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1.
We have simulated asteroid lightcurves for simple shape models using a realistic surface scattering law. The scattering law includes a shadowing function computed with numerical ray‐tracing. We computed lightcurves in a variety of illumination geometries for both the traditional Lommel–Seeliger law and our seminumerical law. We observe a shift in the rotational phase of the lightcurves, which depends on the parameters of the scattering law as well as the illumination geometry and the direction of the spin axis of the asteroid. This phase shift is always zero at opposition, and can be as large as 10° for illumination geometries typical for Main Belt asteroids. The phase shift has implications on the accuracy of other results which are based on asteroid lightcurve analysis, such as spin‐state or shape determination.  相似文献   

2.
As the number of observatories located on the surface of Earth is increasing largely in decades more and more photometric data of asteroids is observed to make the research about their various physical and chemical characteristics. Compared with hundreds of thousands of asteroids found up to now, rare hundreds of three-dimensional shape models of asteroids have been built from the tremendous photometric data with incessant observations, i.e. lightcurves. For some specific asteroid already with many observed lightcurves, the unceasing observation is not too much valuable, nevertheless an additional lightcurve observed in a request viewing aspect can refine the shape model and other related parameters. This article taking the asteroid (6) HEBE for example, attempts to introduce a method to make the observation plan by combining the request of the shape model and the orbital limitation of asteroids. Through analyzing the distribution of lightcurves of (6) HEBE, small cabins without any lightcurve data are found, which can be filled by new observations at some specified dates when the positions of Asteroid, Sun, Earth are limited as the request geometry.  相似文献   

3.
《Icarus》1987,70(3):546-565
A number of large asteroids show irregular lightcurves of relatively small amplitude and/or ambiguous rotational periods. These observations and the fact that their strong gravitational binding probably results in quasi-equilibrium shapes lead to model these bodies as axisymmetric, biaxial ellipsoids covered by albedo markings. We developed a general numerical algorithm for obtaining simulated lightcurves of “spotted” asteroids and varied the most critical geometrical and physical parameters (albedo contrast, size, and position of the spots; polar coordinates, and shape of the asteroid). We then analyzed the case of 4 Vesta by assuming an axisymmetric ellipsoidal shape with a large brighter region on one hemisphere, in agreement with the results of photometric and polarimetric observations. Fitting the numerical simulations to the available data, we obtained the flattening of the ellipsoid (0.79 ± 0.03), the albedo contrast and geometry of the brighter region, and the orientation of the polar axis. If the derived flattenning corresponds to the equilibrium shape of a nearly homogeneous body, a density of 2.4 ± 0.3 g cm−3 can be inferred. These results show satisfactory agreement with values by different techniques. We plan to apply the same method both to other large asteroids and to smaller, irregularly shaped ones; in the latter case, this will allow us to test the uncertainties in current pole determination methods.  相似文献   

4.
We have analyzed photometric lightcurves of 30 asteroids, and present here the obtained shapes, rotational periods and pole directions. We also present new photometric observations of five asteroids. The shape models indicate the existence of many features of varying degrees of irregularity. Even large main-belt asteroids display such features, so the resulting poles and periods are more consistent than those obtained by simple ellipsoid-like models. In some cases the new rotational parameters are rather different from those obtained previously, and in a few cases there were no proper previous estimates at all.  相似文献   

5.
This paper reports results of the incorporation of ellipsoidal geometry into the standard radiometric model for asteroids. For small departures from spherical shape the standard model using spherical geometry predicts fluxes in good agreement with ellipsoidal models. Large departures from spherical shape, however, can produce substantial differences in the calculated flux depending on the subsolar temperature and the wavelength of interest. The results derived here suggest that radiometric measurements of highly nonspherical, low-obliquity asteroids interpreted with spherical models result in systematically smaller diameter and higher albedos. In addition, non-spherical shape can also result in a systematic difference in the diameter of a particular asteroid derived from separate 10- and 20-μm flux measurements interpreted with spherical models. Thermal-infrared diurnal lightcurves calculated for ellipsoids have amplitudes that depend on wavelength as well as projected area, and phase curves calculated for ellipsoids are indistinguishable from those calculated for spheres.  相似文献   

6.
In March 2001, the Hayabusa spacecraft target, Asteroid 25143 Itokawa, made its final close approach to Earth prior to the spacecraft's launch. We carried out an extensive observing campaign from January to September 2001 to better characterize this near-Earth asteroid. Global physical properties of the surface of Itokawa were characterized by analyzing its photometric properties and behavior. Results included here capitalize on analysis of broadband photometric observations taken with a number of telescopes, instruments, and observers. We employed a Hapke model to estimate the surface roughness, single particle scattering albedo, single particle scattering characteristics, phase integral, and geometric and bond albedo. We find that this asteroid has a higher geometric albedo than average main belt S-class asteroids; this is consistent with results from other observers. The broadband colors of Itokawa further support evidence that this is an atypical S-class asteroid. Broadband colors show spectral characteristics more typically found on large-diameter main-belt asteroids believed to be space-weathered, suggesting the surface of this small diameter, near-Earth asteroid could likewise be space-weathered.  相似文献   

7.
Thermal observations of large asteroids at millimeter wavelengths have revealed high amplitude rotational lightcurves. Such lightcurves are important constraints on thermophysical models of asteroids, and provide unique insight into the nature of their surface and subsurface composition. A better understanding of asteroid surfaces provides insight into the composition, physical structures, and processing history of these surviving remnants from the formation of our solar system. In addition, detailed observations of the larger asteroids, accompanied by thermophysical models with appropriate temporal and spatial resolution, promise to decrease uncertainties in their flux predictions. Of particular interest are the near-Earth objects, which can be observed at large phase angles, permitting better assessment of the thermal response of their unilluminated surfaces. The high sensitivity of ALMA will enable us to detect many small bodies in all the major groups, to obtain lightcurves for a large sample of main-belt and near-Earth objects, to resolve the surfaces of some large objects, and to separate the emission from primary and secondary objects in binary pairs. In addition to the science goals of asteroid studies, these bodies may also prove useful operationally because those with known shapes and well-characterized lightcurves could be employed for flux calibration by ALMA and other high frequency instruments.  相似文献   

8.
Pedro Lacerda  Jane Luu 《Icarus》2003,161(1):174-180
We present a statistical study of the detectability of lightcurves of Kuiper belt objects (KBOs). Some Kuiper belt objects display lightcurves that appear “flat”; i.e., there are no significant brightness variations within the photometric uncertainties. Under the assumption that KBO lightcurves are mainly due to shape, the lack of brightness variations may be due to (1) the objects having very nearly spherical shapes or (2) their rotation axes coinciding with the line of sight. We investigate the relative importance of these two effects and relate it to the observed fraction of “flat” lightcurves. This study suggests that the fraction of KBOs with detectable brightness variations may provide clues about the shape distribution of these objects. Although the current database of rotational properties of KBOs is still insufficient to draw any statistically meaningful conclusions, we expect that, with a larger dataset, this method will provide a useful test for candidate KBO shape distributions.  相似文献   

9.
The reflectance coefficient of the regolith layer of celestial bodies has been studied in relation to the physical properties of regolith particles (size, refractive index, and packing density) on the basis of an accurate numerical radiative-transfer algorithm for a semi-infinite flat layer. Using the geometric-optics approximation, we have found that a shape mixture of randomly oriented spheroids can successfully model the single-scattering phase function of independent soil grains. In order to take into account the effect of packing density in a regolith layer, the concept of the so-called static structure factor was used. The main effect of increasing packing density is to suppress the forward-scattering peak of the phase function and to increase the albedo of the reflecting surface. We also investigated the influence of fine dust on the reflected light. An addition of small particles not only increases the surface albedo, but also changes the brightness profile and enhances the backscattering. Although the problem of unique solution, which is inherent in the retrieval of the properties of a medium from the measurements of the intensity of light scattered by this media, cannot be removed in the proposed model, the procedure used here, in contrast to widely used approximations, allows us to fit observational data with a set of real characteristics of the regolith. Semiempirical approaches are able to fit the measurements well with a small number of free parameters, but they do not explicitly contain crucial physical characteristics of the regolith such as grain sizes or the refractive index. We compared the numerical solution of the radiative-transfer equation with the Hapke approximation, which is most often used by investigators. The errors introduced by the Hapke model are small only for near-isotropic scattering by isolated particles. However, independent regolith grains are known to scatter light mainly in the forward direction.  相似文献   

10.
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.  相似文献   

11.
Reliable quantitative mapping of minerals exposed on Vesta's surface is crucial for understanding the crustal composition, petrologic evolution, and surface modification of the howardite, eucrite, and diogenite (HED) parent body. However, mineral abundance estimates derived from visible–near infrared (VIS–NIR) reflectance spectra are complicated by multiple scattering, particle size, and nonlinear mixing effects. Radiative transfer models can be employed to accommodate these issues, and here we assess the utility of such models to accurately and efficiently determine modal mineralogy for a suite of eucrite and olivine‐bearing (harzburgitic) diogenite meteorites. Hapke and Shkuratov radiative transfer models were implemented to simultaneously estimate mineral abundances and particle size from VIS–NIR reflectance spectra of these samples. The models were tested and compared for laboratory‐made binary (pyroxene–plagioclase) and ternary mixtures (pyroxene–olivine–plagioclase) as well as eucrite and diogenite meteorite samples. Results for both models show that the derived mineral abundances are commonly within 5–10% of modal values and the estimated particle sizes are within the expected ranges. Results for the Hapke model suggest a lower detection limit for olivine in HEDs when compared with the Shkuratov model (5% versus 15%). Our current implementation yields lower uncertainties in mineral abundance (commonly <5%) for the Hapke model, though both models have an advantage over typically used parameters such as band depth, position, and shape in that they provide quantitative information on mineral abundance and particle size. These results indicate that both the Hapke and Shkuratov models may be applied to Dawn VIR data in a computationally efficient manner to quantify the spatial distribution of pyroxene, plagioclase, and olivine on the surface of Vesta.  相似文献   

12.
We present a numerical model that allows us to calculate the contribution of a specified scattering order in the geometric optics approximation for media composed of large particles with an arbitrary phase function. It has been demonstrated that the correlated propagation of the incident and emergent rays, which is disregarded in the classical radiative-transfer theory, markedly affects the contributions of different orders of scattering, especially the first-order scattering. If the theory describing the photometric properties of regolith-like media ignores the shadowing effect, the errors of its application may reach several tens of percent even for bright surfaces. The packing density of a medium essentially influences the phase dependence of the first-order scattering, although its effect on the value and the phase curve of the higher scattering orders is relatively weak. The backscattering peaks calculated on the basis of the Hapke theory are narrower than those obtained from the numerical simulations, because the Hapke theory is an approximate approach.  相似文献   

13.
A photometric model of (433) Eros at wavelengths from 450 to 1050 nm is constructed using the combination of the images from the multispectral imager (MSI) obtained during the one-year long orbital phase of the NEAR mission, ground-based lightcurves from earlier observations, and our theoretical forward modeling simulations coupled with the NEAR shape model. The single scattering albedo is found to be 0.33±0.03 at 550 nm, which is smaller than past findings by 30%. The amplitude and width of the opposition effect are 1.4±0.1 and 0.010±0.004 from ground based lightcurves. It is confirmed that the asymmetry factor of the single-particle phase function and the surface roughness parameter do not depend on wavelength from 450 to 1050 nm, and their values are estimated to be −0.25±0.02 and 28°±3°, respectively, comparable with the earlier measurements from the NEAR NIS data. The geometric albedo and the Bond albedo at 550 nm are calculated to be 0.23 and 0.093, respectively, which make Eros less reflective than previous models, but still slightly more reflective than average S-type asteroids. The lower albedos of Eros are more consistent with our forward modeling simulations, as well as with its spectrum. Eros is a typical S-type asteroid like (951) Gaspra and (243) Ida, and has similar surface regolith properties. Combining the single-scattering albedo with the olivine composition of ordinary chondrites, taking into account space weathering darkening, we constrain the grain size of the regolith particles on Eros to a range of 50 to 100 μm.  相似文献   

14.
Typical variations in the opposition effect morphology of laboratory samples at optical wavelengths are investigated to probe the role of the textural properties of the surface (roughness, porosity and grain size). A previously published dataset of 34 laboratory phase curves is re-analyzed and fit with several morphological models. The retrieved morphological parameters that characterize the opposition surge, amplitude, width and slope (A, HWHM and S respectively) are correlated to the single scattering albedo, the roughness, the porosity and the grain size of the samples. To test the universality of the laboratory samples’ trends, we use previously published phase curves of planetary surfaces, including the Moon, satellites and rings of the giant planets. The morphological parameters of the surge (A and HWHM) for planetary surfaces are found to have a non-monotonic variation with the single scattering albedo, similar to that observed in asteroids (Belskaya, I.N., Shevchenko, V.G. [2000]. Icarus 147, 94–105), which is unexplained so far. The morphological parameters of the surge (A and HWHM) for laboratory samples seem to exhibit the same non-monotonic variation with single scattering albedo. While the non-monotonic variation with albedo was already observed by Nelson et al. (Nelson, R.M., Hapke, B.W., Smythe, W.D., Hale, A.S., Piatek, J.L. [2004]. Planetary regolith microstructure: An unexpected opposition effect result. In: Mackwell, S., Stansbery, E. (Eds.), Proc. Lunar Sci. Conf. 35, p. 1089), we report here the same variation for the angular width.  相似文献   

15.
We present near-infrared spectrometer (NIS) observations (0.8 to 2.4 μm) of the S-type asteroid 433 Eros obtained by the NEAR Shoemaker spacecraft and report results of our Hapke photometric model analysis of data obtained at phase angles ranging from 1.2° to 111.0° and at spatial resolutions of 1.25×2.5 to 2.75×5.5 km/spectrum. Our Hapke model fits successfully to the NEAR spectroscopic data for systematic color variations that accompany changing viewing and illumination geometry. Model parameters imply a geometric albedo at 0.946 μm of 0.27±0.04, which corresponds to a geometric albedo at 0.550 μm of 0.25±0.05. We find that Eros exhibits phase reddening of up to 10% across the phase angle range of 0-100°. We observe a 10% increase in the 1-μm band depth at high phase angles. In contrast, we observe only a 5% increase in continuum slope from 1.486 to 2.363 μm and essentially no difference in the 2-μm band depth at higher phase angles. These contrasting phase effects imply that there are phase-dependent differences in the parametric measurements of 1- and 2-μm band areas, and in their ratio. The Hapke model fits suggest that Eros exhibits a weaker opposition surge than either 951 Gaspra or 243 Ida (the only other S-type asteroids for which we possess disk-resolved photometric observations). On average, we find that Eros at 0.946 μm has a higher geometric albedo and a higher single-scatter albedo than Gaspra or Ida at 0.56 μm; however, Eros's single-particle phase function asymmetry and average surface macroscopic roughness parameters are intermediate between Gaspra and Ida. Only two of the five Hapke model parameters exhibit a notable wavelength dependence: (1) The single-scatter albedo mimics the spectrum of Eros, and (2) there is a decrease in angular width of the opposition surge with increasing wavelength from 0.8 to 1.7 μm. Such opposition surge behavior is not adequately modeled with our shadow-hiding Hapke model, consistent with coherent backscattering phenomena near zero phase.  相似文献   

16.
P. Scheirich  P. Pravec 《Icarus》2009,200(2):531-547
We present a numerical method for inverting long-period components of lightcurves of asynchronous binary asteroids. Data of five near-Earth binary asteroids, (175706) 1996 FG3, (65803) Didymos, (66391) 1999 KW4, (185851) 2000 DP107 and (66063) 1998 RO1, for two of them from more than one apparition, were inverted. Their mutual orbits' poles and Keplerian elements, size ratios, and ellipsoidal shape axial ratios were estimated via this inversion. The pole solutions and size ratios for 1999 KW4 and 2000 DP107 are in a good agreement with independent estimates from radar measurements. We show that uncertainties of estimates of bulk densities of binary systems can be large, especially when observed on short arcs.  相似文献   

17.
V photoelectric lightcurves of ten main belt asteroids (11 Partenope, 20 Massalia, 31 Euphrosyne, 41 Daphne, 55 Pandora, 71 Niobe, 79 Eurynome, 129 Antigone, 344 Desiderata, and 387 Aquitania), obtained during the 1981–1983 oppositions, are reported. The rotation period of 11 Partenope is P = 7.83 hr and that of 344 Desiderata P = 10.53 hr. The shape and the pole coordinates of 20 Massalia, 31 Euphrosyne, and 129 Antigone were also derived and those of 41 Daphne confirmed. The lightcurves of the remaining objects are presented: a preliminary discussion of their possible rotational properties and their morphological features is given.  相似文献   

18.
The Hapke (Hapke, B. [1981]. J. Geophys. Res. 86, 3039-3054) photometric model and its modifications are widely used to characterize telescopic, spacecraft, and laboratory observations of the bidirectional reflectance of particulate surfaces. Following work and methods laid out in a companion paper (Helfenstein, P., Shepard, M.K. [2011]. Icarus, in press), we deconstruct the Hapke model and, separating all empirical and ad hoc parameters (opposition surge, particle phase function, surface roughness), combine them into a single parameter called the surface phase function, F(α). We illustrate how to extract this function from scattering data sets acquired with the Bloomsburg University Goniometer (BUG). We show how this method can be used to rapidly and accurately characterize bidirectional reflectance data sets from laboratory and spacecraft measurements, often giving better fits to the data. We examine samples with strong color contrasts in different wavelengths. This allows us to examine the exact same surface, changing only the albedo to investigate how the amplitude and the detailed shape of the surface phase function might systematically depend on wavelength and albedo. We also examine the changes in scattering behavior that result when samples are compacted and find the surface phase function and single scattering albedo to be significantly changed. We suggest that these observations support the hypothesis that much of the scattering behavior attributed to the single particle phase function is instead cause by the surface micro-structure.  相似文献   

19.
Asteroid sizes can be directly measured by observing occultations of stars by asteroids. When there are enough observations across the path of the shadow, the asteroid’s projected silhouette can be reconstructed. Asteroid shape models derived from photometry by the lightcurve inversion method enable us to predict the orientation of an asteroid for the time of occultation. By scaling the shape model to fit the occultation chords, we can determine the asteroid size with a relative accuracy of typically ∼10%. We combine shape and spin state models of 44 asteroids (14 of them are new or updated models) with the available occultation data to derive asteroid effective diameters. In many cases, occultations allow us to reject one of two possible pole solutions that were derived from photometry. We show that by combining results obtained from lightcurve inversion with occultation timings, we can obtain unique physical models of asteroids.  相似文献   

20.
The thermophysics of asteroids has become an important frontier for the research of asteroids in recent years. In this paper, we have introduced the thermophysical models commonly used in this field, by using these thermophysical models and combining with the data observed by the space or ground-based IR telescopes, some thermophysical parameters of asteroids, such as the thermal inertia, geometric albedo, effective diameter, surface roughness, and surface temperature, etc., can be derived. We have mentioned also the shape model and IR observation of asteroids, as well as the obtained thermophysical parameters for a part of asteroids. These thermophysical parameters can be further applied to studying the asteroids’ Yarkovsky effect, YORP effect, and so on, even can provide the relevant information for the spacecraft landing on the asteroid surface and the return mission of a spacecraft after the asteroid sampling.  相似文献   

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