New and updated long-periodic terms in harmonic development of the Earth tide-generating potential

We present a new harmonic development of the long-periodic band of the Earth tide-generating potential (TGP). It updates the corresponding part of the previous TGP expansion, KSM03 (Kudryavtsev, J. Geodesy, 77:829, 2004), and includes 38 terms of period longer than $\simeq$18 years (yr) and amplitude not less than $10^{-8}~{\rm m}^2\,{\rm s}^{-2}$. The development is made through a modified spectral analysis of the TGP numerical values tabulated over more than 30,000 yr (13,200~BC--17,191~AD). The latest JPL NASA's long-term numerical ephemeris DE441 (Park et al., Astron. J., 161:105, 2021) is used as the source of the Moon, the Sun and major planets coordinates. For comparison, the KSM03 series were done on the basis of an older DE406 ephemeris (Standish, JPL IOM 312.F, 1998) and over a shorter time interval of 2000 yr (1000--3000). As a result of using an extended time span several new long-periodic waves in the Earth TGP are found and most of other terms are updated. In particular, a relatively large term of amplitude of $3\times 10^{-5}~{\rm m}^2\,{\rm s}^{-2}$ and period of $\simeq$7.4~kyr is revealed. Several new waves of period close to 18.61 yr (the period of the lunar nodal cycle, LNC) are separated from the main LNC term. The effect of the general precession in longitude (of $\simeq$25.7~kyr period) on the Earth TGP for the first time is evaluated. As a result, a number of updated TGP terms include the precession rate in their arguments. A new catalogue of the long-periodic terms in the Earth TGP spectrum in both standard HW95 and KSM03 format is released.