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Table 2

Orders of the control acceleration magnitudes to compensate for the relative fictitious perturbations (fo and ff) for the secular, long-period, and short-period terms, in comparison to those of the absolute physical perturbations (Fc).

Terms Secular Long-period Short-period
0 c(lp) × (rr/a)(nl/n) c(sp) × (rr /a)
c(s) × (rr / a) c(lp) × (rr/a) c(sp) × (rr /a)
(·) n2 rr c(s) × (rr/a)(nt) c(lp) × (rr/a)(nl/n)−1 c(sp) × (rr /a)

Notes. In the first column, (·) denotes the osculating orbital elements comprising the secular, long-period, and short-period terms as expressed in Eq. (20). The osculating orbital elements of (ex, ey) are substituted to (·)n2rr, and those of (ex, ey, I, Ω, ϕ) are substituted to and for the analysis. In the second to fourth columns, c(s), c(lp) , and c(sp) indicate the orders of the control acceleration magnitudes to compensate for the absolute physical perturbations for the secular, long-period, and short-period terms, respectively. They are defined as , and c(sp) = δ(·)(sp)n2a, respectively.

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