Lunar time ephemeris LTE440: Definitions, algorithm, and performance

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Table 3

Results of Fourier transformation analyses for the periodic terms in LTE₄₃₀ and LTE₄₄₀ in the form of $\begin{array}{l} A_{i} \sin [2 π T_{i}^{- 1} (t - J 2000.0) + ϕ_{i}] \end{array}$ ${A_i}\sin [2\pi T_i^{ - 1}(t - {\rm{J}}2000.0) + {\phi _i}]$ with the amplitude A_i > 1 µs, period T_i, and phase ϕ_i.

Index i	Period T_i [day]	LTE₄₃₀		LTE₄₄₀		Arguments^a
Index i	Period T_i [day]	Amplitude A_i [μs]	Phase ϕ_i [rad]	Amplitude A_i [μs]	Phase ϕ_i [rad]	Arguments^a
1	365.265 909 09	1 651.363 552 04	3.108 951 71	1 651.363 550 77	3.108 951 65	E
2	29.530 538 00	126.308 119 30	5.184 723 42	126.308 131 84	5.184 724 64	D
3	398.999 503 48	19.374 678 66	1.338 558 40	19.374 677 15	1.338 558 43	E–J
4	182.632 954 55	13.700 887 26	3.076 023 07	13.700 887 60	3.076 022 94	2E
5	411.672 643 44	7.475 206 20	3.324 463 76	7.475 204 18	3.324 463 52	D–L
6	4 320.349 462 37	4.243 966 87	3.431 863 07	4.243 973 12	3.431 862 81	J
7	377.979 774 22	3.760 514 19	0.923 586 53	3.760 514 30	0.923 586 39	E–S
8	14.254 026 54	2.933 674 08	1.093 170 21	2.933 681 21	1.093 172 12	D+L
9	369.634 314 63	2.677 531 35	1.512 253 13	2.677 529 83	1.512 253 14	E–U
10	32.127 978 57	2.366 878 30	5.217 486 73	2.366 878 90	5.217 488 01	E–D
11	10 859.256 756 76	1.858 195 62	2.568 428 80	1.858 200 98	2.568 437 62	S
12	584.000 726 74	1.097 425 81	4.676 350 88	1.097 426 15	4.676 351 57	V–E
13	292.000 363 37	1.088 506 49	2.992 490 18	1.088 506 98	2.992 489 81	2V–2E

Notes. ^(a)The argument of each term is a combination of the mean longitudes of the Solar System planets and the Delaunay elements of the Moon. Here “V”, “E”, “J”, “S”, and “U” represent the mean longitudes of Venus, the Earth-Moon barycenter, Jupiter, Saturn and Uranus respectively; “D” is the difference between the mean longitudes of the Sun and the Moon; and “L” is Moon’s mean anomaly.

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