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As a result of collisions during their lifetimes, asteroids have a large variety of different shapes. It is believed that high velocity collisions or rotational spin-up of asteroids continuously replenish the Sun’s zodiacal cloud and debris disks around extrasolar planets (Jewitt (2010)). Knowledge of the spin and shape parameters of the asteroids is very important for understanding collision asteroid processes. Lately photometric observations of asteroids showed that variations in brightness are not accompanied by variations in colour index which indicate that the shape of the lightcurve is caused by varying illuminations of the asteroid surface rather than albedo variations over the surface. This conclusion became possible when photometric investigations were combined with laboratory experiments (Dunlap (1971)). In this article using the convex lightcurve inversion method we obtained the sense of rotation, pole solutions and preliminary shape of 901 Brunsia.

Knowledge of the spin and shape parameters of the asteroids is very important for understanding of the conditions during the creation of our planetary system and formation of asteroid populations. The main belt asteroid and Flora family member 967 Helionape was observed during five apparitions. The observations were made at the Bulgarian National Astronomical Observatory (BNAO) Rozhen, since March 2006 to March 2016. Lihtcurve inversion method (Kaasalainen et al. (2001)), applied on 12 relative lightcurves obtained at various geometric conditions of the asteroid, reveals the spin vector, the sense of rotation and the preliminary shape model of the asteroid. Our aim is to contribute in increasing the set of asteroids with known spin and shape parameters. This could be done with dense lightcurves, obtained during small number of apparitions, in combination with sparse data produced by photometric asteroid surveys such as the Gaia satellite (Hanush (2011)).

The orbital motion of the transiting hot Jupiter TrES-5 b was reported to be perturbed by a planetary companion on a nearby orbit. Such compact systems do not frequently occur in nature, and learning their orbital architecture could shed some light on hot Jupiters' formation processes. We acquired fifteen new precise photometric time series for twelve transits of TrES-5 b between June 2019 and October 2020 using 0.9-2.0 m telescopes. The method of precise transit timing was employed to verify the deviation of the planet from the Keplerian motion. Although our results show no detectable short-time variation in the orbital period of TrES-5 b and the existence of the additional nearby planet is not confirmed, the new transits were observed about two minutes earlier than expected. We conclude that the orbital period of the planet could vary in a long timescale. We found that the most likely explanation of the observations is the line-of-sight acceleration of the system's barycentre due to the orbital motion induced by a massive, wide-orbiting companion.

Aims. We aim to investigate how polarimetric observations can improve our understanding of the nature and diversity of M/X-type asteroids. Methods. Polarimetric observations of the selected M/X-type asteroids were carried out at the Tohoku 0.6-m telescope at Haleakala Observatory, Hawaii (simultaneously in BVR filters), the 2-m telescope of the Bulgarian National Astronomical Observatory in Rozhen (in R filter), and the 2.15-m telescope of the Complejo Astronómico El Leoncito (CASLEO), Argentina (in V filter). We analysed the polarimetric characteristics of M/X-type asteroids along with the available data obtained by other techniques. Results. New polarimetric observations of 22 M/X-type asteroids combined with published observations provide a data set of 41 asteroids for which the depth of a negative polarisation branch and/or inversion angle were determined. We found that the depth of the negative polarisation branch tends to increase with decreasing steepness of the near-infrared spectra. Asteroids with a deeper negative polarisation branch tend to have a higher radar circular polarisation ratio. We show that, based on the relationship of the depth of the negative polarisation branch and inversion angle, two main sub-types can be distinguished among M-type asteroids. We suggest that these groups may be related to different surface compositions similar to (1) irons and stony-irons and (2) enstatite and iron-rich carbonaceous chondrites.

The rotation state of small asteroids is affected by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, which is a net torque caused by solar radiation directly reflected and thermally reemitted from the surface. Due to this effect, the rotation period slowly changes, which can be most easily measured in light curves because the shift in the rotation phase accumulates over time quadratically. We collected archived light curves and carried out new photometric observations for asteroids (10115) 1992 SK, (1620) Geographos, and (1685) Toro. We applied the method of light curve inversion to fit observations with a convex shape model. The YORP effect was modeled as a linear change of the rotation frequency \\(\\upsilon \\equiv \\mathrm{d}\\omega / \\mathrm{d}t\\) and optimized together with other spin and shape parameters. We detected the acceleration \\(\\upsilon = (8.3 \\pm 0.6) \\times 10^{-8}\\,\\mathrm{rad}\\,\\mathrm{d}^{-2}\\) of the rotation for asteroid (10115) 1992 SK. This observed value agrees well with the theoretical value of YORP-induced spin-up computed for our shape and spin model. For (1685) Toro, we obtained \\(\\upsilon = (3.3 \\pm 0.3) \\times 10^{-9}\\,\\mathrm{rad}\\,\\mathrm{d}^{-2}\\), which confirms an earlier tentative YORP detection. For (1620) Geographos, we confirmed the previously detected YORP acceleration and derived an updated value of \\(\\upsilon\\) with a smaller uncertainty. We also included the effect of solar precession into our inversion algorithm, and we show that there are hints of this effect in Geographos' data. The detected change of the spin rate of (10115) 1992 SK has increased the total number of asteroids with YORP detection to ten. In all ten cases, the \\(\\mathrm{d}\\omega / \\mathrm{d}t\\) value is positive, so the rotation of these asteroids is accelerated. It is unlikely to be just a statistical fluke, but it is probably a real feature that needs to be explained.

Lightcurve of the asteroid 3634 Iwan observed at the Bulgarian National Astronomical Observatory Rozhen in 2017 is presented. The asteroid was observed only one night, on 22 March 2017 accidentally in the field of view in which our target for shape modeling asteroid 289 Nenetta was positioned. The Asteroid Lightcurve Database (LCDB; Warner et al. 2009) did not contain any previously reported results for 3634 Iwan. If we accept that the ligtcurve of the asteroid is typical with two maxima and minima, a single night observations covers the whole rotational cycle. The lightcurve plotted by MPO Canopus provides a best fit to synodic period of \\(4.72\\pm 0.06\\) h with amplitude of \\(0.15\\pm 0.02\\) mag. Our assessment is that for the uniqueness of the period solution we need longer observational span which will reveal the number of extrema of the lightcurve and confirm the quality code U=3.

The rotation state of small asteroids is affected in the long term by perturbing torques of gravitational and radiative origin (the YORP effect). Direct observational evidence of the YORP effect is the primary goal of our work. We carried out photometric observations of five near-Earth asteroids: (1862) Apollo, (2100) Ra-Shalom, (85989) 1999 JD6, (138852) 2000 WN10, and (161989) Cacus. Then we applied the light-curve inversion method to all available data to determine the spin state and a convex shape model for each of the five studied asteroids. In the case of (2100) Ra-Shalom, the analysis required that the spin-axis precession due to the solar gravitational torque also be included. We obtained two new detections of the YORP effect: (i) \\((2.9 \\pm 2.0)\\times 10^{-9}\\,\\mathrm{rad\\,d}^{-2}\\) for (2100) Ra-Shalom, and (ii) \\((5.5\\pm 0.7)\\times 10^{-8}\\,\\mathrm{rad\\,d}^{-2}\\) for (138852) 2000 WN10. The analysis of Ra-Shalom also reveals a precession of the spin axis with a precession constant \\(\\sim 3000''\\,\\mathrm{yr}^{-1}\\). This is the first such detection from Earth-bound photometric data. For the other two asteroids, we improved the accuracy of the previously reported YORP detection: (i) \\((4.94 \\pm 0.09)\\times 10^{-8}\\,\\mathrm{rad\\,d}^{-2}\\) for (1862) Apollo, and (ii) \\((1.86\\pm 0.09)\\times 10^{-8}\\,\\mathrm{rad\\,d}^{-2}\\) for (161989) Cacus. Despite the recent report of a detected YORP effect for (85989) 1999 JD6, we show that the model without YORP cannot be rejected statistically. Therefore, the detection of the YORP effect for this asteroid requires future observations. The spin-axis precession constant of Ra-Shalom determined from observations matches the theoretically expected value. The total number of asteroids with a YORP detection has increased to 12. In all cases, the rotation frequency increases in time.

A multi-colour phase-polarization curve of asteroid (3200)~Phaethon has been obtained during the December 2017 apparition by merging measurements taken at the observing station of Calern (France) and at the Rhozen observatory (Bulgaria). All the observations were obtained in the positive polarization branch, the phase angle ranging from 36\\(^\\circ\\) to 116\\(^\\circ\\). The measured values of linear polarization are among the highest ever observed for a Solar system body. The covered interval of phase angle was not sufficiently extended to derive a firm determination of the \\(P_{\\rm max}\\) parameter, but this appears to occur at a phase angle around 130\\(^\\circ\\) and reaches more than 45\\% of linear polarization. Phaethon is the parent body of the Geminid meteor shower, and the real physical nature of this object (asteroid or comet) has been a long-debated subject. Our polarimetric measurements seem to support the asteroid hypothesis with a phase-polarization curve similar to the asteroid (2)~Pallas, but further observations at smaller phase angles are needed to draw definitive conclusions.

Lightcurve analysis of the asteroid 9021 Fagus observed at the Bulgarian National Astronomical Observatory Rozhen during two apparitions in 2013 and 2017 are presented. This asteroid was observed in 2013 accidentally in the field of view in which our long-term target asteroid 901 Brunsia was positioned. A search of the Asteroid Lightcurve Database (Warner et al. 2009) did not find any previously reported results for the rotation period of 9021 Fagus. Unfortunately two nights observations in 2013 showed that the rotation period could be only approximately assumed. The observations during two neighbouring nights in 2017 March 20 and 21 revealed the period of \\(5.065 \\pm 0.002\\) h with amplitude of \\(0.73\\pm0.02\\) mag. Obtained lightcurves in combination with other observational techniques, as well as with data gathered from future space mission will contribute to the enlargement of the database for rotational characteristics of the asteroids.

Context. EE Cep is one of few eclipsing binary systems with a dark, dusty disk around an invisible object similar to {\\epsilon} Aur. The system is characterized by grey and asymmetric eclipses every 5.6 yr, with a significant variation in their photometric depth, ranging from ~ 0 m .5 to ~ 2 m .0. Aims. The main aim of the observational campaign of the EE Cep eclipse in 2014 was to test the model of disk precession (Galan et al. 2012). We expected that this eclipse would be one of the deepest with a depth of ~ 2 m .0. Methods. We collected multicolor observations from almost 30 instruments located in Europe and North America. This photometric data covers 243 nights during and around the eclipse. We also analyse the low- and high-resolution spectra from several instruments. Results. The eclipse was shallow with a depth of 0 m .71 in V-band. The multicolor photometry illustrates small color changes during the eclipse with a total amplitude of order ~ +0 m . 15 in B-I color index. The linear ephemeris for this system is updated by including new times of minima, measured from the three most recent eclipses at epochs E = 9, 10 and 11. New spectroscopic observations were acquired, covering orbital phases around the eclipse, which were not observed in the past and increased the data sample, filling some gaps and giving a better insight into the evolution of the H {\\alpha} and NaI spectral line profiles during the primary eclipse. Conclusions. The eclipse of EE Cep in 2014 was shallower than expected 0 m .71 instead of ~ 2 m . 0. This means that our model of disk precession needs revision.