Orbital Axis Research Articles

MASCARA-2 b

In this paper we present MASCARA-2 b, a hot Jupiter transiting the mV = 7.6 A2 star HD 185603. Since early 2015, MASCARA has taken more than 1.6 million flux measurements of the star, corresponding to a total of almost 3000 h of observations, revealing a periodic dimming in the flux with a depth of 1.3%. Photometric follow-up observations were performed with the NITES and IAC80 telescopes and spectroscopic measurements were obtained with the Hertzsprung SONG telescope. We find MASCARA-2 b orbits HD 185603 with a period of 3.4741119-0.000006+0.000005 days at a distance of 0.057 ± 0.006 au, has a radius of 1.83 ± 0.07 RJ and place a 99% upper limit on the mass of <17 MJ. HD 185603 is a rapidly rotating early-type star with an effective temperature of 8980-130+90 K and a mass and radius of 1.89-0.05+0.06 M⊙, 1.60 ± 0.06 R⊙, respectively. Contrary to most other hot Jupiters transiting early-type stars, the projected planet orbital axis and stellar spin axis are found to be aligned with λ = 0.6 ± 4°. The brightness of the host star and the high equilibrium temperature, 2260 ± 50 K, of MASCARA-2 b make it a suitable target for atmospheric studies from the ground and space. Of particular interest is the detection of TiO, which has recently been detected in the similarly hot planets WASP-33 b and WASP-19 b.

A deorbiter CubeSat for active orbital debris removal

This paper introduces a mission concept for active removal of orbital debris based on the utilization of the CubeSat form factor. The CubeSat is deployed from a carrier spacecraft, known as a mothership, and is equipped with orbital and attitude control actuators to attach to the target debris, stabilize its attitude, and subsequently move the debris to a lower orbit where atmospheric drag is high enough for the bodies to burn up. The mass and orbit altitude of debris objects that are within the realms of the CubeSat’s propulsion capabilities are identified. The attitude control schemes for the detumbling and deorbiting phases of the mission are specified. The objective of the deorbiting maneuver is to decrease the semi-major axis of the debris orbit, at the fastest rate, from its initial value to a final value of about 6471 km (i.e., 100 km above Earth considering a circular orbit) via a continuous low-thrust orbital transfer. Two case studies are investigated to verify the performance of the deorbiter CubeSat during the detumbling and deorbiting phases of the mission. The baseline target debris used in the study are the decommissioned KOMPSAT-1 satellite and the Pegasus rocket body. The results show that the deorbiting times for the target debris are reduced significantly, from several decades to one or two years.

Metrics in Keplerian orbits quotient spaces

Quotient spaces of Keplerian orbits are important instruments for the modelling of orbit samples of celestial bodies on a large time span. We suppose that variations of the orbital eccentricities, inclinations and semi-major axes remain sufficiently small, while arbitrary perturbations are allowed for the arguments of pericentres or longitudes of the nodes, or both. The distance between orbits or their images in quotient spaces serves as a numerical criterion for such problems of Celestial Mechanics as search for common origin of meteoroid streams, comets, and asteroids, asteroid families identification, and others. In this paper, we consider quotient sets of the non-rectilinear Keplerian orbits space $$\mathbb H$$ . Their elements are identified irrespective of the values of pericentre arguments or node longitudes. We prove that distance functions on the quotient sets, introduced in Kholshevnikov et al. (Mon Not R Astron Soc 462:2275–2283, 2016), satisfy metric space axioms and discuss theoretical and practical importance of this result. Isometric embeddings of the quotient spaces into $$\mathbb R^n$$ , and a space of compact subsets of $$\mathbb H$$ with Hausdorff metric are constructed. The Euclidean representations of the orbits spaces find its applications in a problem of orbit averaging and computational algorithms specific to Euclidean space. We also explore completions of $$\mathbb H$$ and its quotient spaces with respect to corresponding metrics and establish a relation between elements of the extended spaces and rectilinear trajectories. Distance between an orbit and subsets of elliptic and hyperbolic orbits is calculated. This quantity provides an upper bound for the metric value in a problem of close orbits identification. Finally the invariance of the equivalence relations in $$\mathbb H$$ under coordinates change is discussed.

Continuous reorientation of synchronous terrestrial planets due to mantle convection.

Many known rocky exoplanets are thought to have been spun down by tidal interactions to a state of synchronous rotation, in which a planet’s period of rotation equals that of its orbit around its host star. Investigations into atmospheric and surface processes occurring on such exoplanets thus commonly assume that day and night sides are fixed with respect to the surface over geological timescales. Here we use an analytical model to show that true polar wander – where a planetary body’s spin axis shifts relative to its surface because of changes in mass distribution – can continuously reorient a synchronous rocky exoplanet. As occurs on Earth, we find that even weak mantle convection in a rocky exoplanet can produce density heterogeneities within the mantle sufficient to reorient the planet. Moreover, we show that this reorientation is made very efficient by the slower rotation rate of a synchronous planet compared to Earth, which limits the stabilizing effect of rotational and tidal deformations. Furthermore, the ability of a lithosphere to support remnant loads and stabilize against reorientation is limited. Although uncertainties exist regarding the mantle and lithospheric evolution of these worlds, we suggest that the axes of smallest and largest moment of inertia of synchronous exoplanets with active mantle convection change continuously over time but remain closely aligned with the star-planet and orbital axes, respectively.

Modeling low-thrust transfers between periodic orbits about five libration points: Manifolds and hierarchical design

The low-thrust version of the fuel-optimal transfers between periodic orbits with different energies in the vicinity of five libration points is exploited deeply in the Circular Restricted Three-Body Problem. Indirect optimization technique incorporated with constraint gradients is employed to further improve the computational efficiency and accuracy of the algorithm. The required optimal thrust magnitude and direction can be determined to create the bridging trajectory that connects the invariant manifolds. A hierarchical design strategy dividing the constraint set is proposed to seek the optimal solution when the problem cannot be solved directly. Meanwhile, the solution procedure and the value ranges of used variables are summarized. To highlight the effectivity of the transfer scheme and aim at different types of libration point orbits, transfer trajectories between some sample orbits, including Lyapunov orbits, planar orbits, halo orbits, axial orbits, vertical orbits and butterfly orbits for collinear and triangular libration points, are investigated with various time of flight. Numerical results show that the fuel consumption varies from a few kilograms to tens of kilograms, related to the locations and the types of mission orbits as well as the corresponding invariant manifold structures, and indicates that the low-thrust transfers may be a beneficial option for the extended science missions around different libration points.

Dynamical evolution of space debris in the vicinity of GNSS regions

Dynamical evolution of space debris in the vicinity of orbits of the global navigation satellite systems: GLONASS, GPS, BeiDou, and Galileo was studied for a time span of 240 years. Time intervals space debris objects reach the regions of motion of navigation satellites were estimated. Initial orbits of the objects were chosen in the GNSS orbit regions as well as 450–1100 km above with respect to nominal semi-major axes of the navigation orbits. The results depend significantly on the orbital plane position. The objects pass through the GNSS region due to long period oscillations of eccentricities and inclinations of orbits, which are caused by dependency of inclination on luni-solar resonances and radiation pressure.

Observations and light curve solutions of three ultrashort-period W UMa binaries

Photometric observations in V, Rc and Ic bands of the ultrashort-period W UMa binaries 1SWASP J044132.96+440613.7, 1SWASP J052926.88+461147.5 and NSVS 2175434 are presented. The results from the modeling and analysis of our observations reveal that: (i) All targets undergo total eclipses and their photometric mass ratios should be accepted with confidence; (ii) All stellar components are late-type dwarfs; (iii) The temperature difference of target components does not exceed 150 K; (iv) All targets have overcontact configurations with fill-out factor around 0.24; (v) The orbit of NSVS 2175434 is slightly eccentric which is unusual for such an ultrashort-period binary; (vi) The orbital periods of all targets were improved. Masses, radii and luminosities of the stellar components were estimated by the empirical relation “period, orbital axis” for short- and ultrashort-period binaries.

High-resolution Imaging of Transiting Extrasolar Planetary systems (HITEP)

Context. The formation and dynamical history of hot Jupiters is currently debated, with wide stellar binaries having been suggested as a potential formation pathway. Additionally, contaminating light from both binary companions and unassociated stars can significantly bias the results of planet characterisation studies, but can be corrected for if the properties of the contaminating star are known. Aim. We search for binary companions to known transiting exoplanet host stars, in order to determine the multiplicity properties of hot Jupiter host stars. We also search for and characterise unassociated stars along the line of sight, allowing photometric and spectroscopic observations of the planetary system to be corrected for contaminating light. Methods. We analyse lucky imaging observations of 97 Southern hemisphere exoplanet host stars, using the Two Colour Instrument on the Danish 1.54 m telescope. For each detected companion star, we determine flux ratios relative to the planet host star in two passbands, and measure the relative position of the companion. The probability of each companion being physically associated was determined using our two-colour photometry. Results. A catalogue of close companion stars is presented, including flux ratios, position measurements, and estimated companion star temperature. For companions that are potential binary companions, we review archival and catalogue data for further evidence. For WASP-77AB and WASP-85AB, we combine our data with historical measurements to determine the binary orbits, showing them to be moderately eccentric and inclined to the line of sight (and hence planetary orbital axis). Combining our survey with the similar Friends of Hot Jupiters survey, we conclude that known hot Jupiter host stars show a deficit of high mass stellar companions compared to the field star population; however, this may be a result of the biases in detection and target selection by ground-based surveys.

Tunable axial gauge fields in engineered Weyl semimetals: semiclassical analysis and optical lattice implementations

In this work, we describe a toolbox to realize and probe synthetic axial gauge fields in engineered Weyl semimetals. These synthetic electromagnetic fields, which are sensitive to the chirality associated with Weyl nodes, emerge due to spatially and temporally dependent shifts of the corresponding Weyl momenta. First, we introduce two realistic models, inspired by recent cold-atom developments, which are particularly suitable for the exploration of these synthetic axial gauge fields. Second, we describe how to realize and measure the effects of such axial fields through center-of-mass observables, based on semiclassical equations of motion and exact numerical simulations. In particular, we suggest realistic protocols to reveal an axial Hall response due to the axial electric field , as well as axial cyclotron orbits and chiral pseudo-magnetic effect due to the axial magnetic field .

Cartography of the b-plane of a close encounter I: semimajor axes of post-encounter orbits

Close planetary encounters play an important role in the evolution of the orbits of small Solar system bodies and are usually studied with the help of numerical integrations. Here we study close encounters in the framework of an analytic theory, focusing on the so-called b-plane, which is the plane centred on the planet and perpendicular to the planetocentric velocity at infinity of the small body. As shown in previous papers, it is possible to identify the initial conditions on the b-plane that lead to post-encounter orbits of given semimajor axis. In this paper we exploit analytical relationships between b-plane coordinates and pre-encounter orbital elements and compute the probability of transition to these post-encounter states, and numerically check the validity of the analytic approach.

Averaged model to study long-term dynamics of a probe about Mercury

This paper provides a method for finding initial conditions of frozen orbits for a probe around Mercury. Frozen orbits are those whose orbital elements remain constant on average. Thus, at the same point in each orbit, the satellite always passes at the same altitude. This is very interesting for scientific missions that require close inspection of any celestial body. The orbital dynamics of an artificial satellite about Mercury is governed by the potential attraction of the main body. Besides the Keplerian attraction, we consider the inhomogeneities of the potential of the central body. We include secondary terms of Mercury gravity field from $$J_2$$ up to $$J_6$$ , and the tesseral harmonics $$\overline{C}_{22}$$ that is of the same magnitude than zonal $$J_2$$ . In the case of science missions about Mercury, it is also important to consider third-body perturbation (Sun). Circular restricted three body problem can not be applied to Mercury–Sun system due to its non-negligible orbital eccentricity. Besides the harmonics coefficients of Mercury’s gravitational potential, and the Sun gravitational perturbation, our average model also includes Solar acceleration pressure. This simplified model captures the majority of the dynamics of low and high orbits about Mercury. In order to capture the dominant characteristics of the dynamics, short-period terms of the system are removed applying a double-averaging technique. This algorithm is a two-fold process which firstly averages over the period of the satellite, and secondly averages with respect to the period of the third body. This simplified Hamiltonian model is introduced in the Lagrange Planetary equations. Thus, frozen orbits are characterized by a surface depending on three variables: the orbital semimajor axis, eccentricity and inclination. We find frozen orbits for an average altitude of 400 and 1000 km, which are the predicted values for the BepiColombo mission. Finally, the paper delves into the orbital stability of frozen orbits and the temporal evolution of the eccentricity of these orbits.

How do external companions affect spin–orbit misalignment of hot Jupiters?

Consider a planet with its orbital angular momentum axis aligned with the spin axis of its host star. To what extent does an inclined distant companion (giant planet or binary star) affect this alignment? We provide an analytic, quantitative answer and apply it to hot Jupiter systems, for which misalignments between the orbital axis and the stellar spin axis have been detected. We also show how similar consideration can be applied to multi-planet systems with distant companions (such as Kepler-56). The result of this paper provides a simple method to assess the dynamical role played by external companions on spin-orbit misalignments in exoplanetary systems.

Extracting the orbital axis from gravitational waves of precessing binary systems

We present a new method for extracting the instantaneous orbital axis only from gravitational wave strains of precessing binary systems observed from a particular observer direction. This method enables us to reconstruct the co-precessing frame waveforms only from observed quantities for the ideal case that the signal-to-noise ratio is high enough to analyze the waveforms directly. Specifically, we do not assume knowledge of the time evolution of the instantaneous orbital axis and the co-precessing waveforms before analyzing the data in our method. We test and measure the accuracy of our method using the numerical relativity simulation data of precessing binary black holes taken from the SXS Catalog. We show that the direction of the orbital axis is extracted within $\approx0.02~{\rm rad}$ error from gravitational waves emitted during the inspiral phase. The co-precessing waveforms are also reconstructed with high accuracy; the mismatch (assuming white noise) between them and the original co-precessing waveforms is typically a few times $10^{-3}$ including the merger-ringdown phase, and can be improved by an order of magnitude focusing only on the inspiral waveform. In this method, the co-precessing frame waveforms are not only the purely technical tools for understanding the complex nature of precessing waveforms but also direct observables.

Observations and Light Curve Solutions of Ultrashort-Period Eclipsing Binaries

AbstractPhotometric observations in V and I bands and low-dispersion spectra of 10 ultrashort-period binaries (NSVS 2175434, NSVS 2607629, NSVS 5038135, NSVS 8040227, NSVS 9747584, NSVS 4876238, ASAS 071829-0336.7, SWASP 074658.62+224448.5, NSVS 2729229, NSVS 10632802) are presented. One of them, NSVS 2729229, is newly discovered target. The results from modelling and analysis of our observations revealed that (i) eight targets have overcontact configurations with considerable fill-out factor (up to 0.5), while NSVS 4876238 and ASAS 0718-03 have almost contact configurations; (ii) NSVS 4876238 is rare ultrashort-period binary of detached type; (iii) all stellar components are late dwarfs; (iv) the temperature difference of the components of each target does not exceed 400 K; (v) NSVS 2175434 and SWASP 074658.62 + 224448.5 exhibit total eclipses and their parameters could be assumed as well determined; (v) NSVS 2729229 shows emission in the Hα line. Masses, radii, and luminosities of the stellar components were estimated by the empirical relation ‘period, orbital axis’ for short- and ultrashort-period binaries. We found linear relations mass–luminosity and mass–radius for the stellar components of our targets.

The CARMENES search for exoplanets around M dwarfs

We report on the first star discovered to host a planet detected by radial velocity (RV) observations obtained within the CARMENES survey for exoplanets around M dwarfs. HD 147379 (V = 8.9 mag, M = 0.58 ± 0.08 M⊙), a bright M0.0 V star at a distance of 10.7 pc, is found to undergo periodic RV variations with a semi-amplitude of K = 5.1 ± 0.4 m s−1 and a period of P = 86.54 ± 0.06 d. The RV signal is found in our CARMENES data, which were taken between 2016 and 2017, and is supported by HIRES/Keck observations that were obtained since 2000. The RV variations are interpreted as resulting from a planet of minimum mass mP sin i = 25 ± 2 M⊕, 1.5 times the mass of Neptune, with an orbital semi-major axis a = 0.32 au and low eccentricity (e < 0.13). HD 147379 b is orbiting inside the temperate zone around the star, where water could exist in liquid form. The RV time-series and various spectroscopic indicators show additional hints of variations at an approximate period of 21.1 d (and its first harmonic), which we attribute to the rotation period of the star.

A physical interpretation of the Titius-Bode rule and its connection to the closed orbits of Bertrandʼs theorem

We consider the geometric Titius-Bode rule for the semimajor axes of planetary orbits. We derive an equivalent rule for the midpoints of the segments between consecutive orbits along the radial direction and we interpret it physically in terms of the work done in the gravitational field of the Sun by particles whose orbits are perturbed around each planetary orbit. On such energetic grounds, it is not surprising that some exoplanets in multiple-planet extrasolar systems obey the same relation. However, it is surprising that this simple interpretation of the Titius-Bode rule also reveals new properties of the bound closed orbits predicted by Bertrand’s theorem, which has been known since 1873.

The Poynting-Robertson effect in the Newtonian potential with a Yukawa correction

We consider a Yukawa-type gravitational potential combined with the Poynting-Robertson effect. Dust particles originating within the asteroid belt and moving on circular and elliptic trajectories are studied and expressions for the time rate of change of their orbital radii and semimajor axes, respectively, are obtained. These expressions are written in terms of basic particle parameters, namely their density and diameter. Then, they are applied to produce expressions for the time required by the dust particles to reach the orbit of Earth. For the Yukawa gravitational potential, dust particles of diameter $10^{ - 3}$ m in circular orbits require times of the order of $8.557 \times 10^{6}$ yr and for elliptic orbits of eccentricities $e =0.1, 0.5$ require times of $9.396 \times 10^{6}$ and $2.129 \times 10^{6}$ yr respectively to reach Earth’s orbit. Finally, various cases of the Yukawa potential are studied and the corresponding particle times to reach Earth’s are derived per case along with numerical results for circular and various elliptical orbits.

Clearing Residual Planetesimals by Sweeping Secular Resonances in Transitional Disks: A Lone-planet Scenario for the Wide Gaps in Debris Disks around Vega and Fomalhaut

Abstract Extended gaps in the debris disks of both Vega and Fomalhaut have been observed. These structures have been attributed to tidal perturbations by multiple super-Jupiter gas giant planets. Within the current observational limits, however, no such massive planets have been detected. Here we propose a less stringent “lone-planet” scenario to account for the observed structure with a single eccentric gas giant and suggest that clearing of these wide gaps is induced by its sweeping secular resonance. With a series of numerical simulations, we show that the gravitational potential of the natal disk induces the planet to precess. At the locations where its precession frequency matches the precession frequency the planet imposes on the residual planetesimals, their eccentricity is excited by its resonant perturbation. Due to the hydrodynamic drag by the residual disk gas, the planetesimals undergo orbital decay as their excited eccentricities are effectively damped. During the depletion of the disk gas, the planet’s secular resonance propagates inward and clears a wide gap over an extended region of the disk. Although some residual intermediate-size planetesimals may remain in the gap, their surface density is too low to either produce super-Earths or lead to sufficiently frequent disruptive collisions to generate any observable dusty signatures. The main advantage of this lone-planet sweeping-secular-resonance model over the previous multiple gas giant tidal truncation scenario is the relaxed requirement on the number of gas giants. The observationally inferred upper mass limit can also be satisfied provided the hypothetical planet has a significant eccentricity. A significant fraction of solar or more massive stars bear gas giant planets with significant eccentricities. If these planets acquired their present-day kinematic properties prior to the depletion of their natal disks, their sweeping secular resonance would effectively impede the retention of neighboring planets and planetesimals over a wide range of orbital semimajor axes.

On the existence of planets around the pulsar PSR B0329+54

Results of timing measurements of the pulsar PSR B0329+54 obtained in 1968--2012 using the Big Scanning Antenna of the Pushchino Radio Astronomy Observatory (at 102 and 111 MHz), the DSS 13 and DSS 14 telescopes of the Jet Propulsion Laboratory (2388 MHz), and the 64 m telescope of the Kalyazin Radio Astronomy Observatory (610 MHz) are presented. The astrometric and rotational parameters of the pulsar are derived at a new epoch. Periodic variations in the barycentric timing residuals have been found, which can be explained by the presence of a planet orbiting the pulsar, with an orbital period $P_{1}$ = 27.8 yr, mass \textit{$m_{c}$}sin\textit{i} = 2$M_{\oplus}$, and orbital semi-major axis $a$ = 10.26 AU. The results of this study do not confirm existence of a proposed second planet with orbital period $P_{2}$ = 3 yr.

A Specific Nongravitational Effect in the Asteroid Belt

The evolution of orbits of asteroids found in the IRAS and WISE albedo databases was calculated numerically from 2005 to 2016. It follows from the analysis of the obtained results that a certain nongravitational effect (NGE) currently affects the motion of a considerable fraction of main-belt asteroids with diameters up to 40 km. This conclusion agrees with the available data regarding the axial rotation of asteroids. The NGE manifests itself in an increase in the semimajor axes of orbits of low-albedo asteroids relative to the semimajor axes of orbits of high-albedo bodies. The NGE-induced rate of elongation of semimajor axes of asteroids with albedos рv < 0.1 may be as high as (2–8) × 10–8 AU/year. Errors in orbital elements of asteroids (unrelated to the accuracy of observational data used to determine these orbital elements) were found in one of the MPC catalogues for 2003 in the process of estimation of the accuracy of calculations.