Autonomous optical navigation using nanosatellite-class instruments: a Mars approach case study

This paper examines the effectiveness of small star trackers for orbital estimation. Autonomous optical navigation has been used for some time to provide local estimates of orbital parameters during close approach to celestial bodies. These techniques have been used extensively on spacecraft dating back to the Voyager missions, but often rely on long exposures and large instrument apertures. Using a hyperbolic Mars approach as a reference mission, we present an EKF-based navigation filter suitable for nanosatellite missions. Observations of Mars and its moons allow the estimator to correct initial errors in both position and velocity. Our results show that nanosatellite-class star trackers can produce good quality navigation solutions with low position (\(<300\,\text {m}\)) and velocity (\(<0.15\,\text {m/s}\)) errors as the spacecraft approaches periapse.     

Mission opportunities for human exploration of Mars

An indirect optimization procedure is applied to find the mission opportunities for a manned or round-trip mission to Mars. Both the conjunction-class and opposition-class high-thrust trajectories are considered, taking into account simple legs (with only departure and arrival impulses), three-impulse legs (departure, midcourse and arrival impulses) and flyby legs, where the non-propelled flyby of the planet Venus is used instead of the midcourse impulse to reduce the propellant consumption. The absolute positions of all the relevant planets repeat almost perfectly after 32 years: therefore, only the mission opportunities in a 32-year syzygistic cycle are analyzed. The two-body problem formulation is sufficient for preliminary analyses of interplanetary missions and the trajectory is approximated by heliocentric conic orbits passing through the centres of the planets. The mission opportunities correspond to the local minima of the characteristic velocity, that is, the sum of the actual velocity changes obtained by expending the propellant. Numerical results are presented to show that the same mathematical approach can be applied to different classes of missions, to emphasize the indications suggested by Pontryagin's Maximum Principle, to point out some periodicities in the solutions and to discuss the problem of providing initial guesses at the solutions.     

Symmetries in the Optimal Control of Solar Sail Spacecraft

The theory of optimal control is applied to obtain minimum-time trajectories for solar sail spacecraft for interplanetary missions. We consider the gravitational and solar radiation forces due to the Sun. The spacecraft is modelled as a flat sail of mass m and surface area A and is treated dynamically as a point mass. Coplanar circular orbits are assumed for the planets. We obtain optimal trajectories for several interrelated problem families and develop symmetry properties that can be used to simplify the solution-finding process. For the minimum-time planet rendezvous problem we identify different solution branches resulting in multiple solutions to the associated boundary value problem. We solve the optimal control problem via an indirect method using an efficient cascaded computational scheme. The global optimizer uses a technique called Adaptive Simulated Annealing. Newton and Quasi-Newton Methods perform the terminal fine tuning of the optimization parameters.     

Could we identify hot ocean-planets with CoRoT, Kepler and Doppler velocimetry?

Planets less massive than about 10 MEarth are expected to have no massive H-He atmosphere and a cometary composition (∼50% rocks, 50% water, by mass) provided they formed beyond the snowline of protoplanetary disks. Due to inward migration, such planets could be found at any distance between their formation site and the star. If migration stops within the habitable zone, this may produce a new kind of planets, called ocean-planets. Ocean-planets typically consist in a silicate core, surrounded by a thick ice mantle, itself covered by a 100 km-deep ocean. The possible existence of ocean-planets raises important astrobiological questions: Can life originate on such body, in the absence of continent and ocean-silicate interfaces? What would be the nature of the atmosphere and the geochemical cycles? In this work, we address the fate of hot ocean-planets produced when migration ends at a closer distance. In this case the liquid/gas interface can disappear, and the hot H₂O envelope is made of a supercritical fluid. Although we do not expect these bodies to harbor life, their detection and identification as water-rich planets would give us insight as to the abundance of hot and, by extrapolation, cool ocean-planets. The water reservoir of these planets seems to be weakly affected by gravitational escape, provided that they are located beyond some minimum distance, e.g. 0.04 AU for a 5-Earth-mass planet around a Sun-like star. The swelling of their water atmospheres by the high stellar flux is expected not to significantly increase the planets' radii. We have studied the possibility of detecting and characterizing these hot ocean-planets by measuring their mean densities using transit missions in space—CoRoT (CNES) and Kepler (NASA)—in combination with Doppler velocimetry from the ground—HARPS (ESO) and possible future instruments. We have determined the domain in the [stellar magnitude, orbital distance] plane where discrimination between ocean-planets and rocky planets is possible with these instruments. The brightest stars of the mission target lists and the planets closest to their stars are the most favorable cases. Full advantage of high precision photometry by CoRoT, and particularly Kepler, can be obtained only if a new generation of Doppler instruments is built.     

The Knorre astronomers' dynasty

We attempt to throw light upon the poorly known astronomical dynasty of Knorre and describe its contribution to astronomy. The founder of the dynasty, Ernst Christoph Friedrich Knorre (1759–1810), was born in Germany in 1759, and since 1802 he was a Professor of Mathematics at the Tartu University, and observer at its temporary observatory. He determined the first coordinates of Tartu by stellar observations. Karl Friedrich Knorre (1801–1883) was the first director of the Naval Observatory in Nikolaev since the age of 20, provided the Black Sea navy with accurate time and charts, trained mariners in astronomical navigation, and certified navigation equipment. He compiled star maps and catalogues, and determined positions of comets and planets. He also participated in Bessel's project of the Academic Star Charts, and was responsible for Hora 4, published by the Berlin Academy of Sciences. This sheet permitted to discover two minor planets, Astraea and Flora. Viktor Knorre (1840–1919) was born in Nikolaev. In 1862 he left for Berlin to study astronomy. After defending his thesis for a doctor's degree, he went to Pulkovo as an astronomical calculator in 1867. Since 1873 Viktor worked as an observer of the Berlin Observatory Fraunhofer refractor. His main research focussed on minor planets, comets and binary stars. He discovered the minor planets Koronis, Oenone, Hypatia and Penthesilea. Viktor Knorre also worked on improving astronomical instrumentation, e.g. the Knorre & Heele equatorial telescope mounting (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Serpentinization and the inorganic synthesis of H2 in planetary surfaces

The near-surface inorganic synthesis of molecular hydrogen (H₂) is a fundamental process relevant to the origins and to the sustenance of early life on Earth and potentially other planets. Hydrogen production through the decomposition of water is thought to be a principal reaction that occurs during hydrothermal alteration of olivine, an iron-magnesium silicate abundant near planetary surfaces. We demonstrate that copious amounts of H₂ are produced only when the olivine undergoing alteration (serpentinization) contains 1 to 50 mol% iron over a variety of planetary surface P-T conditions. This suggests that extrasolar Earth-like planets that are hosted by a star with iron contents up to two times the solar value could support life provided they are hydrothermally active and fall within the habitable zone around the star.     

系外行星系统掩星周期变化研究进展

在掩星法发现的系外行星系统中,如果存在其他未知的伴星绕同一颗恒星运动,掩星行星由于受到伴星引力的影响,运动轨道将发生变化,轨道周期不再是常数,而是变化的。利用这种变化探测掩星系统中的其他行星,已成为一种新的方法。主要介绍了未知行星与掩星行星之间的引力作用引起的掩星周期变化效应,以及掩星周期变化法探测系外行星的理论和研究进展状况,最后简要讨论了几种影响掩星周期变化的其他因素:共轨行星、卫星、潮汐效应、相对论效应及恒星的引力四极矩等。     

The migration and growth of protoplanets in protostellar discs

We investigate the gravitational interaction of a Jovian-mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the protoplanetary disc from which it formed. Different disc surface density distributions are investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protoplanet. Non-linear two-dimensional hydrodynamic simulations are employed using three independent numerical codes.
A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches the central star in a near-circular orbit after a characteristic viscous time‐scale of ∼10⁴ initial orbital periods. This is found to be independent of whether the protoplanet is allowed to accrete mass or not. Inward migration is helped by the disappearance of the inner disc, and therefore the positive torque it would exert, because of accretion on to the central star. Maximally accreting protoplanets reach about 4 Jovian masses on reaching the neighbourhood of the central star. Our results indicate that a realistic upper limit for the masses of closely orbiting giant planets is ∼5 Jupiter masses, if they originate in protoplanetary discs similar to the minimum-mass solar nebula. This is because of the reduced accretion rates obtained for planets of increasing mass.
Assuming that some process such as termination of the inner disc through a magnetospheric cavity stops the migration, the range of masses estimated for a number of close orbiting giant planets as well as their inward orbital migration can be accounted for by consideration of disc–protoplanet interactions during the late stages of giant planet formation.     

Interplanetary dust dynamics: I. Long-term gravitational effects of the inner planets on zodiacal dust

Whereas the inner planets' perturbations on meteoroids' and larger interplanetary bodies' orbits have been studied extensively, they are usually neglected in studies of the dynamics of smaller particles producing the zodiacal light through scattering of sunlight. Forces acting on these dust particles are fairly well known and include radiation forces and interaction with the solar wind. This article is the first in a series aimed at improving our knowledge of the dynamical evolution of dust in interplanetary space by studying the combined effects of these perturbations including gravitational perturbations by the planets Venus, Earth, Mars, and Jupiter. The necessity of including effects of the inner planets in dust dynamics investigations is established. Sample trajectories are presented to illustrate commonly occurring phenomenae, such as nonmonotonic changes in semimajor axis, eccentricity, inclination, and in the line of nodes. These perturbations are shown to be due to the inner planets as opposted to Jupiter or nongravitational forces.     

TESS空间卫星单扇区变星的周期性研究

TESS (Transiting Exoplanet Survey Satellite)空间卫星提供的短曝光、高精度光度测量为寻找并区分变星与搜寻行星提供了良好的数据.利用变星源的光变曲线,使用周期频谱分析与光变折叠等一系列方法分析了TESS空间卫星21扇区19995颗拥有高质量光变数据的目标源,并对这些源进行了分类,共获得4624颗变星,其中食双星322颗、脉动变星470颗、行星凌星37颗.所得变星结果与VSX (The International Variable Star Index)变星表进行了交叉比较,共交叉匹配了625颗变星源,这些交叉源中共有131颗为食双星系统、31颗为脉动变星,并通过周期频谱分析获取了双星绕转以及脉动周期.另外在59颗变星中发现明显耀发现象,交叉源中有8颗变星为行星凌星并同样通过周期频谱分析获取了行星绕转周期,从而验证了TESS空间卫星数据对变星分析的可行性.通过利用TESS空间卫星21扇区获得的变星周期结果与VSX变星表中提供的变星周期对比,发现与VSX变星表中绝大部分变星的周期一致,有一部分结果与VSX变星表中的结果差别较大,对这些变星周期结果做了进一步修正,并给出了变星表未列出的变星周期结果.     

Research on Periodicity of Single Sector Variable Star of TESS Space Satellite

The short exposure and high precision photometry of TESS (Transiting Exoplanet Survey Satellite) space satellite provide good data for distinguishing variable stars and searching planets. In this paper, a series of methods, such as periodic spectrum and phase folding, are used to analyze 19995 target sources with high-quality variable data in TESS sector 21, and these sources are classified. A total of 4624 variable stars are obtained, including 322 binary stars, 470 pulsating variable stars, and 37 planetary transients. A total of 625 variable sources were cross matched with VSX (The International Variable Star Index). Among them, 131 were eclipsing binary systems and 31 were pulsating variables, whose periods are obtained by periodic spectrum. The other 59 variable stars have flare phenomena, and 8 stars have transiting planets, whose rotation periods are also obtained through the periodic spectrum. The feasibility of the analysis of variable stars by TESS space satellite data is verified. By comparing the period results obtained by TESS space satellite sector 21 with the variable star period provided by VSX variable star table, we found that the periods of most variable stars are consistent with those in this paper, and a few of them need to be corrected. Finally, the verified and corrected variable star tables are provided in this paper.     

On the migration of a system of protoplanets

The evolution of a system consisting of a protoplanetary disc with two embedded Jupiter-sized planets is studied numerically. The disc is assumed to be flat and non-self-gravitating; this is modelled by the planar (two-dimensional) Navier–Stokes equations. The mutual gravitational interaction of the planets and the star, and the gravitational torques of the disc acting on the planets and the central star are included. The planets have an initial mass of one Jupiter mass M _Jup each, and the radial distances from the star are one and two semimajor axes of Jupiter, respectively.
During the evolution a joint wide annular gap is created by the planets. Both planets increase their mass owing to accretion of gas from the disc: after about 2500 orbital periods of the inner planet it has reached a mass of 2.3  M _Jup, while the outer planet has reached a mass of 3.2  M _Jup. The net gravitational torques exerted by the disc on the planets result in an inward migration of the outer planet on time-scales comparable to the viscous evolution time of the disc. The semimajor axis of the inner planet remains constant as there is very little gas left in its vicinity to induce any migration. When the distance of close approach eventually becomes smaller than the mutual Hill radius, the eccentricities increase strongly and the system may become unstable.
If disc depletion occurs rapidly enough before the planets come too close to each other, a stable system similar to our own Solar system may remain. Otherwise the orbits may become unstable and produce systems like υ And.     

Asymptotic solution for the two-body problem with constant tangential thrust acceleration

An analytical solution of the two body problem perturbed by a constant tangential acceleration is derived with the aid of perturbation theory. The solution, which is valid for circular and elliptic orbits with generic eccentricity, describes the instantaneous time variation of all orbital elements. A comparison with high-accuracy numerical results shows that the analytical method can be effectively applied to multiple-revolution low-thrust orbit transfer around planets and in interplanetary space with negligible error.     

A new opportunity from space: PLATO mission

The satellite PLATO represents a new challenge for future investigations of exoplanets and oscillations of stars. It is one of the proposed missions of ESA COSMIC VISION 2015–2025 and it is scheduled for launch in 2017. The goal of the mission is a full characterization of the planet star systems with an asteroseismic analysis of the host stars. The PLATO Payload Consortium (PPLC) includes several European countries which are employed in the assessment study of the mission. Thanks to the high precision photometry, PLATO is thought to be able to detect planets and oscillations within a large sample of targets.     

Migration and evolution of extrasolar planets

Giant planets in circumstellar disks can migrate inward from their initial (formation) positions at several AUs. Inward radial migration of the planet is caused by torques between the planet and the disk; outward radial migration of the planet is caused by torques between the planet and the spinning star, and by torques due to Roche lobe overflow and consequent mass loss from the planet. We present self-consistent numerical considerations of the problem of migrating giant planets by summing torques on planets for various physical parameters of the disk and of planets. We find that Jupiter-mass planets can stably arrive and survive at small heliocentric distances, thus reproducing observed properties of some of the recently discovered extra-solar planets. The range of fates of massive planets is broad, and some perish by losing all their mass onto the central star during Roche lobe overflow, while others survive for the lifetime of the central star. Surviving planets cluster into two groups when examined in terms of final mass and final heliocentric distance: those which have lost mass and those which have not. Some of the observed extrasolar planets fall into each of these two exclusive classes. We also find that there is an inner boundary for planets' final heliocentric distances, caused by tidal torques with the central star. Planets in small orbits are shown to be stable against atmospheric loss.     

Capture of stars by rotating homogeneous spherical clusters

Changes of the orbit of a star passing through a homogeneous spherical cluster have been estimated. Before entering the cluster the star is supposed to move in a Keplerian parabolic orbit. When passing through the cluster the star is subject both to the attraction of the smoothed-out distribution of matter in the cluster and to dynamical friction. Due to dynamical friction the energy of the star becomes negative which leads to the elliptic-type motion of the star after leaving the cluster and to capturing the star by the cluster. The formulae for the changes of the star orbit in the cluster are given. Numerical estimation shows that open clusters transform star orbits more noticeably than do globular clusters.     

Planetary microlensing signals from the orbital motion of the source star around the common barycentre

With several detections, the technique of gravitational microlensing has proven useful for studying planets that orbit stars at Galactic distances, and it can even be applied to detect planets in neighbouring galaxies. So far, planet detections by microlensing have been considered to result from a change in the bending of light and the resulting magnification caused by a planet around the foreground lens star. However, in complete analogy to the annual parallax effect caused by the revolution of the Earth around the Sun, the motion of the source star around the common barycentre with an orbiting planet can also lead to observable deviations in microlensing light curves that can provide evidence for the unseen companion. We discuss this effect in some detail and study the prospects of microlensing observations for revealing planets through this alternative detection channel. Given that small distances between lens and source star are favoured, and that the effect becomes nearly independent of the source distance, planets would remain detectable even if their host star is located outside the Milky Way with a sufficiently good photometry (exceeding present-day technology) being possible. From synthetic light curves arising from a Monte Carlo simulation, we find that the chances for such detections are not overwhelming and appear practically limited to the most massive planets (at least with current observational set-ups), but they are large enough for leaving the possibility that one or the other signal has already been observed. However, it may remain undetermined whether the planet actually orbits the source star or rather the lens star, which leaves us with an ambiguity not only with respect to its location, but also to its properties.     

Exoplanetary radio emission under different stellar wind conditions

Radio emission from extrasolar giant planets in close orbits around their host star is an active field of research, including both observational efforts and theoretical work aiming at reasonable predictions for different target planets. So far, most theoretical work assumed a distance-independent, constant stellar wind velocity. This approach is improved and expanded in two respects: first, from stellar wind models, it is known that at close distances the stellar wind is still slow and has not yet reached the velocity it has at larger distances. For this reason, less energy is available for the generation of planetary radio emission than predicted by simplified models. This correspondingly reduces the intensity of stellar wind-driven planetary radio emission, which is calculated taking into account the stellar age. Second, it can be shown that under certain conditions the steady stellar wind has to be replaced by stellar coronal mass ejections. In those cases, the planetary radio flux is strongly increased. The different flux levels expected for planets subject to different stellar wind conditions are analyzed and compared. In addition, different uncertainties in this radio flux estimation are calculated and discussed.     

Limits on the Orbits of Possible Eccentric and Inclined Moons of Extrasolar Planets Orbiting Single Stars

Limits are placed on the range of orbits and masses of possible moons orbiting extrasolar planets which orbit single central stars. The Roche limiting radius determines how close the moon can approach the planet before tidal disruption occurs; while the Hill stability of the star–planet–moon system determines stable orbits of the moon around the planet. Here the full three-body Hill stability is derived for a system with the binary composed of the planet and moon moving on an inclined, elliptical orbit relative the central star. The approximation derived here in Eq. (17) assumes the binary mass is very small compared with the mass of the star and has not previously been applied to this problem and gives the criterion against disruption and component exchange in a closed form. This criterion was applied to transiting extrasolar planetary systems discovered since the last estimation of the critical separations (Donnison in Mon Not R Astron Soc 406:1918, 2010a) for a variety of planet/moon ratios including binary planets, with the moon moving on a circular orbit. The effects of eccentricity and inclination of the binary on the stability of the orbit of a moon is discussed and applied to the transiting extrasolar planets, assuming the same planet/moon ratios but with the moon moving with a variety of eccentricities and inclinations. For the non-zero values of the eccentricity of the moon, the critical separation distance decreased as the eccentricity increased in value. Similarly the critical separation decreased as the inclination increased. In both cases the changes though very small were significant.     

Heliospheric magnetic fields, energetic particles, and the solar cycle

The heliosphere is the region filled with magnetized plasma of mainly solar origin. It extends from the solar corona to well beyond the planets, and is separated from the interstellar medium by the heliopause. The latter is embedded in a complex and still unexplored boundary region. The characteristics of heliospheric plasma, fields, and energetic particles depend on highly variable internal boundary conditions, and also on quasi-stationary external ones. Both galactic cosmic rays and energetic particles of solar and heliospheric origin are subject to intensity variations over individual solar cycles and also from cycle to cycle. Particle propagation is controlled by spatially and temporally varying interplanetary magnetic fields, frozen into the solar wind. An overview is presented of the main heliospheric components and processes, and also of the relevant missions and data sets. Particular attention is given to flux variations over the last few solar cycles, and to extrapolated effects on the terrestrial environment.