<P> The asteroids of the Hilda group (Hildas) are in 3: 2 mean - motion resonance with Jupiter . That is, their orbital periods are 2 / 3 that of Jupiter . They move along the orbits with a semimajor axis near 4.0 AU and moderate values of eccentricity (up to 0.3) and inclination (up to 20 °). Unlike the Jupiter trojans they may have any difference in longitude with Jupiter, nevertheless avoiding dangerous approaches to the planet . </P> <P> The Hildas taken together constitute a dynamic triangular figure with slightly convex sides and trimmed apices in the triangular libration points of Jupiter--the "Hildas Triangle". The "asteroidal stream" within the sides of the triangle is about 1 AU wide, and in the apexes this value is 20 - 40% greater . Figure 1 shows the positions of the Hildas (black) against a background of all known asteroids (gray) up to Jupiter's orbit at January 1, 2005 . </P> <P> Each of the Hilda objects moves along its own elliptic orbit . However, at any moment the Hildas together constitute this triangular configuration, and all the orbits together form a predictable ring . Figure 2 illustrates this with the Hildas positions (black) against a background of their orbits (gray). For the majority of these asteroids, their position in orbit may be arbitrary, except for the external parts of the apexes (the objects near aphelion) and the middles of the sides (the objects near perihelion). The Hildas Triangle has proven to be dynamically stable over a long time span . </P> <P> The typical Hilda object has a retrograde perihelion motion . On average, the velocity of perihelion motion is greater when the orbital eccentricity is lesser, while the nodes move more slowly . All typical objects in aphelion would seemingly approach closely to Jupiter, which should be destabilising for them--but the variation of the orbital elements over time prevents this, and conjunctions with Jupiter occur only near the perihelion of Hilda asteroids . Moreover, the apsidal line oscillates near the line of conjunction with different amplitude and a period of 2.5 to 3.0 centuries . </P>

A family of asteroids is a group of asteroids that