A new expansion of planetary disturbing function and applications to interior, co-orbital and exterior resonances with planets

In this study, a new expansion of planetary disturbing function is developed for describing the resonant dynamics of minor bodies with arbitrary inclinations and semimajor axis ratios. In practice, the disturbing function is expanded around circular orbits in the first step and then, in the second step, the resulting mutual interaction between circular orbits is expanded around a reference point. As usual, the resulting expansion is presented in the Fourier series form, where the force amplitudes are dependent on the semimajor axis, eccentricity and inclination, and the harmonic arguments are linear combinations of the mean longitude, longitude of pericenter and longitude of ascending node of each mass. The resulting new expansion is valid for arbitrary inclinations and semimajor axis ratios. In the case of mean motion resonant configuration, the disturbing function can be easily averaged to produce the analytical expansion of resonant disturbing function. Based on the analytical expansion, the Hamiltonian model of mean motion resonances is formulated, and the resulting analytical developments are applied to Jupiter’s inner and co-orbital resonances and Neptune’s exterior resonances. Analytical expansion is validated by comparing the analytical results with the associated numerical outcomes.

Apparent Motion of the Circumstellar Envelope of CQ Tau in Scattered Light

The study of spiral structures in protoplanetary disks is of great importance for understanding the processes in the disks, including planet formation. Bright spiral arms were detected in the disk of young star CQ Tau by Uyama et al. in the H and L bands. The spiral arms are located inside the gap in millimeter-sized dust, discovered earlier using Atacama Large Millimeter/submillimeter Array observations. To explain the gap, Ubeira Gabellini et al. proposed the existence of a planet with the semimajor axis of 20 au. We obtained multi-epoch observations of a spiral feature in the circumstellar envelope of CQ Tau in the I c band using a novel technique of differential speckle polarimetry. The observations covering a period from 2015 to 2021 allow us to estimate the pattern speed of the spiral: −0.°2 ± 1.°1 yr−1 (68% credible interval; positive value indicates counterclockwise rotation), assuming a face-on orientation of the disk. This speed is significantly smaller than expected for a companion-induced spiral, if the perturbing body has a semimajor axis of 20 au. We emphasize that the morphology of the spiral structure is likely to be strongly affected by shadows of a misaligned inner disk detected by Eisner et al.

Symmetry Breaking in Dynamical Encounters in the Disks of Active Galactic Nuclei

The disks of active galactic nuclei (AGNs) may be important sites of binary black hole (BBH) mergers. Here we show via numerical experiments with the high-accuracy, high-precision code SpaceHub that broken symmetry in dynamical encounters in AGN disks can lead to asymmetry between prograde and retrograde BBH mergers. The direction of the hardening asymmetry depends on the initial binary semimajor axis. Under the assumption that the spin of the BHs becomes aligned with the angular momentum of the disk on a short timescale compared with the encounter timescale, an asymmetric distribution of mass-weighted projected spin χ eff is predicted in LIGO–Virgo detections of BBH mergers from AGN disks. In particular, this model predicts that positive χ eff BBH mergers are most likely for encounters with massive tertiaries in migration traps at radial distances ≳500–600 gravitational radii.

SCExAO/CHARIS Direct Imaging of A Low-mass Companion At A Saturn-like Separation from an Accelerating Young A7 Star

We present the SCExAO direct imaging discovery and characterization of a low-mass companion to the nearby young A7IV star, HD 91312. SCExAO/CHARIS JHK (1.1–2.4 μm) spectra and SCExAO/HiCIAO H-band imaging identify the companion over a two year baseline in a highly inclined orbit with a maximum projected separation of 8 au. The companion, HD 91312 B, induces an 8.8σ astrometric acceleration on the star as seen with the Gaia & Hipparcos satellites and a long-term radial-velocity trend as previously identified by Borgniet et al. HD 91312 B’s spectrum is consistent with that of an early-to-mid M dwarf. Hipparcos and Gaia absolute astrometry, radial-velocity data, and SCExAO/CHARIS astrometry constrain its dynamical mass to be 0.337 − 0.044 + 0.042 M ⊙, consistent with - but far more precise than - masses derived from spectroscopy, and favors a nearly edge-on orbit with a semimajor axis of ∼9.7 au. This work is an example of precisely characterizing properties of low-mass companions at solar system-like scales from a combination of direct imaging, astrometry, and radial-velocity methods.

No Sub-Saturn-mass Planet Desert in the CORALIE/HARPS Radial-velocity Sample

We analyze the CORALIE/HARPS sample of exoplanets found by the Doppler radial-velocity method for signs of the predicted gap or “desert” at 10–100 M ⊕ caused by runaway gas accretion at semimajor axes of <3 au. We find that these data are not consistent with this prediction. This result is similar to the finding by the MOA gravitational microlensing survey that found no desert in the exoplanet distribution for exoplanets in slightly longer period orbits and somewhat lower host masses (Suzuki et al. 2018). Together, these results imply that the runaway gas accretion scenario of the core accretion theory does not have a large influence on the final mass and semimajor axis distribution of exoplanets.

GPS, GLONASS, and Galileo orbit geometry variations caused by general relativity focusing on Galileo in eccentric orbits

Three main effects from general relativity (GR) may change the geometry and orientation of artificial earth satellite orbits, i.e., the Schwarzschild, Lense–Thirring, and De Sitter effects. So far, the verification of GR effects was mainly based on the observations of changes in the orientation of satellite orbital planes. We directly observe changes of the satellite orbit geometry caused by GR represented by the semimajor axis and eccentricity. We measure the variations of orbit size and shape of GPS, GLONASS, and Galileo satellites in circular and eccentric orbits and compare the results to the theoretical effects using three years of real GNSS data. We derive a solution that assumes the GR to be true, and a second solution, in which the post-Newtonian parameters are estimated, thus, allowing satellites to find their best spacetime curvature. For eccentric Galileo, GR changes the orbital shape and size in perigee in such a way that the orbit becomes smaller but more circular. In the apogee, the semimajor axis decreases but eccentricity increases, and thus, the orbit becomes more eccentric. Hence, the orbital size variabilities for eccentric orbits are greatly compensated by the orbital shape changes, and thus the total effect of satellite height change is much smaller than the effects for the size and shape of the orbit, individually. The mean semimajor axis offset based on all GPS, GLONASS, and Galileo satellites is − 17.41 ± 2.90 mm, which gives a relative error of 0.36% with respect to the theoretical value.

Orbital Design and Control for Jupiter-Observation Spacecraft

This paper investigates the evolution of orbits around Jupiter and designs a sun-synchronous repeating ground track orbit. In the dynamical models, the leading terms of the Jupiter’s oblateness are J2 and J4 terms. A reasonable range of ground track repetition parameter Q is given and the best observation orbit elements are selected. Meanwhile, the disturbing function acting on the navigation spacecraft is the atmospheric drag and the third body. The law of altitude decay of the spacecraft’s semimajor orbit axis caused by the atmospheric drag is studied, and the inclination perturbation caused by the sun’s gravity is analyzed. This paper designs a semimajor axis compensation strategy to maintain the orbit’s repeatability and proposes an initial inclination prebiased strategy to limit the local time at the descending node in a permitted range. In particular, these two methods are combined in the context of sun-synchronous repeating ground track orbit for better observation of the surface of Jupiter.

Semi-Analytical Estimates for the Orbital Stability of Earth’s Satellites

Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different estimates for the orbital stability of point-mass satellites orbiting around the Earth. (i) We demonstrate the long-term stability of the semimajor axis within the framework of the $$J_2$$ J 2 problem, by a normal form construction eliminating the fast angle in the corresponding Hamiltonian and obtaining $${\mathcal {H}}_{J_2}$$ H J 2 . (ii) We demonstrate the stability of the eccentricity and inclination in a secular Hamiltonian model including lunisolar perturbations (the ‘geolunisolar’ Hamiltonian $${\mathcal {H}}_\mathrm{gls}$$ H gls ), after a suitable reduction of the Hamiltonian to the Laplace plane. (iii) We numerically examine the convexity and steepness properties of the integrable part of the secular Hamiltonian in both the $${\mathcal {H}}_{J_2}$$ H J 2 and $${\mathcal {H}}_\mathrm{gls}$$ H gls models, which reflect necessary conditions for the holding of Nekhoroshev’s theorem on the exponential stability of the orbits. We find that the $${\mathcal {H}}_{J_2}$$ H J 2 model is non-convex, but satisfies a ‘three-jet’ condition, while the $${\mathcal {H}}_\mathrm{gls}$$ H gls model restores quasi-convexity by adding lunisolar terms in the Hamiltonian’s integrable part.

On the origin of the Kreutz family of sungrazing comets

ABSTRACT We evaluate numerically three different models for the parent comet of the Kreutz family of sungrazers: (i) A Centaur on a highly inclined or retrograde orbit that diffuse to the inner planetary region where it became a sungrazer (Model 1). (ii) A parent comet injected from the Oort cloud straight into a near-parabolic, sungrazing orbit. Near perihelion the comet was disrupted by tidal forces from the Sun giving rise to a myriad of fragments that created the Kreutz family (Model 2). (iii) A two-step process by which an Oort cloud comet is first injected in a non-sungrazing, Earth-crossing orbit where its semimajor axis decreases from typical Oort cloud values (a ∼ 104 au) to around 102 au, and then it evolves to a sungrazing orbit by the Lidov–Kozai mechanism (Model 3). Model 1 fails to produce sungrazers of the Kreutz type. Model 2 produces some Kreutz sungrazers and has the appeal of being the most straightforward. Yet the impulses received by the fragments originated in the catastrophic disruption of the parent comet will tend to acquire a wide range of orbital energies or periods (from short-period to long-period orbits) that is in contradiction with the observations. Model 3 seems to be the most promising one since it leads to the generation of some sungrazers of the Kreutz type and, particularly, it reproduces the clustering of the argument of perihelion ω of the observed Kreutz family members around 60°–90°, as a natural consequence of the action of the Lidov–Kozai mechanism.

The functional relation between three-body mean motion resonances and Yarkovsky drift speeds

ABSTRACT We examined the motion of asteroids across the three-body mean motion resonances (MMRs) with Jupiter and Saturn and with the Yarkovsky drift speed in the semimajor axis of the asteroids. The research was conducted using numerical integrations performed using the Orbit9 integrator with 84 000 test asteroids. We calculated time delays, dtr, caused by the seven three-body MMRs on the mobility of test asteroids with 10 positive and 10 negative Yarkovsky drift speeds, which are reliable for Main Belt asteroids. Our final results considered only test asteroids that successfully crossed over the MMRs without close approaches to the planets. We have devised two equations that approximately describe the functional relation between the average time 〈dtr〉 spent in the resonance, the strength of the resonance SR, and the semimajor axis drift speed da/dt (positive and negative) with the orbital eccentricities of asteroids in the range (0, 0.1). Comparing the values of 〈dtr〉 obtained from the numerical integrations and from the derived functional relations, we analysed average values of 〈dtr〉 in all three-body MMRs for every da/dt. The main conclusion is that the analytical and numerical estimates of the average time 〈dtr〉 are in very good agreement, for both positive and negative da/dt. Finally, this study shows that the functional relation we obtain for three-body MMRs is analogous to that previously obtained for two-body MMRs.