- Email: [email protected]
Astrometric and photometric observations of the potentially hazardous asteroid 2017 VR12
Planetary and Space Science xxx (xxxx) xxx
Contents lists available at ScienceDirect
Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Astrometric and photometric observations of the potentially hazardous asteroid 2017 VR12 A.V. Devyatkin **, D.L. Gorshanov *, K.N. Naumov, A.V. Ivanov, S.N. Petrova, A.A. Martyusheva, V.N. L’vov, S.D. Tsekmeister Pulkovo Observatory, Saint-Petersburg, Russia
A R T I C L E I N F O
A B S T R A C T
Keywords: Near-Earth asteroids Astrometry Orbit determination Photometry
Observations of potentially hazardous asteroid 2017 VR12 during its close approach to the Earth were made at Pulkovo Observatory via ZA-320M telescope at the end of February and the beginning of March 2018. Orbital elements of the asteroid were improved basing on the obtained astrometric data. The orbital evolution was studied and the influence of non-gravitational effects was estimated. The axial rotation period of the asteroid was determined from photometric data.
1. Introduction The asteroid 2017 VR12 was discovered on November 10, 2017 by Pan-STARRS project at Haleakala Observatory (Hawaii, USA). It belongs to the Amor group (the orbit lies completely exterior to the Earth’s orbit) and is classified by the Minor Planet Center (MPC) as a potentially hazardous object (minimum orbit intersection distance (MOID) is 0.0079 AU). On March 7, 2018, the asteroid passed at a distance of 0.0097 AU (3.76 lunar distances) from the Earth. That was its first close encounter with the Earth. Radar observations (https://echo.jpl.nasa.gov/) were made at Arecibo (Puerto Rico) and Goldstone (USA) observatories. According to their results, it was possible to establish that the asteroid has an elongated angular shape, and its dimensions were estimated as 160 m per 100 m. 2. Observations and their processing On March 7, 2018, the asteroid 2017 VR12 approached Earth at a distance of 1.445 million km (0.00966006 AU). It was observed at Pulkovo Observatory from February 21 (the distance was 0.049 AU) to March 8 (0.010 AU) 2018 (see Fig. 1). Its brightness increased from 14.5m to 12m during this period. The observations were carried out using ZA-320M telescope (Devyatkin et al., 2004) installed on the territory of Pulkovo Observatory. This telescope is automated, and can operate both in automatic and remote control mode. Its characteristics are presented in Table 1. The
telescope is equipped with a set of filters of the international broadband photometric system BVRI. Astrometric and photometric processing of CCD observations was performed using the APEX-II software package developed at Pulkovo Observatory (Devyatkin et al., 2010). CCD frames were dark-frame and flat-field corrected, stars images on the frames were approximated by a two-dimensional Gaussian. UCAC-4 astrometric catalogue and 2MASS infrared survey were used as reference catalogs for astrometric and photometric measurements, respectively. Brightness of stars in the optical range was calculated from infrared J and K bands in accordance with the method described in (Warner, 2007). 3. Orbital elements improvement 2315 astrometric positions were obtained during observations with ZA-320M telescope and 2269 of them were used to improve the asteroid orbit that was carried out by means of OrbImpr program of the EPOS software package (L’vov and Tsekmeister, 2012) using DE405 numerical ephemeris. Perturbations caused by planets, the Moon, four massive asteroids and the Earth’s oblateness were taken into account. Orbital elements from the MPCORB database on the epoch JD2458000.5 were taken as the initial ones. The RMS (root mean square) value, which evaluates the observations representation by an improved orbit, turned out to be 0".245. Tables 2 and 3 show the results of the improvement, as well as the comparison of the obtained orbit with the MPC orbit on the epoch JD2458200.5.
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (A.V. Devyatkin), [email protected] (D.L. Gorshanov). https://doi.org/10.1016/j.pss.2019.104739 Received 8 May 2019; Received in revised form 4 September 2019; Accepted 5 September 2019 Available online xxxx 0032-0633/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Devyatkin, A.V. et al., Astrometric and photometric observations of the potentially hazardous asteroid 2017 VR12, Planetary and Space Science, https://doi.org/10.1016/j.pss.2019.104739
A.V. Devyatkin et al.
Planetary and Space Science xxx (xxxx) xxx
special program has been used for searching close approaches (encounters) of the selected asteroid with some set of other known asteroids that have the size not less than the selected one and the appropriate orbit (perihelion distance is less or slightly more than the corresponding selected value). Generally there are tens of thousand such objects. It was found for the years 2017–2050 that the approaches up to the distance 0.01 AU are not numerous. For example, it can be rather surely stated that the number of such phenomena within the half of the current century does not exceed 20. In addition, the larger the asteroids encountered, the greater the distance of their minimum approach to the given object. This is confirmed by Fig. 2, which shows the “minimum mutual distance (AU) – size (m)” distribution for the mentioned interval of time. It is highly probable, that for a quite long period of time this asteroid avoids very close encounters with objects that can drastically change its orbit. This means that it can be a potentially hazardous object for a long time. Fig. 1. The trajectory of the asteroid 2017 VR12 in relation to the Earth at the beginning and in the end of the observation period.
5. Solar radiation pressure influence and the Yarkovsky effect Estimates of solar radiation pressure influence and the Yarkovsky effect on the orbit of the asteroid 2017 VR12 were made. Calculation of solar radiation pressure influence was carried out according to a specially developed technique (Martyusheva et al., 2015) by means of numerical integration of motion equations by the Everhart method. The Yarkovsky effect was taken into account using the Gauss –Everhart integrator (Avdyushev, 2010) and the model was taken from (Vokrouhlicky, 1999; Panasenko and Chernetenko, 2014). The following initial data were taken on the epoch JD2458600.5 (2019-Apr-27.0) to calculate solar radiation pressure influence and the Yarkovsky effect on the orbit of the asteroid 2017 VR12:
Table 1 Parameters of ZA-320M. ZA-320М Optical system Aperture diameter, mm Focal length, mm Scale, "/mm Location Altitude above the sea level, m MPC No. CCD camera Number of pixels Pixel size, μm Matrix size, mm Field of view, ’
Cassegrain 320 3200 64 Saint-Petersburg, Pulkovo 75 084 SBIG STX-16803 4 096 4 096 99 36.9 36.9 39.4 39.4
е ¼ 0.26924346 — the eccentricity (https://ssd.jpl.nasa.gov/), a ¼ 1.369157 AU — the semi-major axis (https://ssd.jpl.nasa.gov/), Hv ¼ 20.6 — the absolute magnitude in V band (https://ssd.jpl.nasa.gov/), D ¼ 0.25 km — the diameter (https://echo.jpl.nasa.gov/), ρ ¼ 2710 kg/m3 — the density (Krasinsky et al., 2002) based on the assumption that the asteroid belongs to V-class (https://echo.jpl.nasa.gov/),
Table 2 The orbital elements of the asteroid 2017 VR12 on the epoch JD2458000.5: initial (the MPC orbit) and improved according to the observations on ZA-320M telescope.
M, º ω, º Ω, º i, º e a, AU q, AU
Initial
Improved
Corrections
Errors
246.94181 180.05212 347.40850 9.17972 0.2724360 1.37528980 1.00061135
246.94144 180.05275 347.40803 9.17968 0.2724360 1.37528645 1.00060885
0.00037 0.00063 0.00047 0.00004 0.0000000 0.00000335
0.000005 0.000005 0.000000 0.000006 0.00000002 0.000000027
Table 3 The orbital elements of the asteroid 2017 VR12 converted to the epoch JD2458200.5: improved according to the observations on ZA-320M telescope and the MPC orbit.
M, º ω, º Ω, º i, º e a, AU q, AU
Improved
MPC catalog
Difference
8.89262 180.74457 347.31609 9.22475 0.2695842 1.36967742 1.00043404
8.89266 180.74451 347.31611 9.22471 0.2695830 1.36967510 1.00043398
0.00004 0.00006 0.00002 0.00004 0.0000012 0.00000232 0.00000006
4. Orbital evolution The asteroid 2017 VR12 is a potentially hazardous object for the Earth. However, a close approach of this asteroid is not expected in the present century either with the Earth or other interior planets. The
Fig. 2. The “minimum distance to other asteroid – other asteroid size” distribution calculated for the asteroid 2017 VR12 for the first half of current century (2017–2050). 2
A.V. Devyatkin et al.
Planetary and Space Science xxx (xxxx) xxx
n ¼ 0.61521121 /d— the mean motion (https://ssd.jpl.nasa.gov/), δ ¼ 0.16 — the albedo derived from log D ¼ 3.122–0.5 log δ – 0.2 HV (Vinogradova et al., 2003), k ¼ 1.07 — the optical coefficient derived from k ¼ 1 þ (4/9) δ (Polyakhova and Shmyrov, 1994), P ¼ 1.37752 h — the rotation period (https://ssd.jpl.nasa.gov/), M ¼ 255.019653 — the mean anomaly (https://ssd.jpl.nasa.gov/), γ ¼ 0 , 45 , 90 , 135 , 180 — the rotation axis orientation (5 values were chosen, since the angle is unknown). The following parameters were taken as average: ε ¼ 0.9 — the emission coefficient, С ¼ 500 J/kg/K — the heat capacity, К ¼ 102 W/ m/K — the thermal conductivity. Table 4 shows the calculations of the asteroid deviations under the influence of solar radiation pressure in the next 20 years for various values of albedo δ. Table 5 shows the results of integration for taking into account the Yarkovsky effect. Its last column indicates the magnitude of the expected change of semi-major axis of the orbit due to the Yarkovsky effect depending on an orientation angle of the asteroid rotation axis. The results of calculations show that the influence of nongravitational effects on asteroids with similar orbital and physical characteristics is relatively small. However, they can lead to significant deviations in orbital motion at large time intervals.
Fig. 3. The light curve of the asteroid 2017 VR12, obtained from observations with ZA-320M telescope and folded with a period of 1.3793 h.
interval of our photometric observations (more than 6 days) allowed us to determine the rotation period of 2017 VR12. On February 27, 28 and March 1, 2, 3, 4, observations of the light curve of the asteroid were made through the R filter, and on March 5 and 7, without the filter. The data obtained as a result of processing were corrected including the change in the distances of the asteroid from the Earth and the Sun and for the phase effect (using the formula described in (Lagerkvist and Williams, 1987)). The parameter G of the phase dependence slope for 2017 VR12 is unknown, and it was not possible to determine from our observations. Thus, the value equal to 0.15 was used as usual in such cases. The obtained series of brightness values of the asteroid were subjected to a frequency analysis by the Scargle method (Lagerkvist and Williams, 1987; Scargle, 1982). As a result, the rotation period of the asteroid 2017 VR12 was determined: 1.3793 0.0005 h. The list of asteroids parameters, which is conducted by the Czech observatory Ondrejov (http://www.asu.cas.cz/~ppravec/newres.txt), gives the value obtained in this observatory and equal to 1.37755 0.00007 h, which is quite close to ours. Fig. 3 shows the light curve of the asteroid, reduced to the period value that we have found. The points on the graph denote the brightness values obtained from CCD frames taken at different nights, the solid curve is the moving mean. The amplitude of the average light curve is about 0.17m.
6. Photometry The sky motion of the asteroid during the observation period was very fast; thus, on March 7, its speed exceeded 50 angular seconds per minute. Therefore, the results of photometric processing of observations have low accuracy (more than 0.05m on average). However, the wide range of brightness variations of the asteroid (more than 0.3m) and the long Table 4 The asteroid displacement in the next 20 years along the heliocentric radiusvector Δr and longitude Δl and the maximum (total) displacement Δd depending on the reflectivity δ.
Δr Δl Δd
δ ¼ 0.16 (the real albedo)
δ ¼ 0.8 (the model albedo, a bright body)
δ ¼ 1.0 (the model albedo, an absolutely white body)
3.5 km 25.52 km 25.52 km
4.4 km 32.43 km 32.44 km
4.71 km 34.34 km 34.35 km
7. Conclusion The astrometric and photometric observations of the potentially hazardous asteroid 2017 VR12 were conducted on ZA-320M telescope at Pulkovo Observatory during its approach to the Earth. The results of astrometric observations were sent to the MPC. Orbital elements of the asteroid were improved and the orbital evolution was studied. Estimates of non-gravitational effects (solar radiation pressure and the Yarkovsky effect) influence showed that over large time intervals they can lead to significant deviations in orbital motion. The axial rotation period of the asteroid is equal to 1.3793 0.0005 h, which confirms the already established value. It was calculated from a series of photometric measurements using frequency analysis of observation series.
Table 5 The components of radius-vector and velocity vector of the asteroid 2017 VR12 in heliocentric coordinate system at the initial moment of integration (2018-1109) and after one revolution around the Sun at different angles of rotation axis orientation γ. The last column shows the values of semi-major axis and the magnitudes of its change due to the Yarkovsky effect.
Initial values
γ ¼ 0
γ ¼ 45
γ ¼ 90
γ ¼ 135
γ ¼ 180
r (X, Y, Z) (AU)
VX, VY, Vz (AU/d)
a, Δa (AU)
1.488932505681 0.834410614389 0.078874600928 1.489158481186 0.834099046709 0.078817203282 1.489158481500 0.834099045158 0.078817203025 1.489158482214 0.834099041585 0.078817202434 1.489158482863 0.834099038256 0.078817201884 1.489158483114 0.834099036948 0.078817201668
6.628424862818⋅103 9.136240552234⋅103 1.683170225912⋅103 6.625412797176⋅103 9.137928090176⋅103 1.683329715681⋅103 6.625412785212⋅103 9.137928098929⋅103 1.683329716639⋅103 6.625412757564⋅103 9.137928119123⋅103 1.683329718848⋅103 6.625412731664⋅103 9.137928137994⋅103 1.683329720909⋅103 6.625412721447⋅103 9.137928145422⋅103 1.683329721720⋅103
1.375212384136
1.375212384132 4.2683⋅1012
Conflicts of interest
1.375212384133 2.9513⋅1012
No conflicts of interest. 1.375212384136 0.1336⋅1012
References
1.375212384139 3.0850⋅1012
Avdyushev, V.A., 2010. Gauss-Everhart integrator. Comput. Technol. 15 (4), 31–46 (in Russian). Devyatkin, A.V., Kanaev, I.I., Kulish, A.P., Rafalsky, V.B., Shumacher, A.B., Koupriyanov, V.V., Bekhteva, A.S., 2004. Automation of Astronomical Observations on the Mirror Astrograph ZA-320. II, vol. 217. Izv. GAO, pp. 505–530 (in Russian).
1.375212384141 4.2683⋅1012
3
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Devyatkin, А.V., Gorshanov, D.L., Kouprianov, V.V., Verestchagina, I.A., 2010. APEX I and APEX II software packages for the reduction of astronomical CCD observations. Sol. Syst. Res. 44 (6). https:echo.jpl.nasa.gov/asteroids/2017VR12/2017VR12_planning.2018.html. https://ssd.jpl.nasa.gov/sbdb.cgi?sstr¼2017%20VR12. Krasinsky, G.A., Pitjeva, E.V., Vasilyev, M.V., Yagudina, E.I., 2002. Hidden mass in the asteroid belt. Icarus 158 (1), 98–105. L’vov, V.N., Tsekmeister, S.D., 2012. The use of the EPOS software package for research of the solar system objects. Sol. Syst. Res. 46 (2), 177–179. Lagerkvist, C.-I., Williams, I.P., 1987. Physical studies of asteroids. XV. Determination of slope parameters and absolute magnitudes for 51 asteroids. A&ASS 68, 295–315. Martyusheva, A.A., Petrov, N.A., Polyakhova, E.N., 2015 (60), iss. 1. Solar Radiation Pressure Effects on Asteroid Motions, Including Near-Earth Objects//Vestnik of SPbU, vol. 2, pp. 135–147 (in Russian).
Panasenko, A.I., Chernetenko, YuA., 2014. Simulation of the Yarkovsky effect in the motion of asteroids. Tr. Inst. Prikl. Astron. Ross. Akad. Nauk (31), 59–65 (in Russian). Polyakhova, E.N., Shmyrov, A.S., 1994. N 8. The Physical Model of the Solar Radiation Pressure on a Sphere and a Plane, vol. 2. Vestnik of SPbU, pp. 87–104 (in Russian). Scargle, J.D., 1982. Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. Ap.J. 263, 835–853. Vinogradova, T.A., Zheleznov, N.B., Kuznetsov, V.B., Chernetenko, YuA., Shor, V.A., 2003. Catalogue of potentially hazardous asteroids and comets. Tr. Inst. Prikl. Astron. Ross. Akad. Nauk (9) (in Russian). Vokrouhlicky, D., 1999. A complete linear model for the Yarkovsky thermal force on spherical asteroid fragments. Astron. Astrophys. 344, 362–366. Warner, B.D., 2007. Initial results from a dedicated H-G project. MPB 34, 113–119.
4
Contents lists available at ScienceDirect
Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Astrometric and photometric observations of the potentially hazardous asteroid 2017 VR12 A.V. Devyatkin **, D.L. Gorshanov *, K.N. Naumov, A.V. Ivanov, S.N. Petrova, A.A. Martyusheva, V.N. L’vov, S.D. Tsekmeister Pulkovo Observatory, Saint-Petersburg, Russia
A R T I C L E I N F O
A B S T R A C T
Keywords: Near-Earth asteroids Astrometry Orbit determination Photometry
Observations of potentially hazardous asteroid 2017 VR12 during its close approach to the Earth were made at Pulkovo Observatory via ZA-320M telescope at the end of February and the beginning of March 2018. Orbital elements of the asteroid were improved basing on the obtained astrometric data. The orbital evolution was studied and the influence of non-gravitational effects was estimated. The axial rotation period of the asteroid was determined from photometric data.
1. Introduction The asteroid 2017 VR12 was discovered on November 10, 2017 by Pan-STARRS project at Haleakala Observatory (Hawaii, USA). It belongs to the Amor group (the orbit lies completely exterior to the Earth’s orbit) and is classified by the Minor Planet Center (MPC) as a potentially hazardous object (minimum orbit intersection distance (MOID) is 0.0079 AU). On March 7, 2018, the asteroid passed at a distance of 0.0097 AU (3.76 lunar distances) from the Earth. That was its first close encounter with the Earth. Radar observations (https://echo.jpl.nasa.gov/) were made at Arecibo (Puerto Rico) and Goldstone (USA) observatories. According to their results, it was possible to establish that the asteroid has an elongated angular shape, and its dimensions were estimated as 160 m per 100 m. 2. Observations and their processing On March 7, 2018, the asteroid 2017 VR12 approached Earth at a distance of 1.445 million km (0.00966006 AU). It was observed at Pulkovo Observatory from February 21 (the distance was 0.049 AU) to March 8 (0.010 AU) 2018 (see Fig. 1). Its brightness increased from 14.5m to 12m during this period. The observations were carried out using ZA-320M telescope (Devyatkin et al., 2004) installed on the territory of Pulkovo Observatory. This telescope is automated, and can operate both in automatic and remote control mode. Its characteristics are presented in Table 1. The
telescope is equipped with a set of filters of the international broadband photometric system BVRI. Astrometric and photometric processing of CCD observations was performed using the APEX-II software package developed at Pulkovo Observatory (Devyatkin et al., 2010). CCD frames were dark-frame and flat-field corrected, stars images on the frames were approximated by a two-dimensional Gaussian. UCAC-4 astrometric catalogue and 2MASS infrared survey were used as reference catalogs for astrometric and photometric measurements, respectively. Brightness of stars in the optical range was calculated from infrared J and K bands in accordance with the method described in (Warner, 2007). 3. Orbital elements improvement 2315 astrometric positions were obtained during observations with ZA-320M telescope and 2269 of them were used to improve the asteroid orbit that was carried out by means of OrbImpr program of the EPOS software package (L’vov and Tsekmeister, 2012) using DE405 numerical ephemeris. Perturbations caused by planets, the Moon, four massive asteroids and the Earth’s oblateness were taken into account. Orbital elements from the MPCORB database on the epoch JD2458000.5 were taken as the initial ones. The RMS (root mean square) value, which evaluates the observations representation by an improved orbit, turned out to be 0".245. Tables 2 and 3 show the results of the improvement, as well as the comparison of the obtained orbit with the MPC orbit on the epoch JD2458200.5.
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (A.V. Devyatkin), [email protected] (D.L. Gorshanov). https://doi.org/10.1016/j.pss.2019.104739 Received 8 May 2019; Received in revised form 4 September 2019; Accepted 5 September 2019 Available online xxxx 0032-0633/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Devyatkin, A.V. et al., Astrometric and photometric observations of the potentially hazardous asteroid 2017 VR12, Planetary and Space Science, https://doi.org/10.1016/j.pss.2019.104739
A.V. Devyatkin et al.
Planetary and Space Science xxx (xxxx) xxx
special program has been used for searching close approaches (encounters) of the selected asteroid with some set of other known asteroids that have the size not less than the selected one and the appropriate orbit (perihelion distance is less or slightly more than the corresponding selected value). Generally there are tens of thousand such objects. It was found for the years 2017–2050 that the approaches up to the distance 0.01 AU are not numerous. For example, it can be rather surely stated that the number of such phenomena within the half of the current century does not exceed 20. In addition, the larger the asteroids encountered, the greater the distance of their minimum approach to the given object. This is confirmed by Fig. 2, which shows the “minimum mutual distance (AU) – size (m)” distribution for the mentioned interval of time. It is highly probable, that for a quite long period of time this asteroid avoids very close encounters with objects that can drastically change its orbit. This means that it can be a potentially hazardous object for a long time. Fig. 1. The trajectory of the asteroid 2017 VR12 in relation to the Earth at the beginning and in the end of the observation period.
5. Solar radiation pressure influence and the Yarkovsky effect Estimates of solar radiation pressure influence and the Yarkovsky effect on the orbit of the asteroid 2017 VR12 were made. Calculation of solar radiation pressure influence was carried out according to a specially developed technique (Martyusheva et al., 2015) by means of numerical integration of motion equations by the Everhart method. The Yarkovsky effect was taken into account using the Gauss –Everhart integrator (Avdyushev, 2010) and the model was taken from (Vokrouhlicky, 1999; Panasenko and Chernetenko, 2014). The following initial data were taken on the epoch JD2458600.5 (2019-Apr-27.0) to calculate solar radiation pressure influence and the Yarkovsky effect on the orbit of the asteroid 2017 VR12:
Table 1 Parameters of ZA-320M. ZA-320М Optical system Aperture diameter, mm Focal length, mm Scale, "/mm Location Altitude above the sea level, m MPC No. CCD camera Number of pixels Pixel size, μm Matrix size, mm Field of view, ’
Cassegrain 320 3200 64 Saint-Petersburg, Pulkovo 75 084 SBIG STX-16803 4 096 4 096 99 36.9 36.9 39.4 39.4
е ¼ 0.26924346 — the eccentricity (https://ssd.jpl.nasa.gov/), a ¼ 1.369157 AU — the semi-major axis (https://ssd.jpl.nasa.gov/), Hv ¼ 20.6 — the absolute magnitude in V band (https://ssd.jpl.nasa.gov/), D ¼ 0.25 km — the diameter (https://echo.jpl.nasa.gov/), ρ ¼ 2710 kg/m3 — the density (Krasinsky et al., 2002) based on the assumption that the asteroid belongs to V-class (https://echo.jpl.nasa.gov/),
Table 2 The orbital elements of the asteroid 2017 VR12 on the epoch JD2458000.5: initial (the MPC orbit) and improved according to the observations on ZA-320M telescope.
M, º ω, º Ω, º i, º e a, AU q, AU
Initial
Improved
Corrections
Errors
246.94181 180.05212 347.40850 9.17972 0.2724360 1.37528980 1.00061135
246.94144 180.05275 347.40803 9.17968 0.2724360 1.37528645 1.00060885
0.00037 0.00063 0.00047 0.00004 0.0000000 0.00000335
0.000005 0.000005 0.000000 0.000006 0.00000002 0.000000027
Table 3 The orbital elements of the asteroid 2017 VR12 converted to the epoch JD2458200.5: improved according to the observations on ZA-320M telescope and the MPC orbit.
M, º ω, º Ω, º i, º e a, AU q, AU
Improved
MPC catalog
Difference
8.89262 180.74457 347.31609 9.22475 0.2695842 1.36967742 1.00043404
8.89266 180.74451 347.31611 9.22471 0.2695830 1.36967510 1.00043398
0.00004 0.00006 0.00002 0.00004 0.0000012 0.00000232 0.00000006
4. Orbital evolution The asteroid 2017 VR12 is a potentially hazardous object for the Earth. However, a close approach of this asteroid is not expected in the present century either with the Earth or other interior planets. The
Fig. 2. The “minimum distance to other asteroid – other asteroid size” distribution calculated for the asteroid 2017 VR12 for the first half of current century (2017–2050). 2
A.V. Devyatkin et al.
Planetary and Space Science xxx (xxxx) xxx
n ¼ 0.61521121 /d— the mean motion (https://ssd.jpl.nasa.gov/), δ ¼ 0.16 — the albedo derived from log D ¼ 3.122–0.5 log δ – 0.2 HV (Vinogradova et al., 2003), k ¼ 1.07 — the optical coefficient derived from k ¼ 1 þ (4/9) δ (Polyakhova and Shmyrov, 1994), P ¼ 1.37752 h — the rotation period (https://ssd.jpl.nasa.gov/), M ¼ 255.019653 — the mean anomaly (https://ssd.jpl.nasa.gov/), γ ¼ 0 , 45 , 90 , 135 , 180 — the rotation axis orientation (5 values were chosen, since the angle is unknown). The following parameters were taken as average: ε ¼ 0.9 — the emission coefficient, С ¼ 500 J/kg/K — the heat capacity, К ¼ 102 W/ m/K — the thermal conductivity. Table 4 shows the calculations of the asteroid deviations under the influence of solar radiation pressure in the next 20 years for various values of albedo δ. Table 5 shows the results of integration for taking into account the Yarkovsky effect. Its last column indicates the magnitude of the expected change of semi-major axis of the orbit due to the Yarkovsky effect depending on an orientation angle of the asteroid rotation axis. The results of calculations show that the influence of nongravitational effects on asteroids with similar orbital and physical characteristics is relatively small. However, they can lead to significant deviations in orbital motion at large time intervals.
Fig. 3. The light curve of the asteroid 2017 VR12, obtained from observations with ZA-320M telescope and folded with a period of 1.3793 h.
interval of our photometric observations (more than 6 days) allowed us to determine the rotation period of 2017 VR12. On February 27, 28 and March 1, 2, 3, 4, observations of the light curve of the asteroid were made through the R filter, and on March 5 and 7, without the filter. The data obtained as a result of processing were corrected including the change in the distances of the asteroid from the Earth and the Sun and for the phase effect (using the formula described in (Lagerkvist and Williams, 1987)). The parameter G of the phase dependence slope for 2017 VR12 is unknown, and it was not possible to determine from our observations. Thus, the value equal to 0.15 was used as usual in such cases. The obtained series of brightness values of the asteroid were subjected to a frequency analysis by the Scargle method (Lagerkvist and Williams, 1987; Scargle, 1982). As a result, the rotation period of the asteroid 2017 VR12 was determined: 1.3793 0.0005 h. The list of asteroids parameters, which is conducted by the Czech observatory Ondrejov (http://www.asu.cas.cz/~ppravec/newres.txt), gives the value obtained in this observatory and equal to 1.37755 0.00007 h, which is quite close to ours. Fig. 3 shows the light curve of the asteroid, reduced to the period value that we have found. The points on the graph denote the brightness values obtained from CCD frames taken at different nights, the solid curve is the moving mean. The amplitude of the average light curve is about 0.17m.
6. Photometry The sky motion of the asteroid during the observation period was very fast; thus, on March 7, its speed exceeded 50 angular seconds per minute. Therefore, the results of photometric processing of observations have low accuracy (more than 0.05m on average). However, the wide range of brightness variations of the asteroid (more than 0.3m) and the long Table 4 The asteroid displacement in the next 20 years along the heliocentric radiusvector Δr and longitude Δl and the maximum (total) displacement Δd depending on the reflectivity δ.
Δr Δl Δd
δ ¼ 0.16 (the real albedo)
δ ¼ 0.8 (the model albedo, a bright body)
δ ¼ 1.0 (the model albedo, an absolutely white body)
3.5 km 25.52 km 25.52 km
4.4 km 32.43 km 32.44 km
4.71 km 34.34 km 34.35 km
7. Conclusion The astrometric and photometric observations of the potentially hazardous asteroid 2017 VR12 were conducted on ZA-320M telescope at Pulkovo Observatory during its approach to the Earth. The results of astrometric observations were sent to the MPC. Orbital elements of the asteroid were improved and the orbital evolution was studied. Estimates of non-gravitational effects (solar radiation pressure and the Yarkovsky effect) influence showed that over large time intervals they can lead to significant deviations in orbital motion. The axial rotation period of the asteroid is equal to 1.3793 0.0005 h, which confirms the already established value. It was calculated from a series of photometric measurements using frequency analysis of observation series.
Table 5 The components of radius-vector and velocity vector of the asteroid 2017 VR12 in heliocentric coordinate system at the initial moment of integration (2018-1109) and after one revolution around the Sun at different angles of rotation axis orientation γ. The last column shows the values of semi-major axis and the magnitudes of its change due to the Yarkovsky effect.
Initial values
γ ¼ 0
γ ¼ 45
γ ¼ 90
γ ¼ 135
γ ¼ 180
r (X, Y, Z) (AU)
VX, VY, Vz (AU/d)
a, Δa (AU)
1.488932505681 0.834410614389 0.078874600928 1.489158481186 0.834099046709 0.078817203282 1.489158481500 0.834099045158 0.078817203025 1.489158482214 0.834099041585 0.078817202434 1.489158482863 0.834099038256 0.078817201884 1.489158483114 0.834099036948 0.078817201668
6.628424862818⋅103 9.136240552234⋅103 1.683170225912⋅103 6.625412797176⋅103 9.137928090176⋅103 1.683329715681⋅103 6.625412785212⋅103 9.137928098929⋅103 1.683329716639⋅103 6.625412757564⋅103 9.137928119123⋅103 1.683329718848⋅103 6.625412731664⋅103 9.137928137994⋅103 1.683329720909⋅103 6.625412721447⋅103 9.137928145422⋅103 1.683329721720⋅103
1.375212384136
1.375212384132 4.2683⋅1012
Conflicts of interest
1.375212384133 2.9513⋅1012
No conflicts of interest. 1.375212384136 0.1336⋅1012
References
1.375212384139 3.0850⋅1012
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