Ellipsoid Shape Model Research Articles

Asteroid spin and shape properties from Gaia DR3 photometry

The third data release of in June 2022, included the first large sample of sparse photometric data for more than 150\,000 Solar System objects (SSOs), mainly asteroids. The SSO photometric data can be processed to derive information on the physical properties for a large number of objects, including spin properties, surface photometric behaviour in a variety of illumination conditions, and overall shape. After selecting a set of 22\,815 objects for which an adequate number of accurate photometric measurements had been obtained by we applied the 'genetic' algorithm of photometric inversion developed by the Data Processing and Analysis Consortium to process SSO photometric data. Given the need to minimise the required data processing time, the algorithm was set to adopt a simple triaxial ellipsoid shape model. Our results show that in spite of the limited variety of observing circumstances and the limited numbers of measurements per object at present (in the majority of cases no greater than $40$ and still far from the number expected at the end of the mission of about $60$ - $70$), the proportion of correct determinations for the spin period among the observed targets is about $85$<!PCT!>. This percentage is based on a comparison with reliable literature data following a moderate filtering procedure developed to remove dubious solutions. The analysis performed in this paper is important in the context of developing further improvements to the adopted data reduction procedure. This includes the possible development of better solution filtering procedures that take into account, for each object, the possible presence of multiple, equivalent spin period solutions that have not been systematically investigated in this preliminary application.

The shape and surface environment of 2016 HO[formula omitted

Asteroid 2016 HO3 is a fast-rotating Near-Earth asteroid (NEA), and a potential target for future exploration. Studying the surface of this asteroid and whether it retains any regolith are primary science objectives, which can provide key clues to the formation and evolution of this small body. In order to support such future explorations, the stability condition for and distribution of regolith on a non-spherical fast-spinning small body are explored in this paper using derived models of 2016 HO3. First, a tri-axial ellipsoid shape model of 2016 HO3 is established based on light curve data. The possible shape configurations are presented. Then, the ambient environment accelerations are analyzed and compared. The stability conditions to retain regolith on the surface of the ellipsoid model is derived and evaluated numerically. The influence of shape, density, cohesion and the angle of friction on the distribution is discussed. Finally, the motion of failed regolith is investigated. The results show that 2016 HO3 is likely an elongated asteroid, which has a length to width ratio smaller than 0.48. A layer of millimeter-sized to centimeter-sized grains can exist on the surface of asteroid 2016 HO3, preferentially kept near the polar and the short axis regions. The required cohesion to bind such particles to the surface is less than 0.2 Pa. Meanwhile, any regolith disturbed from the surface will undergo periods of sliding and bouncing before escaping. This research can provide a reference for preliminary mission design for future missions to asteroid 2016 HO3.

The impact of different computational assumptions in 131 I dosimetry for hyperthyroidism therapy.

The goal of the current study was to investigate the impact of different computational models on 131 I dosimetry prior to hyperthyroidism therapy. It was also aimed to highlight an accurate and cost-effective method for routine dosimetry of graves and toxic adenoma patients. A cohort of 45 patients was recruited in the current study with Graves (n=30) and Toxic Adenoma (n=15) diseases. The eligibility criterion was determined using the patients' blood test, 99m Tc- pertechnetate scintigraphy, and ultrasound scan. A properly calibrated thyroid probe equipped with sodium iodide crystal [NaI(Tl)] was used to obtain the uptake measurements at 2, 24, 48, 72, and 96h following administration of 0.27-0.73MBq 131 I tracer. The absorbed radiation dose of the thyroid gland/nodule was calculated by three different methods. The calculation models were based on the time-integrated activity (recommended by MIRD), effective half-life (recommended by EANM), and ellipsoidal-shape assumption. The mean effective half-life was 138±41h and 110±48h in Graves and Toxic Adenoma patients, respectively. The mean residence time was 125±5h in Graves patients, while it was 93±55h in Toxic Adenoma. The amount of 131 I activity required to deliver 200Gy to the thyroid gland in Graves patients was calculated as 436±381MBq, 426±370MBq, and 488±455MBq according to MIRD, EANM, and ellipsoidal-shape model, respectively. However, the activity required to impart 300Gy in the toxic nodules was computed as 622±332MBq by MIRD, 907±588MBq by EANM, and 1060±639MBq by the ellipsoidal-shape model. Overall, no significant difference was found between the MIRD and both of the EANM and ellipsoidal-shape models in the Graves patients (R2 =0.99, P>0.05). In contrast, less agreement (R2 =0.86) was shown between EANM and MIRD in Toxic Adenoma patients with no statistically significant difference (P>0.05), while the difference was significant (Pvalue <0.05) between the MIRD and the ellipsoidal-shape model with moderate association (R2 =0.66). It was deduced that the effective half-life-based model (EANM model) is a successful and affordable method for performing dosimetry in Graves patients. While, unit density sphere model sounds the most appropriate approach to be used in Toxic Adenoma dosimetry. However, using the ellipsoidal-shape assumption in the thyroid gland/or nodule dose calculation leads to redundantly larger activity administration.

Individual Tree Segmentation Based on Mean Shift and Crown Shape Model for Temperate Forest

Light detection and ranging (LiDAR) provides high-resolution geometric information for monitoring forests at individual tree crown (ITC) level. An important task for ITC delineation is segmentation, and previous studies showed that the adaptive 3-D mean shift (AMS3D) algorithm provides effective results. AMS3D for ITC segmentation has three components for the kernel profile: shape, weight, and size. In this letter, we present an AMS3D approach based on the adaptation of the kernel profile size through an ellipsoid crown shape model. The algorithm parameters are estimated based on allometry equations derived from 22 forest plots in two study sites. After computing the mean shift (MS) vector, we initialize the parameters of the ellipsoid crown shape model to derive the kernel profile size, and further tested two crown shape models for adapting the size of the superellipsoid (SE) kernel profile. These schemes are compared with two other MS algorithms with and without kernel profile size adaptation. We select the best algorithm output per plot based on the maximum F1-score. The ellipsoid crown shape model with a SE kernel profile of n = 1.5 presents the highest recall and the best Jaccard index, especially for conifers.

Updated Equipotential Shapes of Jupiter and Saturn Using Juno and Cassini Grand Finale Gravity Science Measurements

AbstractA commonly used shape model for the giant plants of Jupiter and Saturn is an oblate ellipsoid, a simplified model of the equipotential shape. The ellipsoidal shape models were originally derived from radio occultation data and gravity data after the Voyager flybys in 1979. Through precise Doppler tracking of NASA's Juno and Cassini spacecraft telecommunications links, zonal coefficients in a spherical harmonic expansion of the gravity field of Jupiter and Saturn have been resolved to degree 10, including the detection of nonzero odd zonal harmonics, which have been interpreted as differential rotation in the atmosphere for both planets. In this work, we construct the equipotential surfaces of Jupiter and Saturn using the recently measured gravity fields determined by Juno through perijove 8 and Cassini through end of mission. For both planets, even zonal harmonics dominate the equipotential shape, differing from the reference ellipsoid up to ~32 km at Jupiter and ~125 km at Saturn in the midlatitude regions. Saturn's internal rotation period estimated with ring seismology produces a shape that is fully consistent with the Pioneer and Voyager radio occultation measurements, and Jupiter's shape is fully consistent with the Pioneer and Voyager radio occultation measurements. With current equipotential theory, the recent analysis of the depth of the deep zonal flow on Jupiter and Saturn cannot fully be explained by the shape from current radio occultation measurements; additional occultation measurements and reanalysis of the Pioneer and Voyager radio occultations and will be useful for further constraining the shape of the planets.

Dependence of Light Curves on Phase Angle and Asteroid Shape

Abstract We investigate the phase angle dependence of asteroid light curves using numerical scattering models applied to simple body shapes. For simplicity, the Kaasalainen scattering parameters are obtained from the corresponding Hapke scattering laws for C-type, S-type, and V-type asteroids. The spectral types differ substantially in the role of multiple scattering (which is largely a function of their geometric albedos) but we find that the differences on the light curve versus phase relations are modest. Using a Kaasalainen scattering law, the amplitudes and axis ratios with respect to different phase angles from 0° to 140° are plotted for these types of asteroids based on a biaxial ellipsoid shape model. Additionally, we examine the relationship between amplitude and the axis ratio for a contact binary represented by identical biaxial ellipsoids, including the effects of shadowing of one component by the other. We compare the models with published high phase angle observations, and with interstellar object 1I/‘Oumuamua (Δm = 2.5 mag at a phase angle of α = 23°), finding an axis ratio of 5.2: 1 if represented as a single ellipsoid and 3.5: 1 for each component if represented as a nose-to-nose contact binary. While a detailed fit is not attempted, the comparison shows that the single ellipsoid model is better.

Retrieval of the Fluid Love Number k2 in Exoplanetary Transit Curves

Abstract We are witness to a great and increasing interest in internal structure, composition, and evolution of exoplanets. However, direct measurements of exoplanetary mass and radius cannot be uniquely interpreted in terms of interior structure, justifying the need for an additional observable. The second degree fluid Love number, k 2, is proportional to the concentration of mass toward the body’s center, hence providing valuable additional information about the internal structure. When hydrostatic equilibrium is assumed for the planetary interior, k 2 is a direct function of the planetary shape. Previous attempts were made to link the observed tidally and rotationally induced planetary oblateness in photometric light curves to k 2 using ellipsoidal shape models. Here, we construct an analytical 3D shape model function of the true planetary mean radius that properly accounts for tidal and rotational deformations. Measuring the true planetary mean radius is critical when one wishes to compare the measured k 2 to interior theoretical expectations. We illustrate the feasibility of our method and show, by applying a Differential Evolution Markov Chain to synthetic data of WASP-121b, that a precision ≤65 ppm/ is required to reliably retrieve k 2 with present understanding of stellar limb darkening (LD), therefore improving recent results based on ellipsoidal shape models. Any improvement on stellar LD would increase such performance.

Equilibrium points and associated periodic orbits in the gravity of binary asteroid systems: (66391) 1999 KW4 as an example

The motion of a massless particle in the gravity of a binary asteroid system, referred as the restricted full three-body problem (RF3BP), is fundamental, not only for the evolution of the binary system, but also for the design of relevant space missions. In this paper, equilibrium points and associated periodic orbit families in the gravity of a binary system are investigated, with the binary (66391) 1999 KW4 as an example. The polyhedron shape model is used to describe irregular shapes and corresponding gravity fields of the primary and secondary of (66391) 1999 KW4, which is more accurate than the ellipsoid shape model in previous studies and provides a high-fidelity representation of the gravitational environment. Both of the synchronous and non-synchronous states of the binary system are considered. For the synchronous binary system, the equilibrium points and their stability are determined, and periodic orbit families emanating from each equilibrium point are generated by using the shooting (multiple shooting) method and the homotopy method, where the homotopy function connects the circular restricted three-body problem and RF3BP. In the non-synchronous binary system, trajectories of equivalent equilibrium points are calculated, and the associated periodic orbits are obtained by using the homotopy method, where the homotopy function connects the synchronous and non-synchronous systems. Although only the binary (66391) 1999 KW4 is considered, our methods will also be well applicable to other binary systems with polyhedron shape data. Our results on equilibrium points and associated periodic orbits provide general insights into the dynamical environment and orbital behaviors in proximity of small binary asteroids and enable the trajectory design and mission operations in future binary system explorations.

Force and collapsed shape of a liquid solder bump under load

It is shown that a collapsed solder bump carries load through a bump force that depends on the collapsed shape in a way that closely resembles the Young-Laplace (YLP) equation. The relation between force and shape allows deriving the force constant of the bump, which is important in solder bump reliability. For the commonly used ellipsoid shape model, the new force method gives similar results as the results derived conventionally from the increase in free surface energy but in a mathematically simpler way, omitting the difficult surface integral. The results confirm that the ellipsoid shape model is not a true solution for the collapsed shape. The new force based approach enables developing an improved shape model and it is shown that this satisfies both the YLP equation and minimum increase in surface energy better.

Large Halloween asteroid at lunar distance

The near-Earth asteroid (NEA) 2015 TB145 had a very close encounter with Earth at 1.3 lunar distances on October 31, 2015. We obtained 3-band mid-infrared observations with the ESO VLT-VISIR instrument and visual lightcurves during the close-encounter phase. The NEA has a (most likely) rotation period of 2.939 +/- 0.005 hours and the visual lightcurve shows a peak-to-peak amplitude of approximately 0.12+/-0.02 mag. We estimate a V-R colour of 0.56+/-0.05 mag from MPC database entries. Applying different phase relations to the available R-/V-band observations produced H_R = 18.6 mag (standard H-G calculations) or H_R = 19.2 mag & H_V = 19.8 mag (via the H-G12 procedure), with large uncertainties of approximately 1 mag. We performed a detailed thermophysical model analysis by using spherical and ellipsoidal shape models. The thermal properties are best explained by an equator-on (+/- ~30 deg) viewing geometry during our measurements with a thermal inertia in the range 250-700 Jm-2s-0.5K-1 (retrograde rotation) or above 500 Jm-2s-0.5K-1 (prograde rotation). We find that the NEA has a minimum size of 625 m, a maximum size of just below 700 m, and a slightly elongated shape with a/b ~1.1. The best match to all thermal measurements is found for: (i) Thermal inertia of 900 Jm-2s-0.5K-1; D_eff = 644 m, p_V = 5.5% (prograde rotation); regolith grain sizes of ~50-100 mm; (ii) thermal inertia of 400 Jm-2s-0.5K-1; D_eff = 667 m, p_V = 5.1% (retrograde rotation); regolith grain sizes of ~10-20 mm. A near-Earth asteroid model (NEATM) confirms an object size well above 600 m, significantly larger than early estimates based on radar measurements. We give recommendations for improved observing strategies for similar events in the future.

CassiniISS mutual event astrometry of the mid-sized Saturnian satellites 2005–2012

We present astrometric observations of the Saturnian satellites Mimas, Enceladus, Tethys, Dione and Rhea from Cassini Imaging Science Subsystem (ISS) narrow-angle camera (NAC) images. Image sequences were designed to observe mutual occultations between these satellites. The positions of satellite centres were estimated by fitting ellipsoidal shape models to the measured limbs of the imaged satellites. Spacecraft pointing corrections were computed using the UCAC2 star catalogue. We provide a total of 2303 astrometric observations, resulting in 976 pairs, the remainder consisting of observations of a single satellite. Mean residuals for the individual satellite positions relative to the SAT360 ephemeris were 4.3 km in the line direction and -2.4 km in the sample direction, with standard deviations of 5.6 and 7.0 km respectively, an order of magnitude improvement in precision compared to published HST observations. By considering inter-satellite separations, uncertainties in camera pointing and spacecraft positioning along with possible biases in the individual positions of the satellites can be largely eliminated, resulting in an order-of-magnitude increase in accuracy compared to that achievable using the individual satellite positions. We show how factors relating to the viewing geometry cause small biases in the individual positions of order 0.28 pixel to become systematic across the dataset as a whole and discuss options for reducing their effects . The reduced astrometric data are provided in the form of individual positions for each satellite, together with the measured positions of reference stars, in order to allow more flexibility in the processing of the observations, taking into account possible future advances in limb-fitting techniques as well as the future availability of more accurate star catalogues, such as those from the GAIA mission.

Enhancement of light depolarization by random ensembles of titania-based low-dimensional nanoparticles

Depolarization peculiarities of the light scattered by the random ensembles of titania-based low-dimensional nanoparticles are studied during the experiments with aqueous suspensions of potassium polytitanate nanoplatelets and nanoribbons. The obtained experimental results are compared with the theoretical data obtained for the random systems of oblate and prolate flattened ellipsoidal nanoparticles with various values of the shape factor and dielectric function corresponding the parent material (titanium dioxide). The possibility to recover the effective dielectric function from the depolarization ratio spectra using the ellipsoidal shape model is considered. Ellipsoidal approximation is appropriate for both the nanoplatelets and nanoribbons in the spectral region for which the real part of nanoparticles permittivity is sufficiently negative and the near-resonant excitation of longitudinal mode of charge oscillations in nanoparticles occurs. Also, ellipsoidal approximation is appropriate for nanoplatelets in the region of sufficiently po sitive real part of permittivity but gives remarkably underestimated values of the depolarization ratio for nanoribbons in the region. This is presumably caused by considerable difference in the light-induced charge distributions for nanoribbons and prolate flattened ellipsoidal nanoparticles with the decreasing efficiency in longitudinal mode excitation. The recovered values of nanoparticle permittivity exhibit the red shift with respect to the permittivity values of the parent material due to its modification in the course of nanoparticles synthesis.

Cellinoid Shape Model for Asteroids

The ellipsoid shape model plays an important role in physical research on asteroids. However, its symmetric structure cannot practically simulate real asteroids. This article applies a general shape model, named the cellinoid, instead of the ellipsoid model to simulate the asymmetric shape of asteroids. The cellinoid shape model consists of eight octants of ellipsoids having different semi-axes, with the constraint that adjacent octants must have two equal semi-axes in common. Totally, the shape of the cellinoid model is controlled by six parameters, not three as in the case of the shape of the ellipsoid. Using this shape model, the brightness of asteroids observed from the Earth can be fitted numerically by the surface triangularization of the cellinoid. The Levenberg-Marquardt algorithm is also employed here to solve a nonlinear minimization problem. Owing to the asymmetric shape of the cellinoid, the physical parameters of asteroids, such as the rotation period and pole orientation, can be fitted more accurately than in the case of the ellipsoid model. Finally, this is confirmed numerically by applying the shape to both synthetic light curves and real light curves of asteroids. Additionally, the center of mass and moment of inertia of the cellinoid are analyzed explicitly.

Determination of Porosity and Thickness of Biofilm Attached on Irregular-Shaped Media

AbstractBiofilm density, porosity, and thickness are biofilm architecture properties that are important but often difficult to measure. In this study, wet and dry biofilm densities and biofilm porosity in shredded tire biofilters were measured using a volumetric displacement method and a new porosity equation. Methods for determining the surface area and mean thickness of biofilms attached to shredded tires were developed on the basis of the box- and ellipsoid-shape models with the data of (1) the volume calculated from the measured weight of the filter medium (VMW) or (2) the three longest lines of the filter medium measured with a digital caliper. As a benchmark, the surface area of the shredded tire particles were calculated from X-ray computed tomography (CT) scanning and compared to, and linearly correlated with, the results from the models. The ellipsoid-shape model with the modified length-width-depth data and VMW was determined to be the best model to compute the surface area and biofilm thickness...

Accurate determination of the length of carbon nanotubes using multi-angle light scattering

We have investigated and compared various approaches for calculation and modeling (using multi-angle light scattering; MALS) in order to determine the length of carbon nanotubes (CNTs) following asymmetrical flow field-flow fractionation. Various fit methods and shape models for light scattering were considered with respect to their accuracy and robustness of the data obtained. Both single- and multi-walled CNTs (SWCNTs and MWCNTs) were analyzed to better understand these approaches in view of the different structure of CNTs (i.e., single- and multi-walled). The effect of the angular interval used for extrapolation was investigated by considering the uncertainties in the intensities of MALS at small angles. The determination of the lengths of SWCNT and MWCNT using MALS can be accurately made using two specific approaches. The ellipsoid shape model using the gyration radius as determined by the Zimm method and the rod-like fitting method were found to be most suitable for the determination of the length of SWCNTs and MWCNTs respectively.

Characterization of oxidized gallium droplets on silicon surface: An ellipsoidal droplet shape model for angle resolved X-ray photoelectron spectroscopy analysis

Deposition and oxidation of metallic gallium droplets on Si(111) were studied by angle resolved X-ray photoelectron spectroscopy. Two gallium peaks – Ga 3d and Ga 2p – were simultaneously measured in order to get an advantage of different inelastic mean free paths of photoelectrons from these two energy levels differing in binding energy by 1100 eV. Together with the angular dependent data it enhances the precision of the size characterization of Ga droplets and oxide thickness determination. A model for the calculation of theoretical intensities based on an ellipsoidal shape of droplets is presented and a simple procedure for estimation of droplet height and actual surface coverage based on measurement on a single emission angle is suggested.

Anisotropic Curvature Motion for Structure Enhancing Smoothing of 3D MR Angiography Data

We propose a novel concept of shape prior for the processing of tubular structures in 3D images. It is based on the notion of an anisotropic area energy and the corresponding geometric gradient flow. The anisotropic area functional incorporates a locally adapted template as a shape prior for tubular vessel structures consisting of elongated, ellipsoidal shape models. The gradient flow for this functional leads to an anisotropic curvature motion model, where the evolution is driven locally in direction of the considered template. The problem is formulated in a level set framework, and a stable and robust method for the identification of the local prior is presented. The resulting algorithm is able to smooth the vessels, pushing solution toward elongated cylinders with round cross sections, while bridging gaps in the underlying raw data. The implementation includes a finite-element scheme for numerical accuracy and a narrow band strategy for computational efficiency.

Cell Image Segmentation with Kernel-Based Dynamic Clustering and an Ellipsoidal Cell Shape Model

In this paper, we propose a novel approach to cell image segmentation under severe noise conditions by combining kernel-based dynamic clustering and a genetic algorithm. Our method incorporates a priori knowledge about cell shape. That is, an elliptical cell contour model is introduced to describe the boundary of the cell. Our method consists of the following components: (1) obtain the gradient image; (2) use the gradient image to obtain points which possibly belong to cell boundaries; (3) adjust the parameters of the elliptical cell boundary model to match the cell contour using a genetic algorithm. The method is tested on images of noisy human thyroid and small intestine cells.

Physical model of near-earth asteroid 6489 golevka (1991 JX) from optical and infrared observations.

In 1995 asteroid 6489 Golevka (1991 IX) had a close encounter with the Earth at a distance of 0.034 AU, providing a good opportunity for a detailed study of a small Solar System object. In this paper we report the results of an extensive international observing campaign aimed at determining Golevka's rotational and physical properties from optical photometry and thermal W radiometry. From the analysis of photometric light curves we derive a spin axis model whose coordinates are λ<SUB>p</SUB> (J2000)=347°±10° and β<SUB>p</SUB> (J2000)=350°±10°. The strict periodicity observed in light curves taken during virtually constant illumination and observing conditions argues against free precession of the spin vector. The rotation is prograde with a sidereal period P<SUB>sid</SUB>=0.251101 d (6.02640±0.00024 hr). The derived ellipsoidal shape model results in a/b 1.4±0.2 while not satisfactorily constraining the b/c ratio. No systematic V-R color index variation larger than 0.005 mag (1σ) was observed, suggesting a spectrally uniform surface on a hemispheric scale. The integral phase curve is moderately well represented by the H-G parameter system that fails, however, to reproduce the observed opposition spike. We derive mean H, G values of 19.074±0.029 and 0.138±0.013, respectively. The application of the more accurate Hapke photometric function produces a better fit and allows us to describe the surface scattering properties in terms of model parameters: σ‾=7°±7°,g=-0.435±0.001, ω<SUB>0</SUB>=0.58±0.03, h=0.0114±0.0004, B<SUB>0</SUB>=0.758±0.014. Infrared measurements reveal that the flux at 10.6 μm is unusually small in view of the object's optical brightness. The combined application of a modified Fast Rotating Thermal Model and of the photometric model suggests that Golevka is a small body with approximate dimensions (0.35×0.25×0.25 km) and a very high geometric albedo P<SUB>v</SUB>∼0.6. However, the possible effect of model assumptions on these latter results still has to be explored.

Physical studies of asteroids

Photometric observations of 74 asteroids obtained with the Carlsberg Automatic Meridian Circle between January 1990 and December 1993 are presented. The data from individual asteroid apparitions habe been fitted by phase curves based on the standard HG magnitude system. Statistics on mean G-values for different types of asteroids are presented. A few new determinations of asteroid rotation periods are presented. In addition, we analyse magnitude-aspect relations, and derive ellipsoidal shape models for some asteroids.