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The non-resonant Kuiper belt objects (KBOs) between the 3:2 and 2:1 Neptunian mean motion resonances can be largely divided between a cold classical belt (CCB) and a hot classical belt (HCB). A notable difference between these two subpopulations is the prevalence of widely spaced, equal-mass binaries in the CCB and a much smaller but non-zero number in the HCB. The primary reason for this difference in binary rate remains unclear. Here using N-body simulations we examine whether close encounters with the giant planets during an early outer solar system instability may have disrupted primordial Kuiper Belt binaries that existed within the primordial Kuiper belt before they attained HCB orbits. We find that such encounters are very effective at disrupting binaries down to separations of ~1% of their Hill radius (as measured in the modern Kuiper belt), potentially explaining the paucity of widely spaced, equal mass binaries in the modern HCB. Moreover, we find that the widest binaries observed in the modern HCB are quite unlikely to survive planetary encounters, but these same planetary encounters can widen a small subset of tighter binaries to give rise to the small population of very wide binaries seen in today's HCB., Accepted 2021 April 28. Received 2021 April 26; in original form 2021 February 22. 5 pages, 3 figures, 2 tables

Irregular topography can induce scattering and diffraction of incident seismic waves and cause topographic amplification effects. In this paper, a theoretical model for the scattering and diffraction of cylindrical SH waves caused by a semi-circular hill is established for the first time to reveal the influence of source characteristics on the topographic amplification effects. The analytical solution of the theoretical model is derived via the wave function expansion method and image theory, and its accuracy is verified by checking the given boundary conditions. Base on the presented solution, the influences of source location, incident wave frequency, and hill radius on amplitude amplification are systematically investigated. Comparison of amplitude amplification around the hill caused by cylindrical waves and plane waves indicates that the effect of source distance on topographic amplification effects is not negligible unless the source distance exceeds 15 times the hill radius. It suggests that much attention should be paid to the effects of source location on topographic amplification effects, especially when the source is near the topography.

We develop a Gravity Assist Mapping to quantify the effects of a flyby in a two-dimensional circular restricted three-body situation based on Gaussian Process Regression (GPR). This work is inspired by the Keplerian Map and Flyby Map. The flyby is allowed to occur anywhere above 300 km altitude at the Earth in the system of Sun-(Earth+Moon)-spacecraft, whereas the Keplerian map is typically restricted to the cases outside the Hill sphere only. The performance of the GPR model and the influence of training samples (number and distribution) on the quality of the prediction of post-flyby orbital states are investigated. The information provided by this training set is used to optimize the hyper-parameters in the GPR model. The trained model can make predictions of the post-flyby state of an object with an arbitrary initial condition and is demonstrated to be efficient and accurate when evaluated against the results of numerical integration. The method can be attractive for space mission design.

In this paper, we consider the plane restricted four-body problem taking into account the light pressure forces when the Earth’s orbit is a Keplerian ellipse with a focus at the Sun, the Moon’s orbit is a Keplerian ellipse with a focus at the Earth, and the balloon satellite is a passively gravitating body. The averaged perturbing function of the problem in osculating elements is obtained in the nonresonant case, when the unperturbed orbit of the Earth satellite lies in the outer sphere of the Earth’s gravitational influence, located beyond the lunar Hill sphere. It is found that the integrals of averaged equations in the osculating elements are the semimajor axis of the satellite orbit as well as the average value of the force function. The stationary modes of oscillations and their bifurcation depending on the light pressure coefficient and the semimajor axis are investigated. Phase oscillation portraits are constructed for different values of the light pressure coefficient. The librational and rotational orbits of the satellite in the ecliptic plane are calculated.

We revisit the concept of sphere of gravitational activity, to which we give both a geometrical and physical meaning. This study aims to refine this concept in a much broader context that could, for instance, be applied to exo-planetary problems (in a Galactic stellar disc-Star-Planets system) to define a first order "border" of a planetary system. The methods used in this paper rely on classical Celestial Mechanics and develop the equations of motion in the framework of the 3-body problem (e.g. Star-Planet-Satellite System). We start with the basic definition of planet's sphere of activity as the region of space in which it is feasible to assume a planet as the central body and the Sun as the perturbing body when computing perturbations of the satellite's motion. We then investigate the geometrical properties and physical meaning of the ratios of Solar accelerations (central and perturbing) and planetary accelerations (central and perturbing), and the boundaries they define. We clearly distinguish throughout the paper between the sphere of activity, the Chebotarev sphere (a particular case of the sphere of activity), Laplace sphere, and the Hill sphere. The last two are often wrongfully thought to be one and the same. Furthermore, taking a closer look and comparing the ratio of the star's accelerations (central/perturbing) to that of the planetary acceleration (central/perturbing) as a function of the planeto-centric distance, we have identified different dynamical regimes which are presented in the semi-analytical analysis., Comment: 11 pages, 5 figures

Super-Earths are by far the most dominant type of exoplanet, yet their formation is still not well understood. In particular, planet formation models predict that many of them should have accreted enough gas to become gas giants. Here we examine the role of the protoplanetary disk in the cooling and contraction of the protoplanetary envelope. In particular, we investigate the effects of 1) the thermal state of the disk as set by the relative size of heating by accretion or irradiation, and whether its energy is transported by radiation or convection, and 2) advection of entropy into the outer envelope by disk flows that penetrate the Hill sphere, as found in 3D global simulations. We find that, at 5 and 1 AU, this flow at the level reported in the non-isothermal simulations where it penetrates only to ~ 0.3 times the Hill radius has little effect on the cooling rate since most of the envelope mass is concentrated close to the core, and far from the flow. On the other hand, at 0.1 AU, the envelope quickly becomes fully-radiative, nearly isothermal, and thus cannot cool down, stalling gas accretion. This effect is significantly more pronounced in convective disks, leading to envelope mass orders of magnitude lower. Entropy advection at 0.1 AU in either radiative or convective disks could therefore explain why super-Earths failed to undergo runaway accretion. These results highlight the importance of the conditions and energy transport in the protoplanetary disk for the accretion of planetary envelopes., Comment: 10 pages, 6 figures, accepted for publication in MNRAS

Synchronous satellites of Venus have long been thought unstable, but we use Poincare's surface of section technique to show that synchronous quasi-satellites orbiting just outside Venus' Hill sphere are quite stable, at least for centuries. Such synchrosats always remain within a few degrees of Venus' equator, and drift very slowly in longitude. These synchrosats could be useful for continuous monitoring of points on Venus' surface, such as active landforms or long-lived landers., Advances in Space Research 2021

PDS70 is a unique system in which two protoplanets, PDS70b and c, have been discovered within the dust-depleted cavity of their disk, at $\sim$22 and 34au respectively, by direct imaging at infrared wavelengths. Subsequent detection of the planets in the H$\alpha$ line indicates that they are still accreting material through circumplanetary disks. In this Letter, we present new Atacama Large Millimeter/submillimeter Array (ALMA) observations of the dust continuum emission at 855$\mu$m at high angular resolution ($\sim$20mas, 2.3au) that aim to resolve the circumplanetary disks and constrain their dust masses. Our observations confirm the presence of a compact source of emission co-located with PDS70c, spatially separated from the circumstellar disk and less extended than $\sim$1.2au in radius, a value close to the expected truncation radius of the cicumplanetary disk at a third of the Hill radius. The emission around PDS70c has a peak intensity of $\sim$86$\pm$16 $\mu \mathrm{Jy}~\mathrm{beam}^{-1}$ which corresponds to a dust mass of $\sim$0.031M$_{\oplus}$ or $\sim$0.007M$_{\oplus}$, assuming that it is only constituted of 1 $\mu$m or 1 mm sized grains, respectively. We also detect extended, low surface brightness continuum emission within the cavity near PDS70b. We observe an optically thin inner disk within 18au of the star with an emission that could result from small micron-sized grains transported from the outer disk through the orbits of b and c. In addition, we find that the outer disk resolves into a narrow and bright ring with a faint inner shoulder., Comment: ApJ Letters, in press; 19 pages, 9 figures

Binary evolution is influenced by dynamical scattering with other stars in dense environments. Heggie's law states that, due to their environments, hard binaries (whose orbital energy surpasses the typical energy of single stars) tend to harden (increase their orbital energy), while soft binaries typically soften. Here, we show that Heggie's law sometimes needs to be revised, by accounting for an external potential, for example, for binaries in nuclear stellar discs or AGN discs, that are affected by the central massive black hole, or binary planetesimals in proto-planetary discs, affected by the host star. We find that in such environments, where the Hill radius is finite, binary-single scattering can have different outcomes. In particular, a three-body encounter could be cut short due to stars being ejected beyond the Hill radius, thereby ceasing to participate in further close interactions. This leads to a systematic difference in the energy changes brought about by the encounter, and in particular slows binary hardening, and even causes some hard binaries to soften, on average, rather than harden. We use our previously derived analytical, statistical solution to the bound chaotic three-body problem to quantitatively characterise the revision of the hardening-softening phase transition and evolution of binaries. We also provide an analytical calculation of the mean hardening rate of binaries in any environment (also reproducing the results of detailed N-body simulations). We show that the latter exhibits a non-trivial dependence on the Hill radius induced by the environment., Updated to match version accepted to MNRAS. Comments Welcome

We explore the orbital dynamics of systems consisting of three planets, each as massive as the Earth, on coplanar, initially circular, orbits about a star of one solar mass. The initial semimajor axes of the planets are equally spaced in terms of their mutual Hill radius, which is equivalent to a geometric progression of orbital periods for small planets of equal mass. Our simulations explore a wide range of spacings of the planets, and were integrated for virtual times of up to 10 billion years or until the orbits of any pair of planets crossed. We find the same general trend of system lifetimes increasing exponentially with separation between orbits seen by previous studies of systems of three or more planets. One focus of this paper is to go beyond the rough trends found by previous numerical studies and quantitatively explore the nature of the scatter in lifetimes and the destabilizing effects of mean motion resonances. In contrast to previous results for five-planet systems, a nontrivial fraction of three-planet systems survive at least several orders of magnitude longer than most other systems with similar initial separation between orbits, with some surviving 1010 years at much smaller orbital separations than any found for five-planet systems. Substantial shifts in the initial planetary longitudes cause a scatter of roughly a factor of two in system lifetime, whereas the shift of one planet's initial position by 100 m along its orbit results in smaller changes in the logarithm of the time to orbit crossing, especially for systems with short lifetimes.

A new way to removal small space debris using a heavy collector in GEO is considered. The proposed scenario involves three types of consecutive maneuvers: capturing of debris into an area bounded by Hill sphere of the heavy collector, towing and discharging debris in a graveyard orbit. The plane motion equations of the debris relative to the collector are written in the Local-Vertical-Local-Horizontal frame taking into account the engine thrust of the collector. Also considering the engine thrust, the equation motion of the collector in oscillating elements is written. The interaction of the debris and the collector is described by means of the inelastic impact theory. The values of the thrust force of the collector are determined, at which the debris can be captured and towed or discharged in the graveyard orbit. It has been shown numerical simulation, that the proposed maneuvers can be implemented.

Massive planetary cores embedded in protoplanetary discs are believed to accrete extended atmospheres, providing a pathway to forming gas giants and gas-rich super-Earths. The properties of these atmospheres strongly depend on the nature of the coupling between the atmosphere and the surrounding disc. We examine the formation of gaseous envelopes around massive planetary cores via three-dimensional inviscid and isothermal hydrodynamic simulations. We focus the changes in the envelope properties as the core mass varies from low (sub-thermal) to high (super-thermal) values, a regime relevant to close-in super-Earths. We show that global envelope properties such as the amount of rotational support or turbulent mixing are mostly sensitive to the ratio of the Bondi radius of the core to its physical size. High-mass cores are fed by supersonic inflows arriving along the polar axis and shocking on the densest parts of the envelope, driving turbulence and mass accretion. Gas flows out of the core's Hill sphere in the equatorial plane, describing a global mass circulation through the envelope. The shell of shocked gas atop the core surface delimits regions of slow (inside) and fast (outside) material recycling by gas from the surrounding disc. While recycling hinders the runaway growth towards gas giants, the inner regions of protoplanetary atmospheres, more immune to mixing, may remain bound to the planet., Comment: 16 pages, 15 figures, accepted for publication in MNRAS

The Solar System gas giants are each surrounded by many moons, with at least 50 prograde satellites thought to have formed from circumplanetary material. Just like the Sun is not the only star surrounded by planets, extrasolar gas giants are likely surrounded by satellite systems. Here, we report on ALMA observations of four, 6 pages, 3 figures, accepted for publication in MNRAS

The exotic range of known planetary systems has provoked an equally exotic range of physical explanations for their diverse architectures. However, constraining formation processes requires mapping the observed exoplanet population to that which initially formed in the protoplanetary disc. Numerous results suggest that (internal or external) dynamical perturbation alters the architectures of some exoplanetary systems. Isolating planets that have evolved without any perturbation can help constrain formation processes. We consider the Kepler multiples, which have low mutual inclinations and are unlikely to have been dynamically perturbed. We apply a modelling approach similar to that of Mulders et al. (2018), additionally accounting for the two-dimensionality of the radius ($R =0.3-20\,R_\oplus$) and period ($P= 0.5-730$ days) distribution. We find that an upper limit in planet mass of the form $M_{\rm{lim}} \propto a^\beta \exp(-a_{\rm{in}}/a)$, for semi-major axis $a$ and a broad range of $a_{\rm{in}}$ and $\beta$, can reproduce a distribution of $P$, $R$ that is indistinguishable from the observed distribution by our comparison metric. The index is consistent with $\beta= 1.5$, expected if growth is limited by accretion within the Hill radius. This model is favoured over models assuming a separable PDF in $P$, $R$. The limit, extrapolated to longer periods, is coincident with the orbits of RV-discovered planets ($a>0.2$ au, $M>1\,M_{\rm{J}}$) around recently identified low density host stars, hinting at isolation mass limited growth. We discuss the necessary circumstances for a coincidental age-related bias as the origin of this result, concluding that such a bias is possible but unlikely. We conclude that, in light of the evidence that some planetary systems have been dynamically perturbed, simple models for planet growth during the formation stage are worth revisiting., Comment: 21 pages, 16 figures, accepted for publication in MNRAS

The detection of a wide range of substructures such as rings, cavities and spirals has become a common outcome of high spatial resolution imaging of protoplanetary disks, both in the near-infrared scattered light and in the thermal millimetre continuum emission. The most frequent interpretation of their origin is the presence of planetary-mass companions perturbing the gas and dust distribution in the disk (perturbers), but so far the only bona-fide detection has been the two giant planets around PDS 70. Here, we collect a sample of 15 protoplanetary disks showing substructures in SPHERE scattered light images and present a homogeneous derivation of planet detection limits in these systems. We also estimate the mass of these perturbers through a Hill radius prescription and a comparison to ALMA data. Assuming that one single planet carves each substructure in scattered light, we find that more massive perturbers are needed to create gaps within cavities than rings, and that we might be close to a detection in the cavities of RX J1604, RX J1615, Sz Cha, HD 135344B and HD 34282. We reach typical mass limits in these cavities of 3-10 Mjup. For planets in the gaps between rings, we find that the detection limits of SPHERE are about an order of magnitude away in mass, and that the gaps of PDS 66 and HD 97048 seem to be the most promising structures for planet searches. The proposed presence of massive planets causing spiral features in HD 135344B and HD 36112 are also within SPHERE's reach assuming hot-start models.These results suggest that current detection limits are able to detect hot-start planets in cavities, under the assumption that they are formed by a single perturber located at the centre of the cavity. More realistic planet mass constraints would help to clarify whether this is actually the case, which might point to perturbers not being the only way of creating substructures., 26 pages, 33 figures, accepted for publication in A&A

We perform magnetohydrodynamic simulations of accreting, equal-mass binary black holes in full general relativity focusing on the impact of black hole spin on the dynamical formation and evolution of minidisks. We find that during the late inspiral the sizes of minidisks are primarily determined by the interplay between the tidal field and the effective innermost stable orbit around each black hole. Our calculations support that a minidisk forms when the Hill sphere around each black hole is significantly larger than the black hole's effective innermost stable orbit. As the binary inspirals, the radius of the Hill sphere decreases, and minidisk sconsequently shrink in size. As a result, electromagnetic signatures associated with minidisks may be expected to gradually disappear prior to merger when there are no more stable orbits within the Hill sphere. In particular, a gradual disappearance of a hard electromagnetic component in the spectrum of such systems could provide a characteristic signature of merging black hole binaries. For a binary of given total mass, the timescale to minidisk "evaporation" should therefore depend on the black hole spins and the mass ratio. We also demonstrate that accreting binary black holes with spin have a higher efficiency for converting accretion power to jet luminosity. These results could provide new ways to estimate black hole spins in the future., Comment: 6 pages, 5 figures, matches published version

(Abridged) We present numerical simulations of the formation of the planetary companions to 47 UMa, rho CrB, and 51 Peg. They are assumed to have formed in situ according to the basic model that a core formed first by accretion of solid particles, then later it captured substantial amounts of gas from the protoplanetary disk. In most of the calculations we prescribe a constant accretion rate for the solid core. The evolution of the gaseous envelope assumes that: (1) it is in quasi-hydrostatic equilibrium, (2) the gas accretion rate is determined by the requirement that the outer radius of the planet is the place at which the thermal velocity of the gas allows it to reach the boundary of the planet's Hill sphere, (3) the gas accretion rate is limited, moreover, by the prescribed maximum rate at which the nebula can supply the gas, and (4) the growth of the planet stops once it obtains approximately the minimum mass determined from radial velocity measurements. Calculations are carried out through an initial phase during which solid accretion dominates, past the point of crossover when the masses of solid and gaseous material are equal, through the phase of rapid gas accretion, and into the final phase of contraction and cooling at constant mass. Alternative calculations are presented for the case of 47 UMa in which the solid accretion rate is calculated, not assumed, and the dissolution of planetesimals within the gaseous envelope is considered. In all cases there is a short phase of high luminosity (1e-3-1e-2 Lsun) associated with rapid gas accretion. The height and duration of this peak depend on uncertain model parameters. The conclusion is reached that in situ formation of all of these companions is possible under some conditions. However, it is more likely that orbital migration was an important component of the evolution, at least for the planets around rho CrB and 51 Peg., Comment: 14 pages, 6 figures, 2 tables

Photometric monitoring of Beta Pictoris in 1981 showed anomalous fluctuations of up to 4% over several days, consistent with foreground material transiting the stellar disk. The subsequent discovery of the gas giant planet Beta Pictoris b and the predicted transit of its Hill sphere to within 0.1 au projected distance of the planet provided an opportunity to search for the transit of a circumplanetary disk in this $21\pm 4$ Myr-old planetary system. Continuous broadband photometric monitoring of Beta Pictoris requires ground-based observatories at multiple longitudes to provide redundancy and to provide triggers for rapid spectroscopic followup. These observatories include the dedicated Beta Pictoris monitoring observatory bRing at Sutherland and Siding Springs, the ASTEP400 telescope at Concordia, and observations from the space observatories BRITE and Hubble Space Telescope. We search the combined light curves for evidence of short period transient events caused by rings and for longer term photometric variability due to diffuse circumplanetary material. We find no photometric event that matches with the event seen in November 1981, and there is no systematic photometric dimming of the star as a function of the Hill sphere radius. We conclude that the 1981 event was not caused by the transit of a circumplanetary disk around Beta Pictoris b. The upper limit on the long term variability of Beta Pictoris places an upper limit of $1.8\times 10^{22}$ g of dust within the Hill sphere. Circumplanetary material is either condensed into a non-transiting disk, is condensed into a disk with moons that has a small obliquity, or is below our detection threshold. This is the first time that a dedicated international campaign has mapped the Hill sphere transit of a gas giant extrasolar planet at 10 au., Comment: 12 pages, 9 figures, 1 table, accepted for publication in A&A. Reduced data and reduction scripts on GitHub at https://github.com/mkenworthy/beta_pic_b_hill_sphere_transit

In 2007, the young star 1SWASP J140747.93-394542.6 (V1400 Cen) underwent a complex series of deep eclipses over 56 days. This was attributed to the transit of a ring system filling a large fraction of the Hill sphere of an unseen substellar companion. Subsequent photometric monitoring has not found any other deep transits from this candidate ring system, but if there are more substellar companions and they are coplanar with the potential ring system, there is a chance that they will transit the star as well. This young star is active and the light curves show a 5% modulation in amplitude with a dominant rotation period of 3.2 days due to star spots rotating in and out of view. We model and remove the rotational modulation of the J1407 light curve and search for additional transit signatures of substellar companions orbiting around J1407. We combine the photometry of J1407 from several observatories, spanning a 19 year baseline. We remove the rotational modulation by modeling the variability as a periodic signal, whose periodicity changes slowly with time over several years due to the activity cycle of the star. A Transit Least Squares (TLS) analysis searches for any periodic transiting signals within the cleaned light curve. We identify an activity cycle of J1407 with a period of 5.4 years. A Transit Least Squares search does not find any plausible periodic eclipses in the light curve, from 1.2% amplitude at 5 days up to 1.9% at 20 days. This sensitivity is confirmed by injecting artificial transits into the light curve and determining the recovery fraction as a function of transit depth and orbital period. J1407 is confirmed as a young active star with an activity cycle consistent with a rapidly rotating solar mass star. With the rotational modulation removed, the TLS analysis rules out transiting companions with radii larger than about 1 Jupiter., Comment: 8 pages, 9 figures, 3 tables, accepted for publication in Astronomy & Astrophysics. Reduced data and reduction scripts on github at https://github.com/StanBarmentloo/J1407_transit_search_activity

The circumstellar disk of PDS 70 hosts two forming planets, which are actively accreting gas from their environment. In this work, we report the first detection of PDS 70 b in the Br$\alpha$ and $M'$ filters with VLT/NACO, a tentative detection of PDS 70 c in Br$\alpha$, and a reanalysis of archival NACO $L'$ and SPHERE $H23$ and $K12$ imaging data. The near side of the disk is also resolved with the Br$\alpha$ and $M'$ filters, indicating that scattered light is non-negligible at these wavelengths. The spectral energy distribution of PDS 70 b is well described by blackbody emission, for which we constrain the photospheric temperature and photospheric radius to $T_\mathrm{eff}=1193 \pm 20$ K and $R=3.0 \pm 0.2$ $R_\mathrm{J}$. The relatively low bolometric luminosity, $\log(L/L_\odot) = -3.79 \pm 0.02$, in combination with the large radius, is not compatible with standard structure models of fully convective objects. With predictions from such models, and adopting a recent estimate of the accretion rate, we derive a planetary mass and radius in the range of $M_\mathrm{p}\approx 0.5-1.5$ $M_\mathrm{J}$ and $R_\mathrm{p}\approx 1-2.5$ $R_\mathrm{J}$, independently of the age and post-formation entropy of the planet. The blackbody emission, large photospheric radius, and the discrepancy between the photospheric and planetary radius suggests that infrared observations probe an extended, dusty environment around the planet, which obscures the view on its molecular composition. Finally, we derive a rough upper limit on the temperature and radius of potential excess emission from a circumplanetary disk, $T_\mathrm{eff}\lesssim256$ K and $R\lesssim245$ $R_\mathrm{J}$, but we do find weak evidence that the current data favors a model with a single blackbody component., Comment: 19 pages, 7 figures, accepted for publication in A&A

In this chapter we explore the consequences of capturing a 0.1 moon-mass (~0.01 mars-mass) planetoid from a mars-like heliocentric orbit into a stable retrograde orbit of large major axis and high eccentricity. The capture mechanism is the same as that for a prograde capture scenario but the motion of the satellite is in the opposite direction. The mars-like planet is rotating in the prograde direction and the satellite is revolving in the retrograde direction. In this dynamical situation the angular momentum of planet rotation is systematically cancelled via tidal activity of the satellite revolving in the opposite direction. Thus, the planet rotation slows as the satellite orbit decreases in major axis as well as in angular momentum. The result of the scenario depends on the initial rotation rate of the planet and the angular momentum of the satellite orbit following a stable retrograde capture. For most orbital scenarios of this type, the satellite eventually coalesces with the planet. If the angular momentum of planet rotation is greater than that associated with the satellite orbit, the result is a planet with a slow prograde rotation. If the angular momentum of planet rotation is less than that associated with the satellite orbit, then the result is a planet rotating in the retrograde direction, the rotation rate depending on the quantity of angular momentum associated with the satellite orbit. If the satellite is sufficiently massive, then the mars-like planet can undergo a GLOBAL RESURFACING EVENT caused by massive tidal energy dissipation.

The gravitational capture potential for a planet can be assessed fairly accurately by mapping the geometry of the stable capture zones (SCZs) in two dimensions for the planet-planetoid combination. Major factors that determine the geometry of SCZs are (1) distance from the Sun and (2) eccentricity of the orbit of the planet. If the orbit of the planet is nearly circular like those of Venus and Earth, then the stable capture potential is more easily assessed because the dimensions of the Hill sphere remain fairly constant over the annual cycle. If the orbit of the planet has significant eccentricity, then the dimensions of the Hill sphere gradually change over the annual cycle and satellite escape into heliocentric orbit can occur more easily. In this case of elevated heliocentric eccentricity, the geometry of the resulting SCZ will be diminished. In general, retrograde SCZs are larger in two-dimensional extent than prograde SCZs. However, retrograde orbits are inherently more unstable than prograde orbits. The differences are obvious when running encounter simulations in which insufficient energy is dissipated for stable capture. For prograde encounters with insufficient energy dissipation for capture, the encountering planetoid escapes back into a slightly changed heliocentric orbit and it can have more encounters with the planet in the future. In the case of retrograde encounters with sufficient energy dissipation to keep the planetoid in the vicinity of the planet for several orbits but not enough for capture, the planetoid does not escape back into heliocentric orbit but collides with the planet. These collisions can be grazing collisions (low probability) or solid collisions (high probability) which result in the elimination of the encountering planetoid.

In this chapter we explore the consequences of capturing a 0.1 moon-mass (~0.01 mars-mass) planetoid from a mars-like heliocentric orbit into a stable prograde orbit of large major axis and high eccentricity. One of the major paradoxes of the gravitational capture process is that most of the energy for capture must be stored and subsequently dissipated in the body of the encountering planetoid. This statement seems counterintuitive and has been a major conceptual “hurdle” for capture proponents. Once a planetoid is captured into a planetocentric orbit (marocentric in this case), it then undergoes a lengthy period of marocentric orbit evolution. During this marocentric orbit evolution the primordial rotation rate of the mars-like body decreases systematically from 24.6 to ~88 hr/day as angular momentum is transferred from the rotating planet to the orbit of the satellite. A calculated estimate of the time scale for orbit circularization to 10% eccentricity is about 4.0 billion years. If the satellite mass is increased to 0.2 moon-mass, then the time-scale for orbit circularization decreases considerably to about 1.5 billion years. Equilibrium rock tidal amplitudes on Mars for a 0.1 moon-mass planetoid are about 10 km for the initial (capture) encounter and for a 0.2 moon-mass planetoid the tidal amplitudes are about 20 km. During a prograde capture and orbit circularization sequence of events much of the primitive crust of the mars-like body, especially in the equatorial zone, would be subducted by rock tidal activity over a short period of marologic time and would be replaced by a basaltic-gabbroic crustal complex. Assuming an ample supply of surface water, habitable conditions would prevail for a few eons following the prograde capture episode.

International audience; We explore properties of the long-term dynamics of particles (moonlets, fragments, debris etc.) around KBO 2014 MU69 (Arrokoth), as well as around similar contact-binary objects potentially present in the Kuiper belt. The chaotic diffusion of particles inside the Hill sphere of MU69 (or, generally, a similar object) is studied by means of construction of appropriate stability diagrams and by application of analytical approaches generally based on the Kepler map theory. The formation and evolution of the particle clouds, due to the chaotic diffusion inside the Hill sphere, are studied and the cloud lifetimes are estimated.

Recent analyses have shown that the concluding stages of giant planet formation are accompanied by the development of large-scale meridional flow of gas inside the planetary Hill sphere. This circulation feeds a circumplanetary disk that viscously expels gaseous material back into the parent nebula, maintaining the system in a quasi-steady state. Here we investigate the formation of natural satellites of Jupiter and Saturn within the framework of this newly outlined picture. We begin by considering the long-term evolution of solid material, and demonstrate that the circumplanetary disk can act as a global dust trap, where $s_{\bullet}\sim0.1-10\,$mm grains achieve a hydrodynamical equilibrium, facilitated by a balance between radial updraft and aerodynamic drag. This process leads to a gradual increase in the system's metallicity, and eventually culminates in the gravitational fragmentation of the outer regions of the solid sub-disk into $\mathcal{R}\sim100\,$km satellitesimals. Subsequently, satellite conglomeration ensues via pairwise collisions, but is terminated when disk-driven orbital migration removes the growing objects from the satellitesimal feeding zone. The resulting satellite formation cycle can repeat multiple times, until it is brought to an end by photo-evaporation of the parent nebula. Numerical simulations of the envisioned formation scenario yield satisfactory agreement between our model and the known properties of the Jovian and Saturnian moons., 31 pages, 12 figures, accepted for publication in ApJ

The optimization problem of the expedition to Phobos with returning to the Earth in a pulse setting is considered. The trajectory is assumed to be a combination of a series of Lambert's problems solutions. The problem was solved numerically with taking into account the ephemeris. The gain of three-pulse approach to Phobos in comparison with the direct flight scheme was estimated.

An ice giant planet was recently reported orbiting white dwarf WD J0914+1914 at an approximate distance of 0.07 au. The striking non-detection of rocky pollutants in this white dwarf's photosphere contrasts with the observations of nearly every other known white dwarf planetary system. Here, I analyze the prospects for exterior extant rocky asteroids, boulders, cobbles and pebbles to radiatively drift inward past the planet due to the relatively high luminosity (0.1 L_Sun) of this particularly young (13 Myr) white dwarf. Pebbles and cobbles drift too slowly from Poynting-Robertson drag to bypass the planet, but boulders and asteroids are subject to the much stronger Yarkovsky effect. In this paper, I (i) place lower limits on the timescales for these objects to reach the planet's orbit, (ii) establish 3 m as the approximate limiting radius above which a boulder drifts too slowly to avoid colliding with the planet, and (iii) compute bounds on the fraction of boulders which succeed in traversing mean motion resonances and the planet's Hill sphere to eventually pollute the star. Overall, I find that the planet acts as a barrier against rather than a facilitator for radiatively-driven rocky pollution, suggesting that future rocky pollutants would most likely originate from distant scattering events., Comment: Accepted for publication in MNRAS

After protoplanets have acquired sufficient mass to open partial gaps in their natal protostellar disks, residual gas continues to diffuse onto horseshoe streamlines under effect of viscous dissipation, and meander in and out of the planets' Hill sphere. Within the Hill sphere, the horseshoe streamlines intercept gas flow in circumplanetary disks. The host stars' tidal perturbation induces a barrier across the converging streamlines' interface. Viscous transfer of angular momentum across this tidal barrier determines the rate of mass diffusion from the horseshoe streamlines onto the circumplanetary disks, and eventually the accretion rate onto the protoplanets. We carry out a series of numerical simulations to test the influence of this tidal barrier on super thermal planets. In weakly viscous disks, protoplanets' accretion rate steeply decreases with their masses above the thermal limit. As their growth timescale exceeds the gas depletion time scale, their masses reach asymptotic values comparable to that of Jupiter. In relatively thick and strongly viscous disks, protoplanets' asymptotic masses exceed several times that of Jupiter. Two dimensional numerical simulations show that such massive protoplanets strongly excite the eccentricity of nearby horseshoe streamlines, destabilize orderly flow, substantially enhance the diffusion rate across the tidal barrier, and elevate their growth rate until their natal disk is severely depleted. In contrast, eccentric streamlines remain stable in three dimensional simulations. Based on the upper falloff in the observe mass distribution of known exoplanets, we suggest their natal disks had relatively low viscosity alpha sim 0.001, modest thickness H/R sim 0.03 to 0.05, and limited masses comparable to that of minimum mass solar nebula model., Comment: Accepted by ApJ

Subject of this paper is the design of a space robotic mission to the asteroid 433 Eros. The mission aims to grab a boulder from its surface and transport it inside the Earth’s Hill sphere. This kind of mission was chosen to develop a method of analysis of all the opportune trajectories for a sample-return mission, using a generic Near-Earth asteroid as 433 Eros. This work was inspired by NASA’s Asteroid Redirect Mission, which was cancelled in 2017 due to lack of funding, and whose purpose was to transfer a boulder from the surface of a Near-Earth asteroid to a stable lunar orbit, where it could be further analysed both by robotic probes and by a future manned mission. The propulsion system used for the theorized mission consists of three autonomous ion thrusters fully adjustable in magnitude and direction of thrust. Furthermore, during the return flight an Earth gravity assist is used to increase the mass of boulder that the spacecraft can transport towards Earth. Selecting the same time window of the ARM, different trajectories, separately for the outbound and inbound flights, are calculated using indirect methods. Subsequently, a plausible interpretation of the different performances of the calculated trajectories is given, considering both the solar electric power available to the spacecraft and the geometric configuration of the bodies involved. At the end of this process, all the calculated trajectories for the outbound and inbound flights are compared, and possible final solutions for the mission are discussed.

A restricted 2 + 2 body problem is proposed as a possible mechanism to explain the capture of small bodies by a planet. In particular, we consider two primaries revolving in a circular mutual orbit and two small bodies of equal mass, neither of which affects the motion of the primaries. If the small bodies are temporarily captured in the Hill sphere of the smaller primary, they may get close enough to each other to exchange energy in such a way that one of them becomes permanently captured. Numerical simulations show that capture is possible for both prograde and retrograde orbits.

We searched for dust or debris rings in the Pluto-Charon system before, during, and after the New Horizons encounter. Methodologies included searching for back-scattered light during the approach to Pluto (phase $\sim15^\circ$), in situ detection of impacting particles, a search for stellar occultations near the time of closest approach, and by forward-scattered light during departure (phase $\sim165^\circ$). A search using HST prior to the encounter also contributed to the results. No rings, debris, or dust features were observed, but our detection limits provide an improved picture of the environment throughout the Pluto-Charon system. Searches for rings in back-scattered light covered 35,000-250,000 km from the system barycenter, a zone that starts interior to the orbit of Styx, and extends to four times the orbital radius of Hydra. We obtained our firmest limits using the NH LORRI camera in the inner half of this region. Our limits on the normal $I/F$ of an unseen ring depends on the radial scale of the rings: $2\times10^{-8}$ ($3\sigma$) for 1500 km wide rings, $1\times10^{-8}$ for 6000 km rings, and $7\times10^{-9}$ for 12,000 km rings. Beyond $\sim100,000$ km from Pluto, HST observations limit normal $I/F$ to $\sim8\times10^{-8}$. Searches for dust from forward-scattered light extended from the surface of Pluto to the Pluto-Charon Hill sphere ($r_{\rm Hill}=6.4\times10^6$ km). No evidence for rings or dust was detected to normal $I/F$ limits of $\sim8.9\times10^{-7}$ on $\sim10^4$ km scales. Four occulation observations also probed the space interior to Hydra, but again no dust or debris was detected. Elsewhere in the solar system, small moons commonly share their orbits with faint dust rings. Our results suggest that small grains are quickly lost from the system due to solar radiation pressure, whereas larger particles are unstable due to perturbations by the known moons., Comment: Submitted to Icarus, 38 pages, 24 figures

Asteroid 2007 VW266 is among the rare objects with a heliocentric retrograde orbit, and its semimajor axis is within a Hill sphere radius of that of Jupiter. This raised the interesting possibility that it could be in co-orbital retrograde resonance with Jupiter, a second “counter-orbital” object in addition to recently discovered 2015 BZ509. We find instead that the object is in 13/14 retrograde mean motion resonance (also referred to as 13/-14). The object is shown to have entered its present orbit about 1700 years ago, and it will leave it in about 8000 years, both through close approach to Jupiter. Entry and exit states both avoid 1:1 retrograde resonance, but the retrograde nature is preserved. The temporary stable state is due to an elliptic orbit with high inclination keeping nodal passages far from the associated planet. We discuss the motion of this unusual object based on modeling and theory, and its observational prospects.

Molecular kinetic simulations are typically used to accurately describe the tenuous regions of the upper atmospheres on planetary bodies. These simulations track the motion of particles representing real atmospheric atoms and/or molecules subject to collisions, the object's gravity, and external influences. Because particles can end up in very large ballistic orbits, upper boundary conditions (UBC) are typically used to limit the domain size thereby reducing the time for the atmosphere to reach steady-state. In the absence of a clear altitude at which all molecules are removed, such as a Hill sphere, an often used condition is to choose an altitude at which collisions become infrequent so that particles on escape trajectories are removed. The remainder are then either specularly reflected back into the simulation domain or their ballistic trajectories are calculated analytically or explicitly tracked so they eventually re-enter the domain. Here we examine the effect of the choice of the UBC on the escape rate and the structure of the atmosphere near the nominal exobase in the convenient and frequently used 1D spherically symmetric approximation. Using Callisto as the example body, we show that the commonly used specular reflection UBC can lead to significant uncertainties when simulating a species with a lifetime comparable to or longer than a dynamical time scale, such as an overestimation of escape rates and an inflated exosphere. Therefore, although specular reflection is convenient, the molecular lifetimes and body's dynamical time scales need to be considered even when implementing the convenient 1D spherically symmetric simulations in order to accurately estimate the escape rate and the density and temperature structure in the transition regime.

Made available in DSpace on 2022-04-28T19:44:02Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-08-01 The young star PDS110 in the Ori OB1a association underwent two similar eclipses in 2008 and 2011, each of which lasted for a period of at least 25 days. One plausible explanation for these events is that the star was eclipsed by an unseen giant planet (named PDS110b) circled by a ring system that fills a large fraction of its Hill sphere. Through thousands of numerical simulations of the three-body problem, we constrain the mass and eccentricity of this planet as well the size and inclination of its ring, parameters that are not well determined by the observational data alone. We carried out a broad range of different configurations for the PDS110b ring system and ruled out all that did not match with the observations. The result shows that the ring system could be prograde or retrograde; the preferred solution is that the ring has an inclination lower than 60° and a radius between 0.1 and 0.2 au and that the planet is more massive than 35 MJup and has a low eccentricity (

We present the current status and first results from a Monte Carlo-type simulation toolbox for Solar System small body dynamics. We also present fundamental methods for evaluating the results of this type of simulations using convergence criteria. The calculations consider a body in the Solar System with a mass loss mechanism that generates smaller particles. In our application the body, or parent body, is a comet and the mass loss mechanism is a sublimation process. In order to study mass propagation from parent bodies to Earth, we use the toolbox to sample the uncertainty distributions of relevant comet parameters and to find the resulting Earth influx distributions. The initial distributions considered represent orbital elements, sublimation distance, cometary and meteoroid densities, comet and meteoroid sizes and cometary surface activity. Simulations include perturbations from all major planets, radiation pressure and the Poynting-Robertson effect. In this paper we present the results of an initial software validation performed by producing synthetic versions of the 1933, 1946, 2011 and 2012 October Draconids meteor outbursts and comparing them with observational data and previous models. The synthetic meteor showers were generated by ejecting and propagating material from the recognized parent body of the October Draconids; the comet 21P/Giacobini-Zinner. Material was ejected during 17 perihelion passages between 1866 and 1972. Each perihelion passage was sampled with 50 clones of the parent body, all producing meteoroid streams. The clones were drawn from a multidimensional Gaussian distribution on the orbital elements, with distribution variances proportional to observational uncertainties. In the simulations, each clone ejected 8000 particles. Each particle was assigned an individual weight proportional to the mass loss it represented. This generated a total of 6.7 million test particles, out of which 43 thousand entered the Earth's Hill sphere during 1900–2020 and were considered encounters. The simulation reproduces the predictions and observations of the 1933, 1946, 2011 and 2012 October Draconids, including the unexpected but measured deviation of the meteoroid mass index from a power law in 2012 as compared to 2011. We show that when convergence is sufficient in the simulation, the fraction between two encountered mass distributions is independent of the assumed input mass distribution. Finally, we predict an outburst for the 2018 October Draconids with a peak on October 8–9 that could be up to twice as large as the 2011 and 2012 outbursts.

As a continuation of the work by Granvik et al. (2012), we expand the statistical treatment of Earth’s temporarily-captured natural satellites from temporarily-captured orbiters (TCOs, i.e., objects which make at least one orbit around the Earth) to the newly redefined subpopulation of temporarily-captured flybys (TCFs). TCFs are objects that while being gravitationally bound fail to make a complete orbit around the Earth while on a geocentric orbit, but nevertheless approach the Earth within its Hill radius. We follow the trajectories of massless test asteroids through the Earth-Moon system and record the orbital characteristics of those that are temporarily captured. We then carry out a steady-state analysis utilizing the novel NEO population model by Granvik et al. (2016). We also investigate how an quadratic distribution at very small values of e⊙ and i⊙ affects the predicted population statistics of Earth’s temporarily-captured natural satellites. The steady-state population in both cases (constant and quadratic number distributions inside the e and i bins) is predicted to contain a slightly reduced number of meter-sized asteroids compared to the values of the previous paper. For the combined TCO/TCF population, we find the largest body constantly present on a geocentric orbit to be on the order of 80 cm in diameter. In the phase space, where the capture is possible, the capture efficiency of TCOs and TCFs is O ( 10 − 6 − 10 − 4 ) . We also find that kilometer-scale asteroids are captured once every 10 Myr.

The key aspect determining the post-formation luminosity of gas giants has long been considered to be the energetics of the accretion shock at the planetary surface. We use 1D radiation-hydrodynamical simulations to study the radiative loss efficiency and to obtain post-shock temperatures and pressures and thus entropies. The efficiency is defined as the fraction of the total incoming energy flux which escapes the system (roughly the Hill sphere), taking into account the energy recycling which occurs ahead of the shock in a radiative precursor. We focus here on a constant equation of state to isolate the shock physics but use constant and tabulated opacities. While robust quantitative results will require a self-consistent treatment including hydrogen dissocation and ionization, the results show the correct qualitative behavior and can be understood semi-analytically. The shock is found to be isothermal and supercritical for a range of conditions relevant to core accretion (CA), with Mach numbers greater than ca. 3. Across the shock, the entropy decreases significantly, by a few entropy units (k_B/baryon). While nearly 100 percent of the incoming kinetic energy is converted to radiation locally, the efficiencies are found to be as low as roughly 40 percent, implying that a meaningful fraction of the total accretion energy is brought into the planet. For realistic parameter combinations in the CA scenario, a non-zero fraction of the luminosity always escapes the system. This luminosity could explain, at least in part, recent observations in the LkCa 15 and HD 100546 systems., 15 pages, 4 figures. Accepted for publication in ApJ

Tidal acceleration exerted by the terrestrial planets and Jupiter’s are determined, orbital resonances to evaluate the motion stability in binary asteroid systems are calculated. Radius of the Hill sphere surrounding the main component in approximation of the planetary three-body problem — the Sun-main component-satellite is calculated. Escape velocities from the surface of the asteroid satellites are found and the conclusion on the possibility of substance loss is made.

In order to prepare for the arrival of the Dawn spacecraft at Ceres, a search for satellites was undertaken by the Hubble Space Telescope (HST) to enhance the mission science return and to ensure spacecraft safety. Previous satellite searches from ground-based telescopes have detected no satellites within Ceres’ Hill sphere down to a size of 3 km ( Gehrels et al. 1987 ) and early HST investigations searched to a limit of 1–2 km (Bieryla et al. 2011). The Wide Field Camera 3 (WFC3) on board the HST was used to image Ceres between 14 April–28 April 2014. These images cover approximately the inner third of Ceres’ Hill sphere, where the Hill sphere is the region surrounding Ceres where stable satellite orbits are possible. We performed a deep search for possible companions orbiting Ceres. No natural companions were located down to a diameter of 48 m, over most of the Hill sphere to a distance of 205,000 km (434 Ceres radii) from the surface of Ceres. It was impossible to search all the way to the surface of Ceres because of scattered light, but at a distance of 2865 km (five Ceres radii), the search limit was determined to be 925 m.

We search for transiting exoplanets around the star $\beta$ Pictoris using high resolution spectroscopy and Doppler imaging that removes the need for standard star observations. These data were obtained on the VLT with UVES during the course of an observing campaign throughout 2017 that monitored the Hill sphere transit of the exoplanet $\beta$ Pictoris b. We utilize line profile tomography as a method for the discovery of transiting exoplanets. By measuring the exoplanet distortion of the stellar line profile, we remove the need for reference star measurements. We demonstrate the method with white noise simulations, and then look at the case of $\beta$ Pictoris, which is a $\delta$ Scuti pulsator. We describe a method to remove the stellar pulsations and perform a search for any transiting exoplanets in the resultant data set. We inject fake planet transits with varying orbital periods and planet radii into the spectra and determine the recovery fraction. In the photon noise limited case we can recover planets down to a Neptune radius with an $\sim$80% success rate, using an 8 m telescope with a $R\sim 100,000$ spectrograph and 20 minutes of observations per night. The pulsations of $\beta$ Pictoris limit our sensitivity to Jupiter-sized planets, but a pulsation removal algorithm improves this limit to Saturn-sized planets. We present two planet candidates, but argue that their signals are most likely caused by other phenomena. We have demonstrated a method for searching for transiting exoplanets that (i) does not require ancillary calibration observations, (ii) can work on any star whose rotational broadening can be resolved with a high spectral dispersion spectrograph and (iii) provides the lowest limits so far on the radii of transiting Jupiter-sized exoplanets around $\beta$ Pictoris with orbital periods from 15 days to 200 days with >50% coverage., Comment: Accepted for publication in A&A, 8 pages, 8 figures. The Github repository can be found at https://github.com/lennartvansluijs/Spectroscopic-Transit-Search

We present thermal infrared observations of the active asteroid (and Geminid meteoroid stream parent) 3200 Phaethon using the Very Large Telescope. The images, at 10.7 micron wavelength, were taken with Phaethon at its closest approach to Earth (separation 0.07 AU) in 2017 December, at a linear resolution of about 14 km. We probe the Hill sphere (of radius 66 km) for trapped dust and macroscopic bodies, finding neither, and we set limits to the presence of unbound dust. The derived limits to the optical depth of dust near Phaethon depend somewhat on the assumed geometry, but are of order 1e-5. The upper limit to the rate of loss of mass in dust is 14 kg/s. This is about 50 times smaller than the rate needed to sustain the Geminid meteoroid stream in steady state. The observations thus show that the production of the Geminids does not proceed in steady state., 33 pages, 7 figures

Gap-like structures in protoplanetary disks are likely related to planet formation processes. In this paper, we present and analyze high resolution (0.17*0.11 arcsec) 1.3 mm ALMA continuum observations of the protoplanetary disk around the Herbig Ae star MWC 480. Our observations for the first time show a gap centered at ~74au with a width of ~23au, surrounded by a bright ring centered at ~98au from the central star. Detailed radiative transfer modeling of both the ALMA image and the broadband spectral energy distribution is used to constrain the surface density profile and structural parameters of the disk. If the width of the gap corresponds to 4~8 times the Hill radius of a single forming planet, then the putative planet would have a mass of 0.4~3 M_Jup. We test this prediction by performing global three-dimensional smoothed particle hydrodynamic gas/dust simulations of disks hosting a migrating and accreting planet. We find that the dust emission across the disk is consistent with the presence of an embedded planet with a mass of ~2.3 M_Jup at an orbital radius of ~78au. Given the surface density of the best-fit radiative transfer model, the amount of depleted mass in the gap is higher than the mass of the putative planet, which satisfies the basic condition for the formation of such a planet., Accepted for publication in A&A, 11 pages, 8 figures

Several detections of wide-orbit planet-mass/sub-stellar companions around young solar-like stars were reported in the last decade. The origin of those possible planets is still unclear but accretion tracers and VLT/SPHERE observations indicate that they are surrounded by circumplanetary material or even a circumplanetary disk. We want to investigate if the gas component of disks around wide-orbit companions is detectable with current and future (sub)mm telescopes and what constraints such gas observations can provide on the nature of the circumplanetary material and on the mass of the companion. We applied the radiation thermo-chemical disk code ProDiMo to model the dust and gas component of passive circumplanetary disks and produced realistic synthetic observables. We considered different companion properties, disk parameters and radiative environments and compared the resulting synthetic observables to telescope sensitivities and to existing dust observations. The main criterion for a successful detection is the size of the circumplanetary disk. At a distance of about 150 pc, a circumplanetary disk with an outer radius of about 10 au is detectable with ALMA in about 6 hours in optically thick CO lines. Other aspects such as the companion's luminosity, disk inclination and background radiation fields are also relevant and should be considered to optimize the observing strategy for detection experiments. For most of the known wide-orbit planet-mass companions, their maximum theoretical disk size of one third of the Hill radius would be sufficient to allow detection of CO lines. It is therefore feasible to detect their gas disks and constrain the mass of the companion through the kinematic signature. Even in the case of non-detections such observations will provide stringent constraints on disk size and gas mass, information crucial for formation theories., Comment: 13 pages, 11 figures, accepted for publication in A&A