How closely packed are Jupiter’s Trojan asteroids?

Jupiter’s Trojan asteroids congregate at the L4 and L5 Lagrange points of the Jupiter-Sun system, meaning they orbit in groups that lead and trail the gas giant planet. The density of Trojans is about 10 times less than the density of asteroids in the main belt. Credit: Astronomy: Roen Kelly, after NASA/WMAP Science Team

How closely packed are Jupiter’s Trojan asteroids compared to the density of the main belt?

Doug Kaupa
Council Bluffs, Iowa

Jupiter’s Trojans are asteroids that share the gas giant’s orbit around the Sun, clustering at one of two Lagrange points in the Jupiter-Sun system (L4 or L5, 60° ahead of or behind Jupiter in its orbit, respectively).

It turns out that main-belt asteroids (MBAs) and Trojan asteroids occupy a relatively similar volume in space. The bulk of MBAs lie between 2.1 and 3.3 AU from the Sun, while Jupiter’s Trojans are 5 to 5.3 AU from our star. Most of these bodies (in both groups) have orbital inclinations less than 30°.

You can approximate the volume these asteroids occupy using rings. So, picture a torus with a circular cross-section, with the inner and outer diameter being the inner and outer extents of the orbits just given, so that the volume each occupies is 61 AU³ and 58 AU³, respectively, for MBAs and Trojans. (One AU, or astronomical unit, is the average Earth-Sun distance of 93 million miles [150 million kilometers]. So, 1 AU³ = 8 x 10²³ miles³ [2.7 x 10²⁴ km³].)

There are about 10⁸ MBAs larger than about 330 feet (100 meters) in diameter, and about 10⁷ Trojans of this same size. That makes the volume density of asteroids in the main belt about 10 times higher than that of Jupiter’s Trojan asteroids.

Still, MBAs are hard to come by in the vastness of space. A sphere with a radius of about 249,000 miles (400,000 km) contains only one MBA larger than 330 feet (100 m) in diameter.

Simone Marchi
Staff Scientist, Southwest Research Institute, Boulder, Colorado