The Trojan Asteroids
Last month we introduced the ‘main-belt’ asteroids. However, although ~94% of all known asteroids are within the main-belt region; many of the more interesting objects are elsewhere. The hazardous NEA (Near-earth asteroids) and the potentially lethal PHA (Potentially hazardous asteroids) are dangers to humanity which we discuss next month. This month however we look at the wonderfully named Trojan asteroids.
Les astéroïdes troyens.
Le mois dernier nous avons introduit les astéroïdes de la ceinture principale. Cependant même si 94% de tous les astéroïdes connus se trouvent dans la région de la ceinture principale beaucoup des objets plus intéressants se trouvent ailleurs. Les astéroïdes géocroiseurs et les astéroïdes potentiellement dangereux (APD) posent un risque pour l’humanité: un subjet pour le mois prochain. Mais ce mois nous allons considérer les astéroïdes troyens.
By the start of 1906 a total of 581 asteroids had been identified. Then, in February of that year, the German astronomer and pioneering astro-photographer Maximilian Wolf (b.1863 d.1932) discovered 588 Achilles, the first of what are known as the ‘Trojan’ asteroids. Wolf, a remarkable astronomer, founded the Heidelberg Observatory and detected more than 200 asteroids and three new comets. He was the first astronomer to use time-lapse photography and he co-designed and developed the blink comparator – a device within which two photographs of the same area can be switched in and out of the user’s view, and hence any object with a different position between the time of the two photographs can be easily identified by appearing to ‘jump’ between the two photographs.
En 1906, 581 astéroïdes avaient été découverts. Puis en février de la même année l’astronome allemand Maximilian Wolf (1863 -1932) a découvert 588 Achilles, le premier des astéroïdes ‘dit’ troyens. Wolf, un astronome extraordinaire a fondé l’Observatoire de Heidelberg et il a observé plus de 200 astéroïdes et trois nouvelles comètes. Il a été le premier astronome à utiliser la photographie accélérée, et il a co-conçu et developpé le comparateur à clignotement - (ancien dispositif opto-mécanique autrefois utilisé par les astronomes pour faire apparaître les différences entre deux photographies de la même portion du ciel prises à des instants différents).
The Trojan classes of asteroids are not within the main belt and these share the orbits of some of the major planets, especially Jupiter. The Jovian Trojans co-orbit with Jupiter but are 5.2 astronomical units, AU, ahead of the planet (the ‘L4’ position, near where Achilles was detected) and 5.2AU trailing (the ‘L5’ position) the planet. The first L5 positioned Jovian Trojan to be discovered was 617 Patroclus, detected on the 17th October 1906 by the German astronomer August Kopff (b.1882 d.1960), also at Heidelberg.
The Trojan asteroids are located at the gravitationally stable ‘Lagrangian points’ of a major planet. The Lagrangian points are locations where the nett forces, exerted by two massive objects acting upon an object of insignificant mass, are balanced and the orbit of any insignificant mass object at such points is in gravitational equilibrium. They are described mathematically by the ‘restricted three-body problem’ first formulated and solved by Leonhard Euler (b.1707 d.1783) and Joseph-Louis Lagrange (b.1736 d.1813). There are five Lagrangian points; three (termed L1, L2 and L3) are collinear (where the three objects are in a line configuration) and are unstable. The two other points, named the L4 and L5 points, form an equilateral triangle shape as shown in our picture below. These points are stable; any small-scale deviations from these points means that the object oscillates about the L4/L5 point.
Lagrangian points are thus regions where objects can persist and for example, the intended location for the James Webb space telescope to be launched in March 2021 is the ‘L2’ point (with motors to ensure positional stability). The Trojan asteroids share, to a reasonable degree of approximation, the semi-major axis and orbital period of the major planet. However, the stability of orbits near the L4 and L5 points mean that asteroids which have orbital elements slightly different to the exact L4/L5 point are not chaotic, i.e. they are stable in their positions.
So for example, in the case of the Jovian Trojans, Jupiter’s orbital period is 11.86 years and its semi-major axis is 5.20AU. The Jovian Trojans vary from 4.62 < a < 5.50 AU in semi-major axis and commensurately 9.94 < P < 12.90 years for orbital period.
The IAU naming convention for Jovian Trojans is interesting. Asteroids at Jupiter’s L4 point are named after figures in Greek mythology and Greek heroes of the Trojan Wars, whilst those at L5 are named after the Trojan heroes.
To date 7294 Jovian Trojans have been identified, 65% of which are at/near L4 and 35% near L5.
The existence and search for non-Jovian Trojans, asteroids which share the orbit of a major planet other than Jupiter, has been considered almost since the discovery of Achilles. To date, Trojan asteroids of Earth, Mars, Uranus and Neptune have been confirmed.
In 1990, 5261 Eureka, preliminary designated 1990 MB was discovered and in 1994 it was confirmed as being an ‘L5’ Martian Trojan. Further Martian Trojans were detected in 1998, 1999, 2007 and 2011; the most recent being 2011 UB256 which brought the total number of Martian Trojans to 9.
Neptunian Trojans have also been found. The first, 2001 QR332 was initially classified as a TNO (Trans-Neptunian object) and so 2005 TN53 took the honour of being recognised as the first discovered Neptunian Trojan – although it was initially classified as a ‘Centaur’. (We will look at Centaurs later). Of the 23 Neptunian Trojans found to date, 20 (87%) are at L4 with 3 (13%) being at L5.
Earth and Uranus each have a single identified Trojan. Earth’s solitary (to date) Trojan was discovered in 2010 (2010 TK7) and is at the Earth orbit L4 position. Uranus has 2011 QF99 at L4, although this may possibly be a Centaur rather than a stable positioned Trojan
No Saturnian Trojans have been found to date, possibly because of Jupiter’s effect. And no Mercurian Trojans have been found.