Trojans either lead or trail a planet at a specific distance called - oddly enough - the Trojan Point. This point (actually a 'smear') is similar to a LaGrange point except that the Trojans are not orbiting.
A LaGrange point is that position in space between a planet and its moon wherein the gravitational pull of either is in balance.
I think I have this right but I'm ducking just in case one of my professors reads this.
As for the asteroid belt, in 1772 Johannes Bode publicized a connection between the spacing of planets, now known as Bode's Law. He had found out that the distance from the planets in our solar system to the sun followed the following sequence surprisingly well:
4, 4+(3*2^0), 4+(3*2^1), 4+(3*2^2), 4+(3*2^3),.....
....divided each result by 10,
so arrive at the sequence.....
0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, 19.6, 38.8, 77.2,.....
0.39, 0.72, 1.00, 1.52,....., 5.20, 9.54, 19.2, 30.1, 39.5 is the real spacing of the planets.
By taking into account that the asteroid belt lies at a distance between 2.3 and 3.3 AU and that the two most distant planets (Neptune and Pluto) do not follow the sequence, this law works surprisingly well for the other planets. Since it works so well for our planetary system - it probably holds for other systems as well - scaled for solar mass.
It implies the presence (at one time) of a aborted concretion of 'dust' into a planet.
From Bode's Law follows that the difference of the logarithm of the distances is of the same order of magnitude for every two neighbouring planets (so if you plot the distances from the planets to the sun on a one dimensional logarithmic axis, the space in cm between two successive points is about the same every time.
[ July 31, 2002, 19:21: Message edited by: Elowan ]