Expert: Courtney Seligman - 5/24/2009

Question
Has anyone ever done an estimate of the Mass of the Trojans- & why are they spaced at approx 60 Degrees ?
Thanks.

Answer
I don't know if there is a specific estimate of their total mass, but there are only a few hundred of them, mostly relatively small, so it would be just a fraction of the mass of any of the larger asteroids, such as Ceres, Vesta, Pallas or Juno.

Their 60 degree (equilateral triangle) spacing with the Sun and Jupiter is due to a stability relationship discovered by Lagrange. As a result, their locations are referred to as Lagrange points (specifically, L4 and L5). At these points, the distance from the objects to the Sun and Jupiter is the same, so the relative force acting on them is directly proportional to the relative masses of the two bodies. The result is that the parallelogram of force between the Sun, Jupiter and the Trojans points at the center of mass of the Sun-Jupiter system. With the same distance from the Sun as Jupiter, and the same center of force (the center of mass of the Sun-Jupiter system), they orbit the Sun with the same period as Jupiter, thereby maintaining a constant position relative to the Sun and Jupiter. If they were ahead or behind the 60-degree positions, the center of force wouldn't be quite right, and they would drift a bit over time; but as it happens, they would mostly drift toward the 60-degree point, so the relationship is more stable than not.

This is probably as clear as mud, as trying to explain things like this without diagrams is like trying to tell a fish story without spreading your hands to show how big the fish was. As a result, I'd recommend looking at various web pages for more information. On my own website, Lagrange Points are briefly discussed at http://cseligman.com/text/sky/lagrange.htm and Trojan Asteroids at http://cseligman.com/text/asteroids/trojan.htm

Unfortunately, as currently written, neither of those pages explains the physics behind the Lagrange Points. For L1 and L2, which is where the SOHO and WMAP satellites are posted, the physics is fairly simple. They are the points where the combined gravity of the Sun and the planet (the Earth, in the case of the aforementioned satellites) 'balance', allowing objects to orbit the Sun with the same period of the planet, even though they are closer or further from the Sun, which would normally cause their orbital periods to be different. For L4 and L5, the situation is more complicated, but there is a good diagram and reasonably adequate discussion at http://en.wikipedia.org/wiki/Lagrangian_point (not as clear as I'd like, but better than currently posted on my site, and better than I can do here, without going into far more detail).

Hopefully, these external links will be adequate for your purpose, but if you'd like a better explanation of some point, feel free to contact me again, and I'll do what I can to oblige you.

Courtney Seligman