X.3. Elements and opposition dates in 2015

The elements of the numbered minor planets are given with respect to the ecliptic and equinox J2000.0. The computation of osculating elements for the new standard epoch JDT 2457200.5 = 2015 June 27.0 TT was carried out by numerical integration of relativistic equations of motion in rectangular coordinates taking into account the perturbations from Mercury to Neptune and from Pluto, Ceres, Pallas, and Vesta. Coordinates and masses of perturbing planets were taken from DE 405. The perturbations from the Earth and the Moon were considered separately.

Osculating elements of minor planets are given on p. 824 –5705. The first column of the Table gives the number and name or principal provisional designation of each minor planet. The second gives the absolute magnitude, H, that is, the brightness averaged over rotation for minor planets having known lightcurves and reduced to unit heliocentric and geocentric distances and to zero phase angle. The third column gives the slope parameter, G.

As noted above, the values of H and G are given in this volume in accordance with the listing published in MPC 28103 – 28116 and in subsequent issues. In general the parameters given for the first 3200 minor planets are precisely those of the previous listing, prepared mainly by E. F. Tedesco. When H and G values were determined sufficiently precisely from photoelectric observations, frequently by least-square fitting, although in some instances G was selected, H values are given to 0.01 mag. Actual solutions for G (ranging from – 0.12 to + 0.60) have been made in only 110 cases. In the Table these values are given to 0.01. For by far the majority of minor planets the default value of G equal to 0.15 is used and it is denoted in the Table by X. Magnitudes based solely on photographic or CCD observations or for photoelectrically observed asteroids with large lightcurve and/or aspect variations (cf. lightcurve parameter Table, p. 5734 – 5770) are given to 0.1 mag. For almost all minor planets with numbers greater than 3200 the values of H were found by G. V. Williams (also to 0.1 mag and using G = 0.15) from magnitudes given on the astrometric records collected by the Minor Planet Center. For photoelectrically observed NEAs (3361), (3551), (3554), (3757) and (4015) the more precise H values from previous listing are preserved. For (4179) the H and G values suggested by D. J. Tholen (Institute for Astronomy, University of Hawaii, U.S.A.) are adopted. The new values of H determined by G. V. Williams are also adopted for 98 minor planets with numbers less than 3200. In three other discordant cases the improved H values were suggested by A. W. Harris (Jet Propulsion Laboratory, U.S.A.).

The orbital elements (mean anomaly, M, argument of perihelion, ω, longitude of ascending node, Ω, inclination, i, eccentricity, e, mean motion, μ, and semi-major axis, α) are given in the columns from 4 to 10.

Eleventh column of the Table headed TE contains last two digits of the title year of the EMP in which the orbit was first introduced and where the information on its precision can be found.

12 and 13 columns of the Table contain opposition date of minor planet in 2015 and its apparent magnitude for the fourth ephemeris date. A dash indicates that there is no opposition in 2015.

X.3.1. Elements and opposition dates of NEAs

The Table of elements and opposition dates of the near-Earth asteroids (NEAs) (see p. 5706 – 5726) contains osculating elements of the numbered minor planets with perihelion distances q less or equal to 1.3 a.u., and dates of their oppositions in 2015. It is patterned after corresponding Table of elements of minor planets. The minute differences are as follows: the semi-major axis is given with less number of decimals and instead column headed TE the columns with approximate values of perihelion distance q and aphelion distance Q are given. The column headed T (Type) contains indication of minor planet type where Am stands for Amor type ( a > 1 a.u., 1.017 a.u. < q <= 1.3 a.u.), Ap stands for Apollo type ( a > 1 a.u., q <= 1.017 a.u.), At stands for Aten type ( a < 1 a.u., Q >= 0.983 a.u.), and Ar stands for Atira type ( Q < 0.983 a.u.). (163693) Atira is the first numbered asteroid of new type ( Q < 0.983 a.u.) for which in literature one can find also other names ( Apohele type, Arjuna type and so on).

X.3.2. Elements and opposition dates of Centaurs and transneptunian objects

The Table of elements and opposition dates of Centaurs and transneptunian objects (see p. 5727 – 5730) is constructed like that of NEAs. Column headed T (Type) contains indication of object's type where Ct stands for Centaurs ( a < 30 a.u., q > 5.45 a.u.), Tn stands for transneptunian objects (``kjubiwanos'' (like classical 1992 QB1) or Plutinos (in commensurabilities with Neptune or Uranus), Sd stands for scattered disk objects.

X.3.3. Elements and opposition dates of some unusual minor planets

The Table (p. 5731 – 5732) contains data for Jupiter-crossers, Jupiter-approachers as well as for some Mars-crossers, mainly with unusual orbits. Minor planets whose stability is protected by special mechanisms (like Trojans, Hildas and so on) are not included in the Table except in a few special cases. The Table is constructed like two preceding ones. The header T (Type) indicates type of minor planet where Jc stands for Jupiter-crosser, Ja stands for Jupiter-approacher, Mc stands for Mars-crosser, and MT stands for Mars Trojan.

It should be noted that all objects included into the Tables of NEAs, Centaurs and transneptunian objects, and some unusual planets can be also found in the Table of elements and opposition dates of all minor planets.