Lagrange points are extraordinary locations in the Solar System. Placed in these parking spots, small objects such as asteroids or spaceships can shadow a planet along its orbit around the Sun. Out of the five Lagrange points that each planet generates with the Sun, L4 and L5 are even more special. Under some special conditions, these two points are locations of stable equilibrium. If an object is moved away from the vicinity of L4 or L5, a restoring force acts upon it to move it back to its original position. Out of all the L4 and L5 Lagrange points in the Solar System, the ones for the Sun-Jupiter doublet are extraordinary because Jupiter is the most massive planet. This is their story.

It was the year 1906 when Max Wolf, an astronomer at the Heidelberg Observatory in Germany, discovered an asteroid. The new minor body of the Solar System was interesting — 133 kilometers in diameter, a quasi-spherical shape, and a rotation period just above 7 hours. A sizable asteroid, but nothing groundbreaking. Max Wolf named this asteroid 588 Achilles, after the mythical hero of the Greek camp during the Trojan war.

At the turn of the century, the passion for the mythology of the War of Troy was still running through the veins of people in Europe. Some 30 years earlier, in 1873, the German archeologist Heinrich Schliemann excavated what some consider the site of the mythical city of Troy in modern-day Turkey. Although a long-lasting debate ensued regarding Schliemann’s location in respect to the legendary city, massive publicity surrounded his discoveries.

A few months after Wolf’s detection, his graduate student August Kopff discovered 617 Patroclus, a sizable binary asteroid, and 624 Hektor, the most massive of the group. All these asteroids share names associated with the mythology of the Trojan war and are collectively labeled trojan asteroids.

This class of minor bodies of the Solar System occupies a large volume of space around the Lagrange points L4 and L5 of the Sun-Jupiter system. These asteroids shadow Jupiter along its ride around the Sun — the Greek camp group ahead of the planet's path by 60 degrees, while the Trojan camp trails it by 60 degrees. 

Note that the Sun, the Earth, and the center of the distribution of each camp form an equilateral triangle, adding to the geometric beauty of the configuration. Trojan asteroids have a typical distance from the Sun of about five astronomical units. One astronomical unit is the mean distance between the Sun and the Earth, or about 150 million kilometers.

The presence of minor bodies trapped in L4 and L5 by the gravitational dance of the planets was anticipated long before the 20th century, but it took a long time to observe them due to their low brightness. Just how many trojan asteroids are in the Sun-Jupiter system? About ten thousand have been discovered, but the actual number could be much higher — maybe one million. Calculating the total number of trojan asteroids is challenging because it depends heavily on the assumptions made on the typical albedo of these objects, which is the fraction of solar radiation reflected from their surface. 

This peculiar class of asteroids will continue to shadow Jupiter, the king of gods in Roman mythology, in perpetuity — certainly for longer than the memory of the mythical events that inspired their denomination.

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