Trojan Points Explained

For any astronomical body orbiting another there are 5 hypothetical Lagrange points (named after the French physicist who discovered them mathematically in the eighteenth century).

Diagram of Lagrange Points
  • L1 is approximately halfway between, and in line with, the two bodies.
  • L2 lies outside the orbit of the lesser body but still in line with them.
  • L3 is on the orbit and remains opposite the orbiting body.
  • L4 is on the orbit and remains 60 degrees ahead (leading) of the orbiting body.
  • L5 is on the orbit and remains 60 degrees behind (trailing) the orbiting body.

L1, L2, and L3 are not stable … objects at these points will move away if not perfectly positioned or if disturbed (therefore no debris or space junk problem here). L4 and L5 are stable (objects near these points will gravitate towards them) provided that the orbiting body has less than 4% the mass of the primary (or orbited) body and the object at the L4 or L5 point has negligible mass in comparison with the two bodies (therefore possible debris or space junk problem here).

A cluster of asteroids have been found at Jupiter’s L4 point, and they have been collectively called the Trojans (this is where the term “Trojan points” for L4 and L5 comes from), and are individually named after Trojan heroes from the Greek/Trojan War. A cluster of asteroids have been found at Jupiter’s L5 point, and they have been collectively called the Greeks, and are individually named after Greek heroes from the Greek/Trojan War. (Actually, one of the Trojans is named after a Greek and one of the Greeks is named after a Trojan.)

It is perhaps more accurate to think of the L4/L5 asteroids as ‘orbiting’ these Lagrange points rather than be at the Lagrange points. Some can wander more than 1 AU from the Lagrange point.

Geometry of Jupiter's Trojans
Top view

Jupiter's Trojans as seen from the side
Side view

While all Sol’s planets could have Trojan/Greek asteroids, they have only been found for Jupiter. However, Tethys (a moon of Saturn) has natural L4 and L5 companions, and Dione (another of Saturn’s moons) has a natural L4 companion.


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