Photometric observations of six Mars-crossing asteroids with the 1-m INASAN telescope at Mt.

. We present observations of six asteroids crossing the orbit of Mars obtained at Mt. Koshka observatory of INASAN in 2014–2016. Our multicolor photometry made it possible to determine the apparent magnitudes of asteroids in BVRcIc photometric bands, as well as their taxonomic class according to Tholen’s classiﬁcation. The periods of rotation were determined for asteroids 9773, 32575, 97679


Introduction
Since 2010, multicolor observations of asteroids have been carried out at the 1m telescope in Simeiz. The most important asteroids are those approaching the Earth's orbit (NEA). However, not a lot of NEA have a sufficient brightness to obtain high-quality multicolor photometric observations. So we choose objects from much more numerous Mars-crossing asteroids which are related to the NEA group. These asteroids in some cases can cross the Earth's orbit or approach the Earth. NEA and Mars-crossing asteroids can move from one group to another due to orbit changing. It is important to investigate the taxonomy and rotation of Mars-crossing asteroids, compare them to NEA and follow the evolution of their orbits.
Mars-crossing asteroids are also interesting because of their connection to Mars. Automatic vehicles are visiting Mars' orbit and go down to its surface. Small objects associated with Mars, such as meteor showers and fireballs, can seriously interfere with the work of automatic stations exploring its surface and, in the future, inhabited settlements. We must have comprehensive information about the physical and mineralogical properties of near-Martian asteroids. Some of them can be in future a source of industrial minerals.

Observations
Thoroughly calibrated photometric systems make it possible to obtain reliable data on the physical and mineralogical features of the small bodies in Solar System.
Our photometrical multicolor observations were carried out with a Zeiss-1000 cassegrain (D =1 m, f /12.7) in the Simeiz observatory of INASAN. An FLI PL-09000 (3056x3056) CCD array was equipped with a BVRcIc filter set which realized the Johnson-Cousins photometric system. 5x5 binning provided a 0.97" pixel size. Seeing was usually 3-4". More information about the observatory and telescope one may find in Nikolenko et al. (2019). Table 1 presents the orbital parameters of asteroids under investigation from the Small Body Database 1 . Table 2 contains their physical parameters from the same source. Information about the observations is presented in Table 3. The details of our observations' method and analysis technique are described in Volkov et al. (2019) and Barabanov et al. (2019). The transformation coefficients from the instrumental system to the standard one were published in Barabanov et al. (2021b). Some previous results on asteroids 8355, 9773, and 32575 were published in Barabanov et al. (2021a). For taxonomy derivation, a  set of standard spectra of taxonomic classes were used, see Tholen (1989) and Tholen (1984).

Processing of observations.
Our multicolor observations made it possible to determine with sufficient accuracy the apparent stellar magnitudes and color indices of asteroids -see Table 4. The choice of reference stars in each frame satisfies the following conditions: the stars should be sufficiently bright (10 m -12 m ), their color indices B − V < 1.2 and they should be located at the same frame with the asteroid (Barabanov et al. (2021b)). The number of reference stars in a single frame satisfying these conditions varied from 1 to 4. We interpolated tables from Straižys (1992) to find V − Rc, Rc − Ic color indices of each reference star according to its B − V color index derived from B, V magnitudes taken from the APASS DR10 catalogue 2 . Magnitudes of asteroid 8355, for technical reasons, were derived with only one reference star. In the case of asteroid 32575, the error obtained from observations seems to be underestimated. A set of standard spectra of taxonomic classes we construct using Tholen (1984) description. We transferred stellar magnitudes in different spectral ranges to energetic units, normalized them to the flow in the V band and compare with standard Tholen's spectra. The specific class of asteroids was determined by the minimum of the mean-square deviation of the coarse spectrum of the asteroid obtained from observations (four points) from the standard spectrum, as shown in the Figures with even numbers below.
Next, we present for each asteroid the relative spectrum energy distribution and phased with rotational period light curves Table 5.
Our observations of this asteroid were carried out only for 5 hours, which makes it impossible to correct its period 6.0677 h -from Small Body Database 3 . We can only say that our observations do not contradict previous data, see  Tholen (1989), Tholen (1984). Black circles with error bars are observed data. Everything is normalized to the flux in the V filter, so that this point is considered accurate (indicated without an error bar), and the inaccuracy of observations in V is taken into account in the flux errors in other spectral bands.
We have determined the value of the rotation period P = 2.7461 ± 0.0002 hours -see Fig. 3, which confirms the value determined by Benishek & Brincat (2016) within their errors. We can't get better accuracy due to the short duration of our observations. Estimates of the variability semi-amplitude in different spectral regions are: A B = 0. m 11, A V = 0. m 13, A Rc = 0. m 13, A Ic = 0. m 14. The taxonomic class corresponds to the class S -see Fig. 4. New Mexico.

(32575) 2001 QY78
The rotation period of the asteroid was determined by us as P = 4.5331 ± 0.0017 hours, which coincides with previous measurements (4.5344 h -see the Small Body Database 4 ) within errors. As in the case of asteroid 9733, increasing the duration of observations will improve the accuracy of the value of the rotation period. The phased light curve corresponding to the found period is shown in Fig. 5 We estimated the value of the period P ≈ 7.92 hours, see Fig. 7. The periodogram built with our program (Volkov, 2022) shows two approximately equal peaks at the given period value and at 6.85 hours. After close examination of phased with these periods light curves, we have chosen the larger one as it has less systematic deviations. It is impossible to determine the precise value of the period from the available data. The final conclusion can be made only after additional observations. Estimates of the variability semi-amplitude in different spectral regions are: Very accurate values of the color indices of the asteroid have been obtained, they correspond to Tholen's taxonomic class C, see Fig. 8.

(97679) 2000 GG2
(97679) 2000 GG2 was discovered on April 3, 2000 as part of the LINEAR program at the Socorro Observatory, New Mexico. At the time of processing the observations, no physical and chemical parameters were known, except for the absolute magnitude, see Table 2. We have succeeded in detecting periodic variations in brightness, but the accuracy of observations is comparable to the amplitude of the variations, which can lead to an erroneous value of the rotation period, see Fig. 9. We consider this period to be 7.964 ± 0.004 hours. Further observations will help to confirm this value. Estimates of the variability semiamplitude in different spectral regions are: Multicolor observations have allowed us to determine the taxonomic class of this asteroid as S, although there is a non-zero probability that it can also belong to the R class -see Fig. 10.

(122463) 2000 QP148
(122463) 2000 QP148 was discovered as part of the LINEAR program at the Socorro Observatory, New Mexico. The estimated value of the rotation period is 426.3 hours, i.e. more than 17 days, see Table 2, and examples of asteroid light curves 5 . With only three consecutive nights of observations at hand, we can neither confirm nor deny this value. Our observations are presented in Fig. 11. We did not find any brightness' fluctuations at times from tens of minutes to several hours. To accurately determine the rotation period, it is necessary to organize systematic observations of this object during several months. The distribution of energy in the spectrum is shown in Fig. 12. We believe that the Tholen taxonomic class of this asteroid corresponds to the T class.

Conclusion
Photometric multicolor high-precision observations of six Mars-crossing asteroids were made with the Zeiss-1000 telescope in Simeiz during 2014-2016. For all of them, apparent stellar magnitudes and color indices were obtained, and an assessment of the taxonomic class according to Tholen was made. For asteroids 97679 and 313591 the period of proper rotation was estimated for the first time.
For asteroids 9773 and 32575 our independent determination of the rotation pe-riod coincides with the previous estimates within their errors. Asteroid 122463 requires a long (several months) monitoring to determine the value of the rotation period. Undoubtedly, targeted photometric observations of Mars-crossing asteroids will make it possible to determine their origin. These observations will have not only scientific but also obvious practical value.