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The Hilda family of asteroids is constituted of asteroids with a semi-major axis between 3.7 AU and 4.2 AU, an eccentricity greater than 0.07, and an inclination less than 20°. They do not form a true asteroid family, in the sense that they do not descend from a common parent object. Instead, this is a dynamical family of bodies, made up of asteroids which are in a 2:3 orbital resonance with Jupiter. Hildas move in their orbits so that their aphelia put them opposite Jupiter, or 60 degrees ahead of or behind Jupiter at the L₄ and L₅ Lagrangian points. Over three successive orbits each Hilda asteroid passes through all of these three points in sequence.

SOME PECULIARITIES IN THE HILDAS MOTION←

The asteroids of the Hilda group (Hildas) are in the 3:2 mean motion resonance with Jupiter. They move along the orbits with a semimajor axis near 4.0 AU and the moderate values of eccentricity (up to 0.3) and inclination (up to 20°). Unlike the Trojan asteroids they may have any difference in longitude with Jupiter nevertheless avoiding the dangerous approaches to the planet. The Hildas taken together constitute the figure of triangle with slightly convex sides and trimmed apexes in the triangular libration points of Jupiter - the "Hildas Triangle" (see http://neopage.nm.ru/ENG/GENERAL/DATA/hil-a.pdf). The thickness of the asteroidal stream within the sides of the triangle is about 1 AU, and in the apexes this value is 20-40 % greater. The Fig. 1 shows the positions of the Hildas (black) against a background of all known asteroids (gray) up to Jupiter's orbit for the date January 1, 2005.

           Fig. 1.                              Fig. 2.

Fig. 1. The Hildas Triangle against a background of all known asteroids up to Jupiter's orbit. Fig. 2.The positions of the Hildas against a background of their orbits.

At any moment the Hildas constitute this triangular configuration although each of the objects moves along its elliptic orbit, and all orbits together form quite predicted ring. The Fig. 2 illustrates this statement showing the Hildas positions (black) against a background of their orbits. For majority of these asteroids their position in orbit may be arbitrary except for the external parts of apexes (the objects near aphelion) and the middles of the sides (the objects near perihelion). The Hildas Triangle proved to be dynamically stable for rather long time span. The typical Hildas have a retrograde perihelion motion. At the average the lesser is the orbital eccentricity the greater is the velocity of perihelion motion. At the same time the nodes move more slowly. All typical objects in aphelion seemingly would approach closely to Jupiter that should be very dangerous for them. But the specific evolution of the orbital elements helps to avoid this situation, and the conjunctions with Jupiter occur only near the perihelion of an asteroid. Moreover the apsidal line oscillates near the line of conjunction with different amplitude and the period of 2.5 - 3.0 centuries. In addition to the fact that the Hildas triangle revolves in connection to Jupiter the quasi-periodical waves of the stream density of asteroids in every point are noticed, as if the triangle breathes. But at any time the density of objects in the apexes is more than twice larger than the density of objects within the sides. It is to be added that the Hildas rest at the apexes 5.0-5.5 years at the average whereas they move along the sides more quickly, for 2.5-3.0 years.

Despite the fact that the triangle is close to the equilateral one some asymmetry still exists in it. Due to the eccentricity of Jupiter's orbit the side L4-L5 slightly differs from two other sides. When Jupiter is in aphelion the mean velocity of the objects moving along this side is somewhat smaller than that of the objects related to the other sides. For Jupiter's position in perihelion the picture is reverse. At the apexes of the triangle corresponding to the points L4 and L5 of Jupiter's orbit the Hildas are the neighbors of the Trojans and at the mid-sides they are close to the asteroids of the external part of the Main Belt. The velocity dispersion of Hildas is more evident than that of Trojans in the regions of their intersection. It is to be noted that the dispersion of the Trojans in inclination is as twice as that of Hildas. Due to this not less than a quarter of the Trojans could not intersect with the Hildas, and a great deal of others is situated beyond the limits of Jupiter's orbit. Therefore these regions of intersection can not be too vast. This statement is illustrated by the Fig. 3 that along with Jupiter in the foreground shows the Hildas (black) and the Trojans (gray) visible from the point in the ecliptic plane with the longitude near 190 degrees for the date January 1, 2005. One can see the spherical form of the Trojan swarms.

Fig. 3. The Hildas and the Trojans visible in ecliptic plane

When moving along each side of the triangle the Hildas undergo less long as compared with the Trojans but more numerous neighborhood with the asteroids of the outer Main Belt. But here the velocity dispersion is much smaller. The revealed peculiarities in the Hildas motion base on the data for a few hundred objects known to the date and generate still more questions. The new observations are urgent for the growth of the Hildas list. And these observations are most favorable when the Earth is near conjunction with the mid-sides of the Hildas Triangle. These moments occur each 4 and 1/3 months. And the gain in brilliance for the objects of the same size as compared to the apexes could run up to 2.5 magnitudes. Thus the Hildas can visit the regions of the Solar system located within the ring at least 2 AU wide up to Jupiter's orbit. This will entail the variety of physical conditions and the neighborhood with various groups of asteroids. But this fact could result in the revision of some formed conceptions.

The namesake is 153 Hilda, discovered by Johann Palisa in 1875.

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