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The word co-orbital, which has here its literal meaning of shares the orbit with, is also generally used whenever referring to any nearby orbits.

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... by

Note that Eq. (3) implies that at L₄ (or L₅), a=a₁ and $\lambda-\lambda_1= +60^{\circ}$ (or $-60^{\circ}$ ) and follows from the fact that the three-body potential at L₄ (or L₅) is of keplerian type but with a larger mean motion.

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... axis

Here we refer to a semi-major axis obeying the approximate relation $n^2 a^3={\cal G} m_{\rm c} (1+(3/2) J_2 (R/a_1)^2)$ which follows from the fact that the oblateness potential is of nearly keplerian type but with a larger mean motion (see Greenberg 1981).

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... write

There is an obvious error in the definition of c[l] in Paper I (Eq. (36)). This only takes the unit value when l=0 and when $l\to \infty$ , as can easily be confirmed in Fig. 1b from the same paper.

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... system

Here, we took into account Uranus' oblate shape by adding the terms $\beta(a_k)$ (recall definition of function $\beta$ in Eq. (26)) to A_kk and -B_kk (the diagonal terms of matrices A and -B which we introduced in Sect. 2.3).

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... $\Gamma _k$ )

In our calculations we ignored the contribution $\Delta\bar{\beta}$ (given by Eq. (71)) due to Uranus' oblate shape as in general this is unimportant (cf. last paragraph of Sect. 3.2.2).

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... regions

The use of more accurate values for the eigen-frequencies from Laskar (1988) does not cause any significant alteration in the location of these secular resonances.

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