Observational History
In 1772, Italian-born mathematician Joseph-Louis Lagrange, in studying the restricted three-body problem, predicted that a small body sharing an orbit with a planet but lying 60° ahead or behind it will be trapped near these points. The trapped body will librate slowly around the point of equilibrium in a tadpole or horseshoe orbit. These leading and trailing points are called the L4 and L5 Lagrange points. However, no asteroids trapped in Lagrange points were observed until more than a century after Lagrange's hypothesis. Those associated with Jupiter were the first to be discovered.
E. E. Barnard made the first recorded observation of a Trojan asteroid, (12126) 1999 RM11, in 1904, but neither he nor others appreciated its significance at the time. Barnard believed he saw the recently discovered Saturnian satellite Phoebe, which was only two arc-minutes away in the sky at the time, or possibly a star. The object's identity was not realized until its orbit was constructed in 1999.
The first recognized discovery of a Trojan occurred in February 1906, when astronomer Max Wolf of Heidelberg-Königstuhl State Observatory discovered an asteroid at the L4 Lagrangian point of the Sun–Jupiter system, later named 588 Achilles. In 1906–1907 two more Jupiter Trojans were found by fellow German astronomer August Kopff (624 Hektor and 617 Patroclus). Hektor, like Achilles, belonged to the L4 swarm ("ahead" of the planet in its orbit), while Patroclus was the first asteroid known to reside at the L5 Lagrangian point ("behind" the planet). By 1938, 11 Trojans had been detected. This number increased to 14 only in 1961. As instruments improved, the rate of discovery grew rapidly: by January 2000, a total of 257 had been discovered; by May 2003, the number had grown to 1,600. As of March 2012 there are 3,404 known Trojan asteroids at L4 and 1,759 at L5,
Read more about this topic: Jupiter Trojan
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“Regarding History as the slaughter-bench at which the happiness of peoples, the wisdom of States, and the virtue of individuals have been victimizedthe question involuntarily arisesto what principle, to what final aim these enormous sacrifices have been offered.”
—Georg Wilhelm Friedrich Hegel (17701831)