A consistent numerical integration of orbit, tides, and rotation for synchronous satellites

Open Access

Table C.1

Eccentricity functions G_lpq(e) for each (libration-free) forcing mode.

lmpq	G_lpq(e)	ω_lmpq
220, –6	$\frac{4}{45} e^{6}$ $Mathematical equation: ${4 \over {45}}{e^6}$$	–6n
220, –5	$\frac{81}{1280} e^{5}$ $Mathematical equation: ${{81} \over {1280}}{e^5}$$	–5n
220, –4	$\frac{1}{24} e^{4} + \frac{7}{240} e^{6}$ $Mathematical equation: ${1 \over {24}}{e^4} + {7 \over {240}}{e^6}$$	–4n
220, –3	$\frac{1}{48} e^{3} + \frac{11}{768} e^{5}$ $Mathematical equation: ${1 \over {48}}{e^3} + {{11} \over {768}}{e^5}$$	–3n
220, –2	0	–2n
220, –1	$- \frac{1}{2} e + \frac{1}{16} e^{3} - \frac{5}{384} e^{5}$ $Mathematical equation: $ - {1 \over 2}e + {1 \over {16}}{e^3} - {5 \over {384}}{e^5}$$	–n
2200	$1 - \frac{5}{2} e^{2} + \frac{13}{16} e^{4} - \frac{35}{288} e^{6}$ $Mathematical equation: $1 - {5 \over 2}{e^2} + {{13} \over {16}}{e^4} - {{35} \over {288}}{e^6}$$	0
2201	$\frac{7}{2} e - \frac{123}{16} e^{3} + \frac{489}{128} e^{5}$ $Mathematical equation: ${7 \over 2}e - {{123} \over {16}}{e^3} + {{489} \over {128}}{e^5}$$	n
2202	$\frac{17}{2} e^{2} - \frac{115}{6} e^{4} + \frac{601}{48} e^{6}$ $Mathematical equation: ${{17} \over 2}{e^2} - {{115} \over 6}{e^4} + {{601} \over {48}}{e^6}$$	2n
2203	$\frac{845}{48} e^{3} - \frac{32525}{768} e^{5}$ $Mathematical equation: ${{845} \over {48}}{e^3} - {{32525} \over {768}}{e^5}$$	3n
2204	$\frac{533}{16} e^{2} - \frac{13827}{160} e^{4}$ $Mathematical equation: ${{533} \over {16}}{e^2} - {{13827} \over {160}}{e^4}$$	4n
2205	$\frac{228347}{3840} e^{5}$ $Mathematical equation: ${{228347} \over {3840}}{e^5}$$	5n
2206	$\frac{73369}{720} e^{6}$ $Mathematical equation: ${{73369} \over {720}}{e^6}$$	6n

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