled, where only the argument of perigee and mean anomaly will drift apart at equal and opposite rates. The advantage of this impulsive feedback control, compared to optimal control solutions, is that it can operate with little computational effort and in a near-optimal manner, whilerequiring only a marginal penalty in fuel cost. When applied to the spacecraft formation e ying problem, this control could also be used to perform general orbit corrections. Formulas are developed providing accurate estimates of the sensitivities of the mean semimajor axis and mean eccentricity with respect to the osculating inclination angle. With these sensitivities, the tracking error in semimajor axis, eccentricity, and inclination angle can be canceled within one orbit.

Understanding the long-term evolution of lunar orbit is an essential task in astronomy and astrophysics because lunar and planetary ephemerides are indispensable in many important applications, such as spacecraft navigation and reference frame transformations. Recently, it has been suggested that climate dynamics, particularly sea level change due to melting of polar ice sheets, can subtly modulate ocean tides, thus altering the tidal dissipation and lunar recession rate by ∼2.6% in the 21st century. In our study, we provide a correction to standard models of lunar orbital evolution relevant for astrophysical applications. We use the reconstructed history of ice thickness, paleotopography, and sea level change since the last glacial cycle (∼122,000 yr ago) and adopt a revised tidal dissipation model to argue that the climate-induced changes in the lunar orbit might not be negligible and have likely altered the Earth–Moon distance by variable rates as large as ∼0.9 mm yr −1 , which occur on top of the background trend of ∼38.3 mm yr −1 . However, this is currently absent from dynamical models of lunar evolution. Our results suggest that lunar orbit ephemerides might need to be revised by at least ∼1.5%–2.3% in order to obtain a more accurate representation of the tidal dynamics and orbital motions. The model proposed in this paper might also be relevant for other astrophysical bodies, such as exoplanetary satellites.

Asteroids with large secular orbital variations

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 orbit. A numerical analysis has highlighted how these initial conditions allow, under the third-body effect, an optimal reduction of eccentricity (circularisation phase) with limited variations of the other orbit elements, without requiring orbital manoeuvres. Then, by introducing a small velocity variation, the phase of ballistic capture has been joined to the circularisation phase. The obtained results can encourage the exploitation of this phenomenon in future missions for the exploration of Mercury.

Selected Accelerations and Orbital Elements of the Goce Satellite in the Time Domain

Milgromian dynamics (MD or MOND) uniquely predicts motion in a galaxy from the distribution of its stars and gas in a remarkable agreement with observations so far. In the solar system, MD predicts the existence of some possibly non-negligible dynamical effects, which can be used to constrain the freedom in MD theories. Known extreme trans-Neptunian objects (ETNOs) have their argument of perihelion, longitude of ascending node, and inclination distributed in highly non-uniform fashion; ETNOs are bodies with perihelion distances greater than the orbit of Neptune and with semimajor axes greater than 150 au and less than $\sim1500$ au. It is as if these bodies have been systematically perturbed by some external force. We investigated a hypothesis that the puzzling orbital characteristics of ETNOs are a consequence of MD. We set up a dynamical model of the solar system incorporating the external field effect (EFE), which is anticipated to be the dominant effect of MD in the ETNOs region. We used constraints available on the strength of EFE coming from radio tracking of the Cassini spacecraft. We performed several numerical experiments, concentrating on the long-term orbital evolution of primordial (randomised) ETNOs in MD. The EFE could produce distinct non-uniform distributions of the orbital elements of ETNOs that are related to the orientation of an orbit in space. If we demand that EFE is solely responsible for the detachment of Sedna and 2012 VP$_{113}$, then these distributions are at odds with the currently observed statistics on ETNOs unless the EFE quadrupole strength parameter $Q_{2}$ has values that are unlikely (with probability < 1$\%$) in light of the Cassini data.

A frequency-based hierarchy of dynamical models in cislunar space: leveraging periodically and quasi-periodically perturbed models Understanding the applicability of different dynamical models within cislunar space is a useful yet challenging problem. The current work constructs a hierarchy of dynamical models leveraging a common rotating reference frame that accommodates multiple dynamical models. In such a formulation, the Higher-Fidelity Ephemeris Model (HFEM) is approximated as quasi-periodically perturbed model with multiple frequencies in addition to the autonomous Circular Restricted Three-Body Problem (CR3BP) dynamics. Then, different intermediate models are evaluated within the hierarchy in terms of the types and numbers of the incorporated frequencies. The analysis focuses on three main topics. Firstly, coherent solar gravity modeling is properly defined with analytical and visual criteria that serve as useful metrics in assessing intermediate models. Secondly, two periodically perturbed models, i.e., Quasi Bi-Circular Problem (QBCP) and Hill Restricted Four-Body Problem (HR4BP), are investigated within the common rotating reference frame. The capabilities and limitations of these two models within the hierarchy between the CR3BP and HFEM are examined, focusing on the similarities and differences in the models. Thirdly, novel quasi-periodically perturbed models are introduced. Leveraging the insight from Hill's lunar theory, two models are designed, denoted as In-plane Quasi-Hill Restricted Four-Body Problem (I-QHR4BP) and Out-of-plane Quasi-Hill Restricted Four-Body Problem (O-QHR4BP). These two models selectively introduce the eccentricity between the Earth-Moon system and the inclination of the lunar orbit with respect to the Earth ecliptic plane, respectively, in addition to the HR4BP. The global characteristics of these new models are analyzed within the common rotating reference frame. The capabilities of multiple models within the model hierarchy are analyzed for two sample transition cases from the CR3BP to HFEM: L_2 Lagrange point and the L_2 9:2 synodic halo orbit. An attempt to build a dynamical catalog of present-day solar system co-orbitals In this talk, we will present a full study of the 1:1 mean-motion resonance in the Solar System. We calculated stability points applying a resonant semi-analytic theory valid for any value of eccentricity or inclination. The location of each equilibrium point changes as the orbital elements of an object change, which led us to map the location of them. For the case of low inclination and low eccentriciy we recovered the known L4 and L5 points. The three global types of orbits for this resonance; Tadpoles, Quasi-satellites and Horseshoes, vary as a function of the orbital elements, even disappearing for some cases. In order to build a catalog of real co-orbital object, we filteres the NASA Horizons minor-body catalog inside the maximum resonant width and analyzed which objects are indeed in resonance. In total, we found 173 objects to be in co-orbital resonant motion with Solar System planets excluding Jupiter. We were able to recover all the already knoen objects and to confirm the resonant state of some new ones. As highlights, Mercury remains to be the only planet with zero known co-orbitals and no L5 Earth Trojan has been discovered so far.

Gravitational and third-body perturbations can be modeled with sufficient precision for most applications in low Earth orbit. However, owing to severe uncertainty sources and modeling limitations, computational models of satellite aerodynamics and solar radiation pressure are bound to be biased. Aiming at orbital propagation consistent with observed satellite orbital dynamics, real-time estimation of these perturbations is desired. In this paper, a particle filter for the recursive inference and prediction of nongravitational forces is developed. Specifically, after assuming a parametric model for the desired perturbations, the joint probability distribution of the parameters is inferred by using a prescribed number of weighted particles, each consisting of one set of orbital elements and one set of parameters. The particle evolution is carried out by means of an underlying orbital propagator, and the Bayes rule is used to recursively update weights by comparing propagated orbital elements with satellite observations. The proposed formulation uses mean orbital elements as the only available measurements. This feature makes the algorithm a potentially valuable resource for space situational awareness applications, such as space debris trajectories prediction from two-line elements, or for onboard force estimation from Global Positioning System data. High-fidelity simulations show that nongravitational perturbations can be estimated with 20% accuracy.

This work studies the evolution of several Distant Retrograde Orbits (DROs) of varying size in the Earth-Moon system over durations up to tens of millennia. This analysis is relevant for missions requiring a completely hands off, long duration quarantine orbit, such as a Mars Sample Return mission or the Asteroid Redirect Mission. Four DROs are selected from four stable size regions and are propagated for up to 30,000 years with an integrator that uses extended precision arithmetic techniques and a high fidelity dynamical model. The evolution of the orbit’s size, shape, orientation, period, out-of-plane amplitude, and Jacobi constant are tracked. It has been found that small DROs, with minor axis amplitudes of approximately 45,000 km or less decay in size and period largely due to the Moon’s solid tides. Larger DROs (62,000 km and up) are more influenced by the gravity of bodies external to the Earth-Moon system, and remain bound to the Moon for significantly less time.

Centaurs transitioning to JFCs: thermal and dynamical evolution

Conventional angles-only initial orbit determination algorithms assume Keplerian dynamics and are not always well-adapted to finding the orbits of objects on cislunar trajectories. We propose a solution to this problem based on the concept of dynamic triangulation, which is a type of triangulation algorithm that produces a full state estimate from non-simultaneous, line-of-sight measurements and an approximate dynamical model. In this approach, an object’s motion is approximated as rectilinear over a short segment of its orbit, which permits dynamic triangulation to generate an initial guess. This guess is then refined using the full dynamical model and a nonlinear least squares solver. The performance of this technique was tested on several types of scenarios where the observer is in low lunar orbit and the target follows a periodic cislunar orbit or an Earth-Moon transfer orbit. In these scenarios it was found that the rectilinear initial guess is typically accurate enough to converge to the true trajectory after refinement with the full dynamical model. An analytic expression for the state covariance was derived and validated.

Aims. TZ Fornacis is a double-lined eclipsing binary system with similar masses (2.057 ± 0.001 and 1.958 ± 0.001 M⊙) but characterized by very different radii (8.28 ± 0.22 and 3.94 ± 0.17 R⊙). This similarity in terms of mass makes it possible to study the system’s differential stellar evolution as well as some aspects of its tidal evolution. With regard to its orbital elements, it was recently confirmed that its orbit is circular with an orbital period of 75.7 days. The less massive component rotates about 17 times faster than the primary one, which is synchronized with the mean orbital angular velocity. Our main objective in this work is to study both the nuclear and the tidal evolution of the system. Methods. To model the TZ For system, we used the MESA package, computing the grids using the exact observed masses, radii, and effective temperatures as input, and then varying the metallicity, the core overshooting amount, and the mixing-length parameter. A χ2 statistic was used to infer the optimal values of the core overshooting and the mixing-length parameters. The same procedure was used to generate rotating models with the GRANADA code. The respective errors in the average age of TZ For were less than 5%. On the other hand, the differential equations that govern the tidal evolution were integrated using the fifth-order Runge–Kutta method, ith a tolerance of 1 × 10−7. Results. We explored two scenarios regarding the initial eccentricities: a high one (0.30) and a case of an initial circular orbit. A good agreement has been found between the observational values of the eccentricity, synchronism levels, and orbital period with the values predicted by the integration of the tidal evolution equations. The influence of the friction timescale on the evolution of the orbital elements of TZ For is also studied here. The orbital elements most affected by the uncertainties in the friction timescale are the synchronism levels of the two components. On the other hand, we used the properties of the rotating models generated by the GRANADA code as the initial angular velocities instead of using trial values. In this case, comparisons between the theoretical values of the orbital elements and their observed counterparts also lead to a good interagreement.

The orbital evolution of about 26,000 Jupiter-crossing objects and 1,500 resonant asteroids under the gravitational influence of planets was investigated. The rate of their collisions with terrestrial planets was estimated by computing the probabilities of collisions based on random-phase approximations and the orbital elements sampled with a 500 yr step. The Bulirsh-Stoer and a symplectic orbit integrator gave similar results for orbital evolution, but sometimes give different collision probabilities with the Sun. For orbits close to that of Comet 2P, the mean collision probabilities of Jupiter-crossing objects with terrestrial planets were greater by two orders of magnitude than for some other comets. For initial orbital elements close to those of Comets 2P, 10P, 44P, and 113P, a few objects (about 0.1%) entered Earth-crossing orbits with semi-major axes a < 2 AU and aphelion distances Q < 4.2 AU, and moved in such orbits for more than 1 Myr (up to tens or even hundreds of Myr). Some of them even got inner-Earth orbits (Q < 0.983 AU) and Aten orbits. A few comets achieve typical asteroidal orbits for hundreds of Myr. Most former trans-Neptunian objects that have typical near-Earth object orbits moved in such orbits for millions of years; thus, during most of this time they were extinct comet, if they did not disintegrate.

Context. We studied the dynamical orbital and physical evolution of all 21 numbered and 13 selected unnumbered asteroids in retrograde orbits. Aims. Based on all published observations of studied asteroids in retrograde orbits, we computed their starting orbital elements, absolute magnitudes, and diameters, together with the non-gravitational parameters A2 and da/dt. Methods. Using publicly available orbital computation methods, we studied the dynamical evolution of orbital elements and the physical parameters of asteroids: rotation period, spin direction, and the non-gravitational parameters A2. Results. Lyapunov times (LT) for studied asteroids are short, from 60 to 36 496 yr, with a mean of 5978. Without considering non-gravitational effects, LT is longer: values range from 328 to 63 165 yr, with a mean of 6392. Over the next 10 Myr and beyond, the rotation period of the studied asteroids P decreases by approximately 8%. Moreover, 15% of the clones slow down. Conclusions. The starting spin distribution becomes flatter, with only one large maximum in the range (0–5) deg containing 279 clones (i.e. approximately 13%). However, the non-gravitational parameter da/dt has a maximum value of around (0–0.04)× 10−5 au day−2 .

We present simulations of Triton's postcapture orbit that confirm the importance of Kozai-type oscillations in its orbital elements. In the context of the tidal orbital evolution model, these variations require average pericenter distances much higher than previously published, and the timescale for the tidal orbital evolution of Triton becomes longer than the age of the solar system. Recently discovered irregular satellites present a new constraint on Triton's orbital history. Our numerical integrations of test particles indicate a timescale for Triton's orbital evolution to be less than 105 yr for a reasonable number of distant satellites to survive Triton's passage. This timescale is inconsistent with the exclusively tidal evolution (timescale of over 108 yr), but consistent with the interaction with the debris from satellite-satellite collisions. Any major regular satellites will quickly collide among themselves after being perturbed by Triton, and the resulting debris disk would eventually be swept up by Triton; given that the total mass of the Uranian satellite system is 40% of that of Triton, large-scale evolution is possible. This scenario could have followed either collisional capture or the recently discussed capture based on three-body interactions.