Deriving high quality lightcuves for asteroids and other periodic sources from survey data is challenging due to many factors, including the sparsely sampled observational record and diurnal aliasing which is a signature imparted into the periodic signal of a source that is a function of the observing schedule of ground-based telescopes. In this paper, we examine the utility of combining asteroid observational records from the Zwicky Transient Facility (ZTF) and the Transiting Exoplanet Survey Satellite (TESS) which are the ground- and space-based facilities, respectively, to determine to what degree the data from the space-based facility can suppress diurnal aliases. Furthermore, we examine several optimizations that are used to derive the rotation periods of asteroids which we then compare to the reported rotation periods in the literature. Through this analysis we find that we can reliably derive the rotation periods for ~85% of our sample of 222 objects that are also reported in the literature and that the remaining ~15% are difficult to reliably derive as many are asteroids that are insufficiently elongated which produces a lightcurve with an insufficient amplitude and consequently, an incorrect rotation period. We also investigate a binary classification method that biases against reporting incorrect rotation periods. We conclude the paper by assessing the utility of using other ground- or space-based facilities as companion telescopes to the forthcoming Rubin Observatory.
Asteroid detections in astronomical images may appear as trails due to a combination of their apparent rate of motion and exposure duration. Nearby asteroids in particular typically have high apparent rates of motion and acceleration. Their recovery, especially on their discovery apparition, depends upon obtaining good astrometry from the trailed detections. We present an analytic function describing a trailed detection under the assumption of a Gaussian point spread function (PSF) and constant rate of motion. We have fit the function to both synthetic and real trailed asteroid detections from…
Asteroid photometry has three major applications: providing clues about asteroid surface physical properties and compositions, facilitating photometric corrections, and helping design and plan ground-based and spacecraft observations. The most significant advances in asteroid photometry in the past decade were driven by spacecraft observations that collected spatially resolved imaging and spectroscopy data. In the mean time, laboratory measurements and theoretical developments are revealing controversies regarding the physical interpretations of models and model parameter values. We will revie…
Small aperture telescopes provide the opportunity to conduct high frequency, targeted observations of near-Earth Asteroids that are not feasible with larger facilities due to highly competitive time allocation requirements. Observations of asteroids with these types of facilities often focus on rotational brightness variations rather than longer-term phase angle dependent variations (phase curves) due to the difficulty of achieving high precision photometric calibration. We have developed an automated asteroid light curve extraction and calibration pipeline for images of moving objects from th…
We present the results of short observational program for asteroid 6478 Gault with using of V and R Johnson filters realized at the Kyiv Comet Station during January-April 2019. Color indices and distribution of brightness in the comet-like tail were calculated. We made a comparative analysis of circumstances of the asteroid 6478 Gault activity with others morphologically similar active Main Belt asteroids.
Rotation properties (spin-axis direction and rotation period) and coarse shape models of asteroids can be reconstructed from their disk-integrated brightness when measured from various viewing geometries. These physical properties are essential for creating a global picture of structure and dynamical evolution of the main belt. The number of shape and spin models can be increased not only when new data are available, but also by combining independent data sets and inverting them together. Our aim was to derive new asteroid models by processing readily available photometry. We used asteroid pho…
The Asteroid Terrestrial-impact Last Alert System (ATLAS) is an all-sky survey primarily aimed at detecting potentially hazardous near-Earth asteroids. Apart from the astrometry of asteroids, it also produces their photometric measurements that contain information about asteroid rotation and their shape. To increase the current number of asteroids with a known shape and spin state, we reconstructed asteroid models from ATLAS photometry that was available for approximately 180,000 asteroids observed between 2015 and 2018. We made use of the light-curve inversion method implemented in the Astero…
Context. The 4th release of the SDSS Moving Object Catalog (SDSSMOC) is presently the largest photometric dataset of asteroids. Up to this point, the release of large asteroid datasets has always been followed by a redefinition of asteroid taxonomy. In the years that followed the release of the first SDSSMOC, several classification schemes using its data were proposed, all using the taxonomic classes from previous taxonomies. However, no successful attempt has been made to derive a new taxonomic system directly from the SDSS dataset. Aims. The scope of the work is to propose a different interp…
We carried out low-resolution optical spectroscopy of 51 main-belt asteroids, most of which have highly-inclined orbits. They are selected from D-type candidates in the SDSS-MOC 4 catalog. Using the University of Hawaii 2.2 m telescope and the Inter-University Centre for Astronomy and Astrophysics 2 m telescope in India, we determined the spectral types of 38 asteroids. Among them, eight asteroids were classified as D-type asteroids. Fractions of D-type asteroids are 3.0+/-1.1 for low orbital inclination main-belt asteroids and 7.3+/-2.0 for high orbital inclination main-belt asteroids. The re…
We present the results of BVRI photometry and classification of 53 unusual asteroids, including 35 near-Earth asteroids (NEAs), 6 high eccentricity/inclination asteroids, and 12 recently-identified asteroid-pair candidates. Most of these asteroids were not reportedly classified prior to this work. For the few asteroids that have been previously studied, the results are generally in rough agreement. In addition, we merge the results from several photometric/spectroscopic surveys to create a largest-ever sample with 449 spectrally classified NEAs for statistical analysis. We identify a "transiti…
We present $V$-band photometry of the 20,000 brightest asteroids using data from the All-Sky Automated Survey for Supernovae (ASAS-SN) between 2012 and 2018. We were able to apply the convex inversion method to more than 5,000 asteroids with more than 60 good measurements in order to derive their sidereal rotation periods, spin axis orientations, and shape models. We derive unique spin state and shape solutions for 760 asteroids, including 163 new determinations. This corresponds to a success rate of about 15%, which is significantly higher than the success rate previously achieved using photo…
Results of photometric observations of a small sample of selected Main Belt asteroids are presented. The obtained measurements can be used to achieve a better calibration of the asteroid photometric system $(H, G_1, G_2)$ adopted by the IAU, and to make comparisons with best-fit curves that can be obtained using different photometric systems. The new data have been obtained as a first feasibility study of a more extensive project planned for the future, aimed at obtaining a reliable calibration of possible relations between some parameters characterizing the phase-magnitude curves and the geom…
In addition to stellar data, Gaia Data Release 2 (DR2) also contains accurate astrometry and photometry of about 14,000 asteroids covering 22 months of observations. We used Gaia asteroid photometry to reconstruct rotation periods, spin axis directions, and the coarse shapes of a subset of asteroids with enough observations. One of our aims was to test the reliability of the models with respect to the number of data points and to check the consistency of these models with independent data. Another aim was to produce new asteroid models to enlarge the sample of asteroids with known spin and sha…
Aiming at exploring the relationship between asteroids in cometary orbits and other minor body populations from the observational point of view, I explore the large photometric database of the Sloan Digital Sky Survey - Moving Objects Catalog. The sample of interest was carefully selected analyzing colors and orbital properties within the data in the catalog. I computed the spectral slope for each object and compared with published spectroscopic results of other Asteroids in Cometary Orbits, as well as with other populations of asteroids in the outer region of the Main belt and Trojans. Using …
The amount of sparse asteroid photometry being gathered by both space- and ground-based surveys is growing exponentially. This large volume of data poses a computational challenge owing to both the large amount of information to be processed and the new methods needed to combine data from different sources (e.g. obtained by different techniques, in different bands, and having different random and systematic errors). The main goal of this work is to develop an algorithm capable of merging sparse and dense data sets, both relative and differential, in preparation for asteroid observations origin…
Asteroid (130) Elektra belongs to one of the six known triple asteroids in the main belt, so its mass has been reliably determined. We aim to use all available disk-resolved images of (130) Elektra obtained by the SPHERE instrument at VLT and by the Nirc2 of the Keck telescope together with the disk-integrated photometry to determine its shape model and its size. The volume can be then used in combination with the known mass to derive the bulk density of the primary. We apply the All-Data Asteroid Modeling (ADAM) algorithm to the optical disk-integrated data, 2 disk-resolved images obtained by…
We have combined the NEOWISE and Sloan Digital Sky Survey data to study the albedos of 24,353 asteroids with candidate taxonomic classifications derived using Sloan photometry. We find a wide range of moderate to high albedos for candidate S-type asteroids that are analogous to the S-complex defined by previous spectrophotometrically-based taxonomic systems. The candidate C-type asteroids, while generally very dark, have a tail of higher albedos that overlaps the S types. The albedo distribution for asteroids with a photometrically derived Q classification is extremely similar to those of the …
These are the first results of an observational program devoted to the complete physical data of asteroids that could produce or feed meteoroid streams. Our results are based on the optical observation at Pic du Midi observatory in April 6-7, 2016 and January 17-18, 2018. We will present the light curve of asteroid (259221) 2003 BA21, associated with Daytime Sextantids (221 DSX) and November theta Aurigids (390 THA); the light curves and colors of asteroid (363599) 2004 FG11, associated with Daytime zeta Perseids (172 ZPE) as well as g-r and g-i; and the corresponding reflectances for the (859…
We present ultraviolet photometry (NUV band, 180--280 nm) of 405 asteroids observed serendipitously by the Galaxy Evolution Explorer (GALEX) from 2003--2012. All asteroids in this sample were detected by GALEX at least twice. Unambiguous visible-color-based taxonomic labels (C type versus S type) exist for 315 of these asteroids; of these, thermal-infrared-based diameters are available for 245. We derive NUV-V color using two independent models to predict the visual magnitude V at each NUV-detection epoch. Both V models produce NUV-V distributions in which the S types are redder than C types w…
We present here the discovery of a new class of super-slow rotating asteroids (P>1000 hours) in data extracted from the Asteroid Terrestrial-impact Last Alert System (ATLAS) and Zwicky Transient Facility (ZTF) all-sky surveys. Of the 39 rotation periods we report here, 32 have periods longer than any previously reported unambiguous rotation periods currently in the Asteroid Light Curve Database. In our sample, 7 objects have a rotation period > 4000 hours and the longest period we report here is 4812 hours (~200 days). We do not observe any correlation between taxonomy, albedo, or orbital prop…
The need for more accurate asteroid models is perhaps secondary to the need to measure their quality. The uncertainties of models' parameters propagate to quantities like volume or density -- the most important and informative properties of asteroids -- affecting conclusions about their physical nature. Our knowledge on shapes and spins of small solar system bodies comes mostly from visual, disk-integrated photometry. In this work we present a method for asteroid model uncertainty assessment based on visual photometry (lightcurves and sparse-in-time absolute measurements) allowing the determin…
The nature and origin of the asteroids orbiting in near-Earth space, including those on a potentially hazardous trajectory, is of both scientific interest and practical importance. We aim here at determining the taxonomy of a large sample of near-Earth (NEA) and Mars-crosser (MC) asteroids and analyze the distribution of these classes with orbit. We use this distribution to identify their source regions and to study the strength of planetary encounters to refresh asteroid surfaces. We measure the photometry of these asteroids over four filters at visible wavelengths on images taken by the SDSS…
Optical lightcurves can be used for the shape and spin reconstruction of asteroids. Due to unknown albedo, these models are scale-free. When thermal infrared data are available, they can be used for scaling the shape models and for deriving thermophysical properties of the surface by applying a thermophysical model. We introduce a new method of simultaneous inversion of optical and thermal infrared data that allows the size of an asteroid to be derived along with its shape and spin state. The method optimizes all relevant parameters (shape and its size, spin state, light-scattering properties,…
In the era of wide-field surveys like the Zwicky Transient Facility and the Rubin Observatory's Legacy Survey of Space and Time, sparse photometric measurements constitute an increasing percentage of asteroid observations, particularly for asteroids newly discovered in these large surveys. Follow-up observations to supplement these sparse data may be prohibitively expensive in many cases, so to overcome these sampling limitations, we introduce a flexible model based on Gaussian Processes to enable Bayesian parameter inference of asteroid time series data. This model is designed to be flexible …
We present shape models and volume estimates of twenty asteroids based on relative photometry and adaptive optics images. We discuss error estimation and the effects of myopic deconvolution on shape solutions. For further analysis of the information capacities of data sources, we also present and discuss ambiguity and uniqueness results for the reconstruction of nonconvex shapes from photometry.
We investigated the reliability of the genetic algorithm which will be used to invert the photometric measurements of asteroids collected by the European Space Agency Gaia mission. To do that, we performed several sets of simulations for 10 000 asteroids having different spin axis orientations, rotational periods and shapes. The observational epochs used for each simulation were extracted from the Gaia mission simulator developed at the Observatoire de la Côte d'Azur, while the brightness was generated using a Z-buffer standard graphic method. We also explored the influence on the inversion re…
Asteroid phase curves are used to derive fundamental physical properties through the determination of the absolute magnitude H. The upcoming visible Legacy Survey of Space and Time (LSST) and mid-infrared Near-Earth Object Surveillance Mission (NEOSM) surveys rely on these absolute magnitudes to derive the colours and albedos of millions of asteroids. Furthermore, the shape of the phase curves reflects their surface compositions, allowing for conclusions on their taxonomy. We derive asteroid phase curves from dual-band photometry acquired by the Asteroid Terrestrial-impact Last Alert System te…
It is common practice nowadays to derive spins and 3D shapes of asteroids from the inversion of photometric light curves. However, this method requires a good number of photometric points and dedicated observing sessions. On the other hand, the photometric observations carried out by the Gaia mission will be sparse and their number relatively small. For this reason, a multi-parametric shape described by a large number of elementary facets cannot probably be derived from Gaia data alone. Therefore, the Data Processing and Analysis Consortium (DPAC), implemented a simpler solution as an unattend…
We present new photometric observations for twelve asteroids ((122) Gerda, (152) Atala, (260) Huberta, (665) Sabine, (692) Hippodamia, (723) Hammonia, (745) Mauritia, (768) Struveana, (863) Benkoela, (1113) Katja, (1175) Margo, (2057) Rosemary) from the outer part of the main belt aimed to obtain the magnitude-phase curves and to verify geometric albedo and taxonomic class based on their magnitude-phase behaviors. The measured magnitude-phase relations confirm previously determined composition types of (260) Huberta (C-type), (692) Hippodamia (S-type) and (1175) Margo (S-type). Asteroids (665)…
The {\it Transiting Exoplanet Survey Satellite} (TESS) searches for planets transiting bright and nearby stars using high-cadence, large-scale photometric observations. Full Frame Images provided by the TESS mission include large number of serendipitously observed main-belt asteroids. Due to the cadence of the published Full Frame Images we are sensitive to periods as long as of order tens of days, a region of phase space that is generally not accessible through traditional observing. This work represents a much less biased measurement of the period distribution in this period range. We have d…
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 m…
We present fully covered phased light curves for 56 Jovian Trojan asteroids as acquired by the K2 mission of the Kepler space telescope. This set of objects has been monitored during Campaign 6 and represents a nearly unbiased subsample of the population of small Solar System bodies. We derived precise periods and amplitudes for all Trojans, and found their distributions to be compatible with the previous statistics. We point out, however, that ground-based rotation periods are often unreliable above 20h, and we find an overabundance of rotation periods above 60h compared with other minor plan…
Context. The object 2012 DA14 is a near-Earth asteroid with a size of several tens of meters. It had approached closely the Earth on 15 February, 2013 UT, providing an opportunity for precise measurements of this tiny asteroid. Aims. The solar phase angle of 2012 DA14 had varied widely around its closest approach but was almost constant during the following night. We performed time-series photometric observations on those two nights to determine the rotational properties and phase effect. Methods. The observations were carried out using the 0.55-m telescope at Saitama University, Japan. The R-…
Context. A lot of photometric data is produced by surveys such as Pan-STARRS, LONEOS, WISE or Catalina. These data are a rich source of information about the physical properties of asteroids. There are several possible approaches for utilizing these data. Lightcurve inversion is a typical method that works with individual asteroids. Our approach in this paper is statistical when we focused on large groups of asteroids like dynamical families and taxonomic classes, and the data were not sufficient for individual models. Aims. Our aim was to study the distributions of shape elongation $b/a$ and …
We have searched Microvariability and Oscillations of STars (MOST) satellite photometry obtained in 2004, 2005, and 2007 of the solar-type star HD 209458 for Trojan asteroid swarms dynamically coupled with the system's transiting "hot Jupiter" HD 209458b. Observations of the presence and nature of asteroids around other stars would provide unique constraints on migration models of exoplanetary systems. Our results set an upper limit on the optical depth of Trojans in the HD 209458 system that can be used to guide current and future searches of similar systems by upcoming missions. Using cross-…
Near-Earth asteroid 2012 DA14 made its closest approach on February 15, 2013, when it passed at a distance of 27,700 km from the Earth's surface. It was the first time an asteroid of moderate size was predicted to approach that close to the Earth, becoming bright enough to permit a detailed study from ground-based telescopes. Asteroid 2012 DA14 was poorly characterized before its closest approach. We acquired data using several telescopes on four Spanish observatories: the 10.4m Gran Telescopio Canarias (GTC) and the 3.6m Telescopio Nazionale Galileo (TNG), both in the El Roque de los Muchacho…
Many asteroid databases with lightcurve brightness measurements (e.g. WISE, Pan-STARRS1) contain enormous amounts of data for asteroid shape and spin modelling. While lightcurve inversion is not plausible for individual targets with scarce data, it is possible for large populations with thousands of asteroids, where the distributions of the shape and spin characteristics of the populations are obtainable. We aim to introduce a software implementation of a method that computes the joint shape elongation p and spin latitude beta distributions for a population, with the brightness observations gi…
We present here the c-o colors for identified Flora, Vesta, Nysa-Polana, Themis, and Koronis family members within the historic data set (2015-2018) of the Asteroid Terrestrial-impact Last Alert System (ATLAS). The Themis and Koronis families are known to be relatively pure C- and S-type Bus-DeMeo taxonomic families, respectively, and the extracted color data from the ATLAS broadband c- and o-filters of these two families is used to demonstrate that the ATLAS c-o color is a sufficient parameter to distinguish between the C- and S-type taxonomies. The Vesta and Nysa-Polana families are known to…
We describe a method of determining the V magnitude of an asteroid using differential photometry, with the magnitudes of comparison stars derived from Carlsberg Meridian Catalogue 14 (CMC14) data. The availability of a large number of suitable CMC14 stars enables a reasonably accurate magnitude (\pm0.05 mag) to be found without having to resort to more complicated absolute or all-sky photometry. An improvement in accuracy to \pm0.03 mag is possible if an ensemble of several CMC14 stars is used. This method is expected to be less accurate for stars located within \pm10deg of the galactic equato…
The larger number of models of asteroid shapes and their rotational states derived by the lightcurve inversion give us better insight into both the nature of individual objects and the whole asteroid population. With a larger statistical sample we can study the physical properties of asteroid populations, such as main-belt asteroids or individual asteroid families, in more detail. Shape models can also be used in combination with other types of observational data (IR, adaptive optics images, stellar occultations), e.g., to determine sizes and thermal properties. We use all available photometri…
We investigate the potential of the sparse data produced by the Catalina Sky Survey astrometric project (CSS for short) in asteroid shape and rotational state determination by the lightcurve inversion method. We show that although the photometric quality of the CSS data, compared to the dense data, is significantly worse, it is in principle possible that these data are for some asteroids with high lightcurve amplitudes sufficient for a unique shape determination. CSS data are available for $\sim$180 asteroids for which shape models were previously derived from different photometric data sets. …
We fit 54,296 sparsely-sampled asteroid lightcurves in the Palomar Transient Factory to a combined rotation plus phase-function model. Each lightcurve consists of 20+ observations acquired in a single opposition. Using 805 asteroids in our sample that have reference periods in the literature, we find the reliability of our fitted periods is a complicated function of the period, amplitude, apparent magnitude and other attributes. Using the 805-asteroid ground-truth sample, we train an automated classifier to estimate (along with manual inspection) the validity of the remaining 53,000 fitted per…
We present here multi-band photometry for over 2000 Main-belt asteroids. For each target we report the probabilistic taxonomy using the measured V-R and V-I colors in combination with a machine-learning generated decision surface in color-color space. Through this method we classify >85% of our targets as one the four main Bus-DeMeo complexes: S-, C-, X-, or D-type. Roughly one third of our targets have a known associated dynamic family with 69 families represented in our data. Within uncertainty our results show no discernible difference in taxonomic distribution between family members and no…
133P/Elst-Pizarro is an object that has been described as either an active asteroid or a cometary object in the main asteroid belt. Here we present a photometric and polarimetric study of this object in an attempt to infer additional information about its origin. With the FORS1 instrument of the ESO VLT, we have performed during the 2007 apparition of 133P/Elst-Pizarro quasi-simultaneous photometry and polarimetry of its nucleus at nine epochs in the phase angle range 0 - 20 deg. For each observing epoch, we also combined all available frames to obtain a deep image of the object, to seek signa…
Dynamically different groups of comets and active asteroids with orbits at 2 - 5 a. u. show dust activity in varying degrees and forms. Photometric study and comparison of physical parameters can help to classify mechanisms and nature of the activity for such objects. We present new observations using broadband photometry of 15 active objects in the main asteroid belt and surrounding regions obtained during 2012 - 2016. The study aims to compare the physical properties of main-belt comets (MBCs), quasi-Hilda comets (QHCs), and active asteroids (AAs). The observations were carried out with the …
On 4 March 2021 at 9 UTC a 30-m in diameter near-Earth asteroid 2021 DW1 passed the Earth at a distance of 570000 km, reaching the maximum brightness of V=14.6 mag. We observed it photometrically from 2 March, when it was visible at V=16.5 mag, until 7 March (V=18.2 mag). During that time 2021 DW1 swept a 170 degrees long arc in the northern sky, spanning solar phase angles in the range from 36 to 86 degrees. This made it an excellent target for physical characterisation, including spin axis and shape derivation. Convex inversion of the asteroid lightcurves gives a sidereal period of rotation …
The GBOT group is in charge of the Ground Based Optical Tracking of the Gaia satellite. In concrete terms, since the launch of Gaia, our task is to take every night, using ground based medium-class telescopes, short sequences of $10$ or $20$ images of the Gaia satellite close to its meridian transit. For this purpose, we mainly use the VLT Survey Telescope and the Liverpool Telescope. In these images, taken close to the Sun's opposition - since Gaia is in L$_2$ - we observe many asteroids: between $30$ and $100$ asteroids every night, up to magnitude $22$. In order to extract the astrometric p…
The asteroid (21) Lutetia is the target of a planned close encounter by the Rosetta spacecraft in July 2010. To prepare for that flyby, Lutetia has been extensively observed by a variety of astronomical facilities. We used the Hubble Space Telescope (HST) to determine the albedo of Lutetia over a wide wavelength range, extending from ~150 nm to ~700 nm. Using data from a variety of HST filters and a ground-based visible light spectrum, we employed synthetic photometry techniques to derive absolute fluxes for Lutetia. New results from ground-based measurements of Lutetia's size and shape were u…
Long-baseline ATLAS photometry of the seven main-belt asteroid targets of the Emirates Mission to the Asteroid Belt
South African Astronomical Observatory（南非天文台）；Stellenbosch University（斯泰伦博斯大学）；Charles University（查理大学）；Northern Arizona University（北亚利桑那大学）；University of Hawaii（夏威夷大学）；University of Oxford（牛津大学）；Queen’s University Belfast（贝尔法斯特女王大学）；Instituto de Astrofísica de Canarias (IAC)（加那利天体物理学研究所）；Universidad de La Laguna (ULL)（拉帕鲁纳大学）
We present physical models, i.e. convex shapes, directions of the rotation axis, and sidereal rotation periods, of 18 asteroids out of which 10 are new models and 8 are refined models based on much larger data sets than in previous work. The models were reconstructed by the lightcurve inversion method from archived publicly available lightcurves and our new observations with BlueEye600 robotic observatory. One of the new results is the shape model of asteroid (1663)~van~den~Bos with the rotation period of 749\,hr, which makes it the slowest rotator with known shape. We describe our strategy fo…
Time-resolved photometry of asteroids can be used for shape and spin reconstruction. If the number of measurements per asteroid is not sufficient to create a model, the whole data set can be used to reconstruct the distribution of shape elongations and pole latitudes in the population. This is done by reconstructing amplitudes of lightcurves that are estimated from dispersion of points observed at (assumed) constant aspect angle. Here, we formulate orbit-averaged approach where the observable is the orbit-averaged dispersion of brightness.
We introduce a new method for analyzing sparse photometric data of asteroids and apply it to Zwicky Transient Facility observations of the Jupiter Trojan asteroids. The method relies on the creation of a likelihood model that includes the probability distribution of rotational brightness variations at an unknown rotation phase. The likelihood model is analyzed via a Markov Chain Monte Carlo to quantify the uncertainty in our parameter estimates. Using this method, we provide color, phase parameter, absolute magnitude and amplitude of rotation measurements for 1049 Jupiter Trojans. We find that…
