Jupiter Trojan - Numbers and Mass

Numbers and Mass

Estimates of the total number of Trojans are based on deep surveys of limited areas of the sky. The L₄ swarm is believed to hold between 160–240,000 asteroids with diameters larger than 2 km and about 600,000 with diameters larger than 1 km. If the L₅ swarm contains a comparable number of objects, there are more than 1 million Trojans 1 km in size or larger. For the objects brighter than absolute magnitude 9.0 the population is probably complete. These numbers are similar to that of comparable asteroids in the asteroid belt. The total mass of the Trojans is estimated at 0.0001 of the mass of Earth or one-fifth of the mass of the asteroid belt.

Two more recent studies indicate, however, that the above numbers may overestimate the number of Trojans by several-fold. This overestimate is caused by (1) the assumption that all Trojans have a low albedo of about 0.04, whereas small bodies may actually have an average albedo as high as 0.12; (2) an incorrect assumption about the distribution of Trojans in the sky. According to the new estimates, the total number of Trojan asteroids with a diameter larger than 2 km is 6.3 ± 1.0×104 and 3.4 ± 0.5×104 in the L₄ and L₅ swarms, respectively. These numbers would be reduced by a factor of 2 if small Trojans are more reflective than large ones.

The number of Trojans observed in the L₄ swarm is slightly larger than that observed in L₅; however, since the brightest Trojans show little variation in numbers between the two populations, this disparity is probably due to observational bias. However, some models indicate that the L₄ swarm may be slightly more stable than the L₅ swarm.

The largest of the Trojans is 624 Hektor, which has an average diameter of 203 ± 3.6 km. There are few large Trojans in comparison to the overall population. With decreasing size, the number of Trojans grows very quickly down to 84 km, much more so than in the asteroid belt. A diameter of 84 km corresponds to an absolute magnitude of 9.5, assuming an albedo of 0.04. Within the 4.4–40 km range the Trojans' size distribution resembles that of the main-belt asteroids. An absence of data means that nothing is known about the masses of the smaller Trojans. The size distribution suggests that the smaller Trojans are the products of collisions by larger Trojans.