Observational data and orbits of the asteroids discovered at the Baldone Observatory in 2015–2018

Abstract This paper is devoted to the discovery of 37 asteroids at the Baldone Astrophysical Observatory (MPC 069) from 2015 to 2018, and one of dynamically interesting Mars-crosser (MC) observed at the Baldone Astrophysical Observatory, namely 2008 LX16. In Baldone Observatory, was independently discovered the Near-Earth Object 2018 GE3 on the image of 13 April 2018. Also, the NEO 2006 VB14 was observed doing its astrometry and photometry. Moreover, we observed asteroids 1986 DA and 2014 LJ1. We computed orbits and analyzed the orbital evolution of these asteroids. 566 positions and photometric observations of NEO objects 345705 (2006 VB14) and 6178 (1986 DA) were obtained with Baldone Schmidt telescope in 2018 and 2019. We detected their rotation period and other physical characteristics. Also, a Fourier transform was applied to determine the rotation period of asteroid 6178 (1986 DA). Value (3.12 ± 0.02)h was obtained. Our observations confirm the previously obtained rotation periodP=3.25hfor2006VB14.


Discoveries of minor planets at the Baldone Observatory in 2015-2018
In (Černis et al. 2015), we presented the discovered asteroids at the Baldone Observatory in 2008-2013. In this work, we gathered the discoveries of asteroids in period of 2015-2018. Table 1 lists 37 asteroids discovered at the Baldone Observatory, and Table 2 presents statistics and astrometric observations of the asteroids (both new and known) at the Baldone Observatory in 2015-2018. Table 3 presents high precision orbital elements of discovered asteroids at the Baldone Astrophysical Observatory in 2015-2018. All orbital computations of asteroids were made using the OrbFit software v.5.0.5 and v.5.0.6. In the last version, the NEODyS Team introduced the error weighing model described by Vereš et al. (2017), as announced by F. Bernardi on the Minor Planet Mailing List. We used the JPL DE431 Ephemerides with 17 perturbing massive asteroids as was described in Farnocchia et al. (2013a,b) and similar to Wlodarczyk (2015).

Investigation of NEO asteroids 2006 VB14 and 1986 DA
Two NEO type asteroids 2006 VB14 and 1986 DA were successfully observed over seven and five nights respectively in the autumn of 2018 and spring of 2019. There is no previously reported rotation period for 1986 DA in the Asteroid Lightcurve Database (LCDB) and two possible periods for 2006 VB14 was mentioned in paper Skiff et al. (2012). Images at Baldone Astrophysical Observatory were captured with a 0.80/1.20 m, f/3 Schmidt telescope and SBIG STX-16803 CCD camera with an array of 4090×4090 pixels. The field-of-view is 53 × 53 arcmin. The plate scale was 0.78 arcsec per pixel in 1×1 binning mode. Photometric data re-ductions for the images were done using the MPO Canopus and MaxIM DL programs. GAIA2 R magnitudes are used for thirty reference stars. Through experimentation with different rotation periods using Fourier fitting, the best fit was 3.25 ± 0.02h for the 2006 VB14 and 3.12 ± 0.02h for the 1986 DA. More detailed processing and the result is described in Eglitis (2019). Obtained rotation periods are typical for similar-sized asteroids.    We computed residuals, RMS equal to 0.381" for observations of asteroid 345705 (2006 VB14) using total 1168 observation from which 1164 were selected. Similarly, for asteroid 6178 we have 1041 observations with 1039 selected with RMS=0.479". Due to the long observational arcs, about 12 years and 42 years, respectively, it was possible to compute the non-gravitational parameter A2.
Parameter A2 depends on the Yarkovsky effect. The Yarkovsky effect is the thermal re-emission of absorbed solar radiation. The non-gravitational acceleration arises from the anisotropic re-emission at thermal wavelengths of absorbed solar absorption. The Yarkovsky effect acts on the semimajor axis, a. The drift of semimajor axis, da/dt depends on the obliquity γ of the asteroid, the bulk density ρ, and diameter D of the asteroid (Chesley et al. 2014): Next, according to Farnocchia et al. (2013a, p. 9) we averaged the Yarkovsky effect as a transverse acceleration, a t =A 2 /r 2 , where r is heliocentric distance and A 2 is a function of the physical quantities of the asteroid. Then, according to Farnocchia et al. (2013b), the semimajor axis drift of asteroid is where e is the eccentricity, n is the mean motion and p is the semi latus rectum. As it was shown in Farnocchia et al. (2013a), A 2 can be computed either using physical parameters of an asteroid or by fitting observation. The last method is used when we have computed the orbit of an asteroid with small uncertainties. Then, we solved seven orbital parameters instead of the previously six. The NEODyS team have developed the software OrbFit v.5.0 (http://adams.dm.unipi.it/~orbmaint/orbfit/) which computed non-gravitational parameter da/dt or A 2 . We used this publicly available software and computed nongravitational parameter. Table 4 presents the starting orbital elements of the asteroids 345705 (2006 VB14) and 6178 (1986 DA) computed with the non-gravitational parameter A2 and using the same method as in computing results in Table 3. A negative value of A2 of asteroid 345705 (2006 VB14) denotes that the mean semimajor axis drifts da/dt<0 and hence the asteroid can be retrograde rotator; in contrary, the positive value of A2 of asteroid 6178 (1986 DA) denotes that the mean semimajor axis drifts da/dt>0 and hence asteroid can be a prograde rotator. We can see that the orbital elements have small errors and the non-gravitational parameters A2 have typical values as for NEAs computed by Wlodarczyk (2019a,b).

2008 LX16 -an asteroid with
Mars-crosser type orbit   881806. The Baldone published nine observations of this asteroid. The object 2008 LX16 was observed at three observational nights in April 2018. The asteroid moved at speed 0.11 " per minute being 19.2 R magnitude object. It was independently discovered by the Baldone and by Pan-STARRS observatories at the opposition of 2018.
We computed the orbit of the asteroid 2008 LX16, one of the known MCs, based on all observations using the OrbFit software (http://adams.dm.unipi.it/~orbmaint/orbfit/). Sixteen perturbing massive asteroids and dwarf planet Pluto were used according to Farnocchia et al. (2013a,b) and similar to Wlodarczyk (2015).
We also used the new version of the OrbFit Software, namely OrbFit v.5.0.5, which has the new error model desribed in Chesley et al. (2010), as well as the debiasing and weighting scheme described in Farnocchia et al. (2015) called after that error model 2015 (see Table 4). Moreover, we used the DE431 version of JPL's planetary ephemerides. Recently, the possibility of calculating orbits according to the OrbFit software v.5.0.6 has appeared with implemented error model 2017, according to Vereš et al. (2017) (see Table 4). Table 5 presents the starting orbital elements of the asteroid 2008 LX16 computed with the non-gravitational parameter A2. A positive value of A2 for asteroid 2008 LX16 denotes that the mean semimajor axis drifts da/dt>0 and hence the asteroid can be the prograde rotator. Table 5 shows that orbital elements have only changed a little, but A2 has also changed. Also, the error of all calculated orbital elements and A2 is smaller.  Figure 2 presents the orbit of 2008 LX16 in the ecliptic plane. The position of the planets, the asteroid 2008 LX16, the dwarf planet (1) Ceres and three massive asteroids: (2) Pallas, (4) Vesta and (10) Hygiea are also presented for the epoch 2008 15 June, i.e. for the date of the first observation at Siding Spring Survey. According to the International Astronomical, a discoverer will be defined when the object is numbered, see https://minorplanetcenter.net/mpec/K10/ K10U20.html.

2008 LX16 -Long time orbital evolution
To study the orbital evolution of asteroid 2008 LX16, we computed its Virtual Asteroids (VAs) with the use of the OrbFit software v. 5.0.5 and the method of Milani et al. (2005a,b). VAs, or variant orbits or clones denote swarm of orbits which lie somewhere in the con dence region. Each of these orbits fits well with observations. Line of Variation (LOV) is usually obtaining by fixing the value of all the orbital elements, six or seven when we used the Yarkovsky effect. Next, we changed only the mean anomaly.
LOV is a one-dimensional part of a (curved) line in the initial conditions space generally computed with the uniform sampling of the LOV parameter. σLOV denotes the position along the Line of Variation, LOV in the σ space.
Values of σ are usually in the interval (−3,3). LOV is used to compute multiple solutions which are useful in the orbit determination and their propagation (Milani et al. 2005a,b).
We are computing 500 VAs on both sides of the nominal orbit on the LOV where the nominal orbit has σ = 0. Hence we have 1001 VAs. We computed 500 clones of both sides of the LOV with the uniform sampling of the LOV parameter.
Then we propagate all the VAs 100 My forward.
Time evolutions of orbital elements of all clones are calculated using the software swi _rmvs developed by Levison and Levison (1994) This software takes into account the gravitational influence of all planets (variant swi _rmvs3_f ), i.e. from Mercury to Neptune, and in the second case by adding four massive objects: dwarf planet (1) Ceres and three massive asteroids: (2) Pallas, (4) Vesta and (10) Hygiea. Our calculations were done for a case without the Yarkovsky effect. Figure 3 presents the position of the remaining clones from the starting 1001 clones with σ = 3, of the asteroid 2008 LX16 after 100 My forward integration. Great star in Figure 3 presents the starting position of the nominal asteroid 2008 LX16. Small stars denote 30 remaining clones of 2008 LX16 using the old error model based on Farnocchia et al. (2015) and additional massive asteroids, (1) Ceres, (2) Pallas, (4) Vesta and (10) Hygiea (CPVH). The dots denote 45 remaining clones of 2008 LX16 using the same gravitational model, i.e. with CPVH and using the new error model based on Vereš et al. (2017). The open circles denote 46 remaining clones using the gravitational model without CPVH and with the new error model based on Vereš et al. (2017). It is visible that almost all remaining clones in phase space have orbits with aphelia smaller than the semimajor axes of Mars and perihelia larger to the semimajor axis of Venus.
In Figure 3 we can see that using the new error model, more clones remain in the Solar System model, i.e. 46 clones, in contrary to the old error model with 30 remaining clones. Probably we have a smaller dispersion of startup elements, i.e. smaller errors of these orbital elements -see Table 4. Furthermore, the number of clones remaining at the end of the integration period in the new Solar System model, hardly depends on the use of additional perturbing massive asteroids (CPVH).
It is visible that only several % of starting clones remain after 100 My integration. It can be explained by the fact that 2008 LX16 is close to the line of the perihelion of the Earth. Generally, from all starting 1001 clones of the asteroid 2008 LX16 45% hit the Sun, (35÷38)% reached distance from the Sun greater than 1000 au, (13÷15)% have a collision with planets or perturbing massive asteroids, and (3÷5)% remain in the solar system, respectively.

2008 LX16 -Computation of the predicted theoretical meteor-stream radiant
Next, we computed theoretical meteor-stream radiant for asteroid 2008 LX16 according to the program of Neslusan et al. (1998). As the input parameters are orbital elements of the orbit of the parent body and its time of perihelion passage.
Results of computations are in Table 6 where:  Table 6 shows that predicted theoretical meteor shower radiants will be visible at the turn of May and June in the following years.

Summary
Between 2015 and 2018, 37 asteroids were discovered at the Baldone Astrophysical Observatory (MPC 069). We studied one of the interesting Mars-crosser (MC) observed at the Baldone Astrophysical Observatory, namely 2008 LX16. Also, NEO object 2006 VB14 and 1986 DA and 2014 LJ1 were observed. We computed orbits and analyzed the orbital evolution of these asteroids. 566 positions and photometric observations were obtained with Baldone Schmidt telescope in 2018 and 2019. We detected the rotation period, and other physical characteristics of NEO objects 345705 (2006 VB14) and 6178 (1986 DA). We determined the rotational period of asteroid 6178 (1986DA), P=(3.12 ± 0.02)h.