...L

As of March 6, there are 1121 L₄ Trojans and 885 L₅ Trojans.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... output

In the following we will only present the pictures obtained with the hybrid integration method (HYB). Additional calculations have shown that all three methods give the same output; thus for all future integrations we have neglected the LIE and B-S methods.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... stability

For an initial value of $\Delta \sigma =0^\circ$, the stability region encloses all values of proper eccentricity that are lower than $\approx$0.21; this value decreases to $\approx$0.1 for an initial $\Delta \sigma$ of $43^\circ$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...$e_{{\rm INI}}=0.20$)

We have omitted the figure for $e_{{\rm INI}}=0.25$ because it shows no new information.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... left

Note that for high eccentricities the position of Lagrangian points differs from $\sigma=60^\circ$ and $\sigma=300^\circ$. Strictly speaking, these values are only valid for the restricted (circular) three-body problem.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

...L

The behavior of L₅ was not different from L₄ - thus we omit the corresponding figure.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... choice

Note that we have obtained similar results for $3^\circ$ or $5^\circ$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... model 3

The percentage gives the number of stable orbits in between $\sigma=[0^\circ,120^\circ]$ for L₄ and $\sigma=[240^\circ,360^\circ]$ for L₅.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.