[TML] BSG RPG

[Jerry W Barrington]

On 10/22/07 8:12 AM, Leonard Erickson wrote:

> The primary (star) and secondary (planet) have to have at least a
> 25(?)... 50(?) to one mass ratio. And the stuff at the leading and
> trailing points has to be even less massive than the secondary
> (hundreds or thousands to 1)

Well, mathematically, no.  The Primary and secondary can range from equal to
very unequal.  That just leads to different numerical solutions.  The "very
unequal" results are the typical equilateral triangle.  Even the tertiary
mass *can* be large, but this is harder to make stable.

Interestingly while there is a precise mathematical Trojan point in a pure
circular 3-body setting, in real world elliptical many-body settings, there
is no stable point.  A Trojan orbits around the vague Trojan area, sometimes
at quite a distance.  Many Trojans actually circulate back and forth between
roughly L-4 and L-5, arcing around the side of the orbit away from the
secondary (240 degree horseshoe).  Some are even weirder.

<http://en.wikipedia.org/wiki/Horseshoe_orbit>