Hilda family
Encyclopedia
Asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...
s with a semi-major axis
Semi-major axis
The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape...
between 3.7 AU and 4.2 AU, an eccentricity less than 0.3, and an inclination
Inclination
Inclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...
less than 20°. They do not form a true asteroid family
Asteroid family
An asteroid family is a population of asteroids that share similar proper orbital elements, such as semimajor axis, eccentricity, and orbital inclination. The members of the families are thought to be fragments of past asteroid collisions...
, in the sense that they do not descend from a common parent object. Instead, this is a dynamical group of bodies, made up of asteroids which are in a 2:3 orbital resonance
Orbital resonance
In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
with Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...
. Hildas move in their elliptical orbits so that their aphelia put them opposite Jupiter, or 60 degrees ahead of or behind Jupiter at the and Lagrangian point
Lagrangian point
The Lagrangian points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects...
s. Over three successive orbits each Hilda asteroid passes through all of these three points in sequence. The namesake is 153 Hilda
153 Hilda
153 Hilda is a large asteroid in the outer main belt, with a diameter of 170 km. Because it is composed of primitive carbonaceous materials, it has a very dark surface. It was discovered by Johann Palisa on November 2, 1875 from the Austrian Naval Observatory at Pula...
, discovered by Johann Palisa
Johann Palisa
Johann Palisa was an Austrian astronomer, born in Opava in Austrian Silesia .He was a prolific discoverer of asteroids, discovering 122 in all, from 136 Austria in 1874 to 1073 Gellivara in 1923...
in 1875. There are more than 1,100 known Hilda asteroids including unnumbered objects.
Hildas' surface colors often correspond to the low-albedo D-type
D-type asteroid
D-type asteroids have a very low albedo and a featureless reddish electromagnetic spectrum. It has been suggested that they have a composition of organic rich silicates, carbon and anhydrous silicates, possibly with water ice in their interiors...
and P-type
P-type asteroid
P-type asteroids have low albedo and a featureless reddish electromagnetic spectrum. It has been suggested that they have a composition of organic rich silicates, carbon and anhydrous silicates, possibly with water ice in their interior...
; however, a small portion are C-type
C-type asteroid
C-type asteroids are carbonaceous asteroids. They are the most common variety, forming around 75% of known asteroids, and an even higher percentage in the outer part of the asteroid belt beyond 2.7 AU, which is dominated by this asteroid type...
. D-type and P-type asteroids, such as Hildas and Trojans
Trojan (astronomy)
In astronomy, a Trojan is a minor planet or natural satellite that shares an orbit with a larger planet or moon, but does not collide with it because it orbits around one of the two Lagrangian points of stability , and , which lie approximately 60° ahead of and behind the larger body,...
found in the outer main asteroid belt, have surface colors, and thus also surface mineralogies, similar to those of cometary nuclei. This implies that they share a common origin.
Dynamics
The asteroids of the Hilda group (Hildas) are in 3:2 mean motion resonanceOrbital resonance
In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
with Jupiter. That is, their orbital period
Orbital period
The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...
s 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 Trojan asteroid
Trojan asteroid
The Jupiter Trojans, commonly called Trojans or Trojan asteroids, are a large group of objects that share the orbit of the planet Jupiter around the Sun. Relative to Jupiter, each Trojan librates around one of the planet's two Lagrangian points of stability, and , that respectively lie 60° ahead...
s they may have any difference in longitude with Jupiter, nevertheless avoiding dangerous approaches to the planet.
The Hildas taken together constitute a dynamic triangular figure with slightly convex sides and trimmed apexes in the triangular libration points of Jupiter - the "Hildas Triangle". The "asteroidal stream" within the sides of the triangle is about 1 AU
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....
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.
Each of the Hilda objects moves along its own elliptic orbit
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....
. However, at any moment the Hildas together constitute this triangular configuration, and all the orbits together form a quite 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 for a long time span.
Retrograde motion
Retrograde motion is motion in the direction opposite to the movement of something else, and is the contrary of direct or prograde motion. This motion can be the orbit of one body about another body or about some other point, or the rotation of a single body about its axis, or other phenomena such...
. On average the velocity of perihelion motion is greater as 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 adjustment of orbital elements over time helps to avoid this, and conjunctions with Jupiter occur only near the perihelion of Hilda asteroids. Moreover the apsidal
Apsis
An apsis , plural apsides , is the point of greatest or least distance of a body from one of the foci of its elliptical orbit. In modern celestial mechanics this focus is also the center of attraction, which is usually the center of mass of the system...
line oscillates near the line of conjunction with different amplitude and a period of 2.5 to 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". At any time the density of objects in the triangle's apexes is more than twice the density within the sides. The Hildas rest at their aphelia in the apexes for an average of 5.0-5.5 years whereas they move along the sides more quickly for 2.5 to 3.0 years. The orbital period
Orbital period
The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...
s of these asteroids are approximately 7.9 years, or 2/3 that of Jupiter.
Although the triangle is nearly equilateral
Equilateral
In geometry, an equilateral polygon is a polygon which has all sides of the same length.For instance, an equilateral triangle is a triangle of equal edge lengths...
some asymmetry exists. Due to the eccentricity of Jupiter's orbit the side - slightly differs from the 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. When Jupiter is in perihelion the reverse is true.
Trojan asteroid
The Jupiter Trojans, commonly called Trojans or Trojan asteroids, are a large group of objects that share the orbit of the planet Jupiter around the Sun. Relative to Jupiter, each Trojan librates around one of the planet's two Lagrangian points of stability, and , that respectively lie 60° ahead...
. At the mid-sides of the triangle 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 where they intersect. It should also be noted that the dispersion of Trojans in inclination
Inclination
Inclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...
is twice that of the Hildas. Due to this as much as one quarter of the Trojans cannot intersect with the Hildas, and at all times a great deal of other Trojans are located outside Jupiter's orbit. Therefore the regions of intersection are limited. This is illustrated by the figure below and to the right that shows the Hildas (black) and the Trojans (gray) along the ecliptic plane
Plane of the ecliptic
The plane of the ecliptic is the plane of the Earth's orbit around the Sun. It is the primary reference plane when describing the position of bodies in the Solar System, with celestial latitude being measured relative to the ecliptic plane. In the course of a year, the Sun's apparent path through...
. One can see the spherical form of the Trojan swarms.
When moving along each side of the triangle the Hildas travel more slowly than the Trojans, but encounter a denser neighborhood of outer Main Belt asteroids. Here the velocity dispersion is much smaller.
Research
The observed peculiarities in the Hildas' motion are based on data for a few hundred objects known to date and generate still more questions. Further observations are needed to expand on the list of Hildas. Such 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. In these circumstances the brilliance of objects of similar size could run up to 2.5 magnitudes as compared to the apexes.The Hildas traverse regions of the Solar system from approximately 2 AU up to Jupiter's orbit. This entails a variety of physical conditions and the neighborhood of various groups of asteroids. On further observation some theories on the Hildas may have to be revised.