Hilda's Triangle

Hilda's Triangle

Hilda’s triangle is the unofficial name given to a triangle-like structure that is traced out by the Hilda family of asteroids. At a distance of about 3.9 AU (an AU is the distance between the Earth and the sun), the Hilda asteroids are named after a single asteroid named 153 Hilda. This asteroid was discovered in 1875 by J. Palisa who named the asteroid after the oldest daughter of astronomer Theodor von Oppolzer. They have an orbital resonance with Jupiter of 3:2 which means that every time Jupiter makes 2 rounds around the sun, the Hilda family makes three. It is the asteroid's smaller bodies coupled with its closer orbit to the sun that allow it to take the lead in this cosmic dance of cold stardust. Additional measurements include Hilda's eccentricity of .3, which is a measure of how elongated the orbit is from a perfect circle. The inclination of the Hilda family is measured at an angle of ≤ 20 degrees from the plane of the solar system.

Hildas are mostly D and P-type asteroids with a small amount of C types. C types are defined as having carbon-rich material which can be determined using methods of spectroscopy. D and P-type asteroids are identified as having red albedos and residing further out in the solar system. This suggests that the Hilda family may have originated from the outer edges of the solar system so learning more about the Hildas will shed more light on the solar system in its outer reaches. A family of asteroids is classified by grouping together space objects with common characteristics.

The answer to why a triangle shape emerges in our solar system lies in Lagrangian mechanics, a branch of mathematics developed by Joseph-Louis Lagrange. All space objects have a gravitational pull that permeates throughout its entire orbit. However, in certain areas in a space object's orbit, other celestial forces can work to cancel out an object's gravitational pull as if it were a stalemate in a cosmic game of tug-of-war. These forces can include anything from the gravitational pull of other objects to the centrifugal force that exerts itself away from any spinning object. This leaves five spots in an object's orbit, called Lagrange points, where objects can accumulate in a stationary manner relative to the objects in orbit. This rule applies to any space object that is in orbit around another.

Image displays the locations of a space object's Lagrange points.

The positions of these points are often labeled with a number following a capital ‘L’. L1 is located between Jupiter and the sun while L2 is located on the opposite side of Jupiter. In the case of Earth, these Lagrange points have been taken advantage of as parking spots for our spacecrafts. Such is the case for the Solar and Heliospheric Observatory (SOHO) at Earth's L1 point, and the Wilkinson Microwave Anisotropy Probe (WMAP) at L2. Earth's L2 will also occupy the James Webb Space Telescope which will be the most powerful space telescope ever built, seeing all the way to the edge of the observable universe.

Jupiter's L3 is located 180 degrees relative to the sun. This means that from the view of Jupiter, L3 is always behind the sun. However, the answer to Hilda’s triangle lies in L3 and L4 which are located 60 degrees in front of and behind the orbit of Jupiter. An equilateral triangle (one where all sides are equal in length) is defined as having 60-degree angles at all three of its vertices. This is what makes the Lagrange points a perfect match to let the Hilda asteroids trail with Jupiter in a triangular formation.