Analytical attitude prediction of spin stabilized spacecrafts perturbed by magnetic residual torque

An analytical approach for spin-stabilized spacecraft attitude prediction is presented for the influence of the residual magnetic torques. Assuming an inclined dipole model for the Earth's magnetic field, an analytical averaging method is applied to obtain the mean residual torque every orbital period. The orbit mean anomaly is utilized to compute the average components of residual torque in the spacecraft body frame reference system. The theory is developed for time variations in the orbital elements, and non-circular orbits, giving rise to many curvature integrals. It is observed that the residual magnetic torque does not have component along the spin axis. The inclusion of this torque on the rotational motion differential equations of a spin stabilized spacecraft yields conditions to derive an analytical solution. The solution shows that residual torque does not affect the spin velocity magnitude, contributing only for the precession and the drift of the spin axis of the spacecraft. (c) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

Spin-Stabilized Spacecrafts: Analytical Attitude Propagation Using Magnetic Torques

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Spin stabilized satellite's attitude analytical prediction

An analytical approach for spin stabilized attitude propagation is presented, considering the coupled effect of the aerodynamic torque and the gravity gradient torque. A spherical coordination system fixed in the satellite is used to locate the satellite spin axis in relation to the terrestrial equatorial system. The spin axis direction is specified by its right ascension and the declination angles and the equation of motion are described by these two angles and the magnitude of the spin velocity. An analytical averaging method is applied to obtain the mean torques over an orbital period. To compute the average components of both aerodynamic torque and the gravity gradient torque in the satellite body frame reference system, an average time in the fast varying orbit element, the mean anomaly, is utilized. Afterwards, the inclusion of such torques on the rotational motion differential equations of spin stabilized satellites yields conditions to derive an analytical solution. The pointing deviation evolution, that is, the deviation between the actual spin axis and the computed spin axis, is also availed. In order to validate the analytical approach, the theory developed has been applied for spin stabilized Brazilian satellite SCD1, which are quite appropriated for verification and comparison of the data generated and processed by the Satellite Control Center of the Brazil National Research Institute (INPE). Numerical simulations performed with data of Brazilian Satellite SCD1 show the period that the analytical solution can be used to the attitude propagation, within the dispersion range of the attitude determination system performance of Satellite Control Center of the Brazilian Research Institute.

Analytical prediction of the spin stabilized satellite's attitude using the solar radiation torque

The aim of this paper is to present an analytical solution for the spin motion equations of spin-stabilized satellite considering only the influence of solar radiation torque. The theory uses a cylindrical satellite on a circular orbit and considers that the satellite is always illuminated. The average components of this torque were determined over an orbital period. These components are substituted in the spin motion equations in order to get an analytical solution for the right ascension and declination of the satellite spin axis. The time evolution for the pointing deviation of the spin axis was also analyzed. These solutions were numerically implemented and compared with real data of the Brazilian Satellite of Data Collection - SCD1 an SCD2. The results show that the theory has consistency and can be applied to predict the spin motion of spin-stabilized artificial satellites.

Extraction of spin periods of space debris from optical light curves

The population of space debris increased drastically during the last years. These objects have become a great threat for active satellites. Because the relative velocities between space debris and satellites are high, space debris objects may destroy active satellites through collisions. Furthermore, collisions involving massive objects produce large number of fragments leading to significant growth of the space debris population. The long term evolution of the debris population is essentially driven by so-called catastrophic collisions. An effective remediation measure in order to stabilize the population in Low Earth Orbit (LEO) is therefore the removal of large, massive space debris. To remove these objects, not only precise orbits, but also more detailed information about their attitude states will be required. One important property of an object targeted for removal is its spin period, spin axis orientation and their change over time. Rotating objects will produce periodic brightness variations with frequencies which are related to the spin periods. Such a brightness variation over time is called a light curve. Collecting, but also processing light curves is challenging due to several reasons. Light curves may be undersampled, low frequency components due to phase angle and atmospheric extinction changes may be present, and beat frequencies may occur when the rotation period is close to a multiple of the sampling period. Depending on the method which is used to extract the frequencies, also method-specific properties have to be taken into account. The astronomical Institute of the University of Bern (AIUB) light curve database will be introduced, which contains more than 1,300 light curves acquired over more than seven years. We will discuss properties and reliability of different time series analysis methods tested and currently used by AIUB for the light curve processing. Extracted frequencies and reconstructed phases for some interesting targets, e.g. GLONASS satellites, for which also SLR data were available for the period confirmation, will be presented. Finally we will present the reconstructed phase and its evolution over time of a High-Area-to-Mass-Ratio (HAMR) object, which AIUB observed for several years.

Effects of spin on high-energy radiation from accreting black holes

Observations of jets in X-ray binaries show a correlation between radio power and black hole spin. This correlation, if confirmed, points toward the idea that relativistic jets may be powered by the rotational energy of black holes. In order to examine this further, we perform general relativistic radiative transport calculations on magnetically arrested accretion flows, which are known to produce powerful jets via the Blandfordâ Znajek (BZ) mechanism. We find that the X-ray and γ-ray emission strongly depend on spin and inclination angle. Surprisingly, the high-energy power does not show the same dependence on spin as the BZ jet power, but instead can be understood as a redshift effect. In particular, photons observed perpendicular to the spin axis suffer little net redshift until originating from close to the horizon. Such observers see deeper into the hot, dense, highly magnetized inner disk region. This effect is largest for rapidly rotating black holes due to a combination of frame dragging and decreasing horizon radius. While the X-ray emission is dominated by the near horizon region, the near-infrared (NIR) radiation originates at larger radii. Therefore, the ratio of X-ray to NIR power is an observational signature of black hole spin.

General classical theory of spinning particles in a meson field

An exact classical theory of the motion of a point dipole in a meson field is given which takes into account the effects of the reaction of the emitted meson field. The meson field is characterized by a constant $\chi =\mu /\hslash $ of the dimensions of a reciprocal length, $\mu $ being the meson mass, and as $\chi \rightarrow $ 0 the theory of this paper goes over continuously into the theory of the preceding paper for the motion of a spinning particle in a Maxwell field. The mass of the particle and the spin angular momentum are arbitrary mechanical constants. The field contributes a small finite addition to the mass, and a negative moment of inertia about an axis perpendicular to the spin axis. A cross-section (formula (88 a)) is given for the scattering of transversely polarized neutral mesons by the rotation of the spin of the neutron or proton which should be valid up to energies of 10$^{9}$ eV. For low energies E it agrees completely with the old quantum cross-section, having a dependence on energy proportional to p$^{4}$/E$^{2}$ (p being the meson momentum). At higher energies it deviates completely from the quantum cross-section, which it supersedes by taking into account the effects of radiation reaction on the rotation of the spin. The cross-section is a maximum at E $\sim $ 3$\cdot $5$\mu $, its value at this point being 3 $\times $ 10$^{-26}$ cm.$^{2}$, after which it decreases rapidly, becoming proportional to E$^{-2}$ at high energies. Thus the quantum theory of the interaction of neutrons with mesons goes wrong for E $\gtrsim $ 3$\mu $. The scattering of longitudinally polarized mesons is due to the translational but not the rotational motion of the dipole and is at least twenty thousand times smaller. With the assumption previously made by the present author that the heavy partilesc may exist in states of any integral charge, and in particular that protons of charge 2e and - e may occur in nature, the above results can be applied to charged mesons. Thus transversely polarised mesons should undergo a very big scattering and consequent absorption at energies near 3$\cdot $5$\mu $. Hence the energy spectrum of transversely polarized mesons should fall off rapidly for energies below about 3$\mu $. Scattering plays a relatively unimportant part in the absorption of longitudinally polarized mesons, and they are therefore much more penetrating. The theory does not lead to Heisenberg explosions and multiple processes.

Isotropic heating of galaxy cluster cores via rapidly reorienting active galactic nucleus jets

Active galactic nucleus (AGN) jets carry more than sufficient energy to stave off catastrophic cooling of the intracluster medium (ICM) in the cores of cool-core clusters. However, in order to prevent catastrophic cooling, the ICM must be heated in a near-isotropic fashion and narrow bipolar jets with P-jet = 10(44-45) erg s(-1), typical of radio AGNs at cluster centers, are inefficient in heating the gas in the transverse direction to the jets. We argue that due to existent conditions in cluster cores, the supermassive black holes (SMBHs) will, in addition to accreting gas via radiatively inefficient flows, experience short stochastic episodes of enhanced accretion via thin disks. In general, the orientation of these accretion disks will be misaligned with the spin axis of the black holes (BHs) and the ensuing torques will cause the BH's spin axis (and therefore the jet axis) to slew and rapidly change direction. This model not only explains recent observations showing successive generations of jet-lobes-bubbles in individual cool-core clusters that are offset from each other in the angular direction with respect to the cluster center, but also shows that AGN jets can heat the cluster core nearly isotropically on the gas cooling timescale. Our model does require that the SMBHs at the centers of cool-core clusters be spinning relatively slowly. Torques from individual misaligned disks are ineffective at tilting rapidly spinning BHs by more than a few degrees. Additionally, since SMBHs that host thin accretion disks will manifest as quasars, we predict that roughly 1-2 rich clusters within z < 0.5 should have quasars at their centers.

Structure of the earth's core and lowermost mantle from seismic PKP waves

This thesis addresses the fine structure, both radial and lateral, of compressional wave velocity and attenuation of the Earth's core and the lowermost mantle using waveforms, differential travel times and amplitudes of PKP waves, which penetrate the Earth's core.

The structure near the inner core boundary (ICB) is studied by analyzing waveforms of a regional sample. The waveform modeling approach is demonstrated to be an effective tool for constrainning the ICB structure. The best model features a sharp velocity jump of 0.78km/s at the ICB and a low velocity gradient at the lowermost outer core (indicating possible inhomogeneity) and high attenuation at the top of the inner core.

A spherically symmetric P-wave model of the core, is proposed from PKP differential times, waveforms and amplitudes. The ICB remains sharp with a velocity jump of 0. 78km/ s. A very low velocity gradient at the base of the fluid core is demonstrated to be a robust feature, indicating inhomogeneity is practically inevitable. The model also indicates that the attenuation in the inner core decreases with depth. The velocity at D" is smaller than PREM.

The inner core is confirmed to be very anisotropic, possessing a cylindrical symmetry around the Earth spin axis with the N-S direction 3% faster than the E-W direction. All of the N-S rays through the inner core were found to be faster than the E-W rays by 1.5 to 3.5s. Exhaustive data selection and efforts in insolating contributions from the region above ensure that this is an inner core feature.

The anisotropy at the very top of the inner core is found to be distinctly different from the deeper part. The top 60km of the inner core is not anisotropic. From 60km to 150km, there appears to be a transition from isotropy to anisotropy.

PKP differential travel times are used to study the P velocity structure in D". Systematic regional variations of up to 2s in AB-DF times were observed, attributed primarily to heterogeneities in the lower 500km of the mantle. However, direct comparisons with tomographic models are not successful.

Demographic studies of extrasolar planets

Uncovering the demographics of extrasolar planets is crucial to understanding the processes of their formation and evolution. In this thesis, we present four studies that contribute to this end, three of which relate to NASA's Kepler mission, which has revolutionized the field of exoplanets in the last few years.

In the pre-Kepler study, we investigate a sample of exoplanet spin-orbit measurements---measurements of the inclination of a planet's orbit relative to the spin axis of its host star---to determine whether a dominant planet migration channel can be identified, and at what confidence. Applying methods of Bayesian model comparison to distinguish between the predictions of several different migration models, we find that the data strongly favor a two-mode migration scenario combining planet-planet scattering and disk migration over a single-mode Kozai migration scenario. While we test only the predictions of particular Kozai and scattering migration models in this work, these methods may be used to test the predictions of any other spin-orbit misaligning mechanism.

We then present two studies addressing astrophysical false positives in Kepler data. The Kepler mission has identified thousands of transiting planet candidates, and only relatively few have yet been dynamically confirmed as bona fide planets, with only a handful more even conceivably amenable to future dynamical confirmation. As a result, the ability to draw detailed conclusions about the diversity of exoplanet systems from Kepler detections relies critically on understanding the probability that any individual candidate might be a false positive. We show that a typical a priori false positive probability for a well-vetted Kepler candidate is only about 5-10%, enabling confidence in demographic studies that treat candidates as true planets. We also present a detailed procedure that can be used to securely and efficiently validate any individual transit candidate using detailed information of the signal's shape as well as follow-up observations, if available.

Finally, we calculate an empirical, non-parametric estimate of the shape of the radius distribution of small planets with periods less than 90 days orbiting cool (less than 4000K) dwarf stars in the Kepler catalog. This effort reveals several notable features of the distribution, in particular a maximum in the radius function around 1-1.25 Earth radii and a steep drop-off in the distribution larger than 2 Earth radii. Even more importantly, the methods presented in this work can be applied to a broader subsample of Kepler targets to understand how the radius function of planets changes across different types of host stars.

通过第一性原理计算研究内地核的结构与成分

The determination of the composition and structure of the Earth’s inner core has long been the major subject in the study of the Earth’s deep interior. It’s widely believed that the Earth’s core is formed by iron with a fraction of nickel. However, light elements must exist in the inner core because the earth core is less dense than pure iron-nickel alloy (~2-3% in the solid inner core and ~6-7% in the liquid outer core). The questions are what and how much light element is there in the iron-nickel alloy. Besides the composition, the crystal structure of the iron with or without light element is also not well known. According to the seismological observations, the sound waves propagate 3-4% faster along the spin axis than in the equatorial plane. That means the inner core is anisotropic. The densest structure of iron-nickel alloy should be h.c.p structure under the very high pressures. However, the h,c,p structure does not propagate waves anisotropic ally. Then what is the structure of the iron-nickel alloy or the iron-nickle-light element alloy. In this study, we tried to predict the composition and the structure of the inner core through ab initio calculation of the Gibbs free energy, which is a function of internal energy, density and entropy. We conclude that the h.c.p structure is more stable than the b.c.c structure under high pressure and 0 K, but with the increase of temperature, the free energy of the b.c.c structure is decreasing much faster than the h.c.p structure caused by the vibration of the atomics, so the b.c.c structure is more stable at high temperatures. With the addition of light elements (S or Si or both), the free energy of b.c.c. decreases even faster, about 3at% of Si not only explains why the inner core is about 2-3 % lighter than the iron-nickle alloy, but also reasons why the inner core is anisotropic, since the b.c.c. structure becomes more stable than the h.c.p structure at 5500-6000K and b.c.c. is anisotropic in propagating seismic waves. Therefore, we infer that the inner core of the earth is formed by b.c.c iron and a fraction of nickel plus ~3at.% Si, with a temperature higher than 5500K, which is consistent with the studies from other approaches.

Modele fizyczne planetoid pojedynczych i podwójnych otrzymane na podstawie przeglądów fotometrycznych: przygotowanie do naukowego wykorzystania danych z kosmicznej misji Gaia

Wydział Fizyki

The Well-Aligned Orbit of Wasp-84b: Evidence for Disk Migration of a Hot Jupiter

We report the sky-projected orbital obliquity (spin–orbit angle) of WASP-84 b, a 0.69MJup planet in an 8.52 day orbit around a G9V/K0V star, to be λ = −0.3 ± 1.7°. We obtain a true obliquity of ψ = 17.3 ± 7.7° from a measurement of the inclination of the stellar spin axis with respect to the sky plane. Due to the young age and the weak tidal forcing of the system, we suggest that the orbit of WASP-84b is unlikely to have both realigned and circularized from the misaligned and/or eccentric orbit likely to have arisen from high-eccentricity migration. Therefore we conclude that the planet probably migrated via interaction with the protoplanetary disk. This would make it the first “hot Jupiter” (P d < 10 ) to have been shown to have migrated via this pathway. Further, we argue that the distribution of obliquities for planets orbiting cool stars (Teff < 6250 K) suggests that high-eccentricity migration is an important pathway for the formation of short-orbit, giant planets.

Critical reappraisal of Late Mesozoic-Cenozoic Central and North Atlantic, Caribbean and Mediterranean evolution

(l) The Pacific basin (Pacific area) may be regarded as moving eastwards like a double zip fastener relative to the continents and their respective plates (Pangaea area): opening in the East and closing in the West. This movement is tracked by a continuous mountain belt, the collision ages of which increase westwards. (2) The relative movements between the Pacific area and the Pangaea area in the W-E/E-W direction are generated by tidal forces (principle of hypocycloid gearing), whereby the lower mantle and the Pacific basin or area (Pacific crust = roof of the lower mantle?) rotate somewhat faster eastwards around the Earth's spin axis relative to the upper mantle/crust system with the continents and their respective plates (Pangaea area) (differential rotation). (3) These relative West to East/East to West displacements produce a perpetually existing sequence of distinct styles of opening and closing ocean basins, exemplified by the present East to West arrangement of ocean basins around the globe (Oceanic or Wilson Cycle: Rift/Red Sea style; Atlantic style; Mediterranean/Caribbean style as eastwards propagating tongue of the Pacific basin; Pacific style; Collision/Himalayas style). This sequence of ocean styles, of which the Pacific ocean is a part, moves eastwards with the lower mantle relative to the continents and the upper-mantle/crust of the Pangaea area. (4) Similarly, the collisional mountain belt extending westwards from the equator to the West of the Pacific and representing a chronological sequence of collision zones (sequential collisions) in the wake of the passing of the Pacific basin double zip fastener, may also be described as recording the history of oceans and their continental margins in the form of successive Wilson Cycles. (5) Every 200 to 250 m.y. the Pacific basin double zip fastener, the sequence of ocean styles of the Wilson Cycle and the eastwards growing collisional mountain belt in their wake complete one lap around the Earth. Two East drift lappings of 400 to 500 m.y. produce a two-lap collisional mountain belt spiral around a supercontinent in one hemisphere (North or South Pangaea). The Earth's history is subdivided into alternating North Pangaea growth/South Pangaea breakup eras and South Pangaea growth/North Pangaea breakup eras. Older North and South Pangaeas and their collisional mountain belt spirals may be reconstructed by rotating back the continents and orogenic fragments of a broken spiral (e.g. South Pangaea, Gondwana) to their previous Pangaea growth era orientations. In the resulting collisional mountain belt spiral, pieced together from orogenic segments and fragments, the collision ages have to increase successively towards the West. (6) With its current western margin orientated in a West-East direction North America must have collided during the Late Cretaceous Laramide orogeny with the northern margin of South America (Caribbean Andes) at the equator to the West of the Late Mesozoic Pacific. During post-Laramide times it must have rotated clockwise into its present orientation. The eastern margin of North America has never been attached to the western margin of North Africa but only to the western margin of Europe. (7) Due to migration eastwards of the sequence of ocean styles of the Wilson Cycle, relative to a distinct plate tectonic setting of an ocean, a continent or continental margin, a future or later evolutionary style at the Earth's surface is always depicted in a setting simultaneously developed further to the West and a past or earlier style in a setting simultaneously occurring further to the East. In consequence, ahigh probability exists that up to the Early Tertiary, Greenland (the ArabiaofSouth America?) occupied a plate tectonic setting which is comparable to the current setting of Arabia (the Greenland of Africa?). The Late Cretaceous/Early Tertiary Eureka collision zone (Eureka orogeny) at the northern margin of the Greenland Plate and on some of the Canadian Arctic Islands is comparable with the Middle to Late Tertiary Taurus-Bitlis-Zagros collision zone at the northern margin of the Arabian Plate.

Propagação da atitude de satélites artificiais estabilizados por rotação: torque residual médio com o modelo de quadripolo para o campo geomagnético

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)