M. Chapront-Touzé; J. Chapront (1983). "The lunar ephemeris ELP-2000". Astronomy & Astrophysics. 124: 54. Bibcode:1983A&A...124...50C.
M. Chapront-Touzé; J. Chapront (1988). "ELP2000-85: a semi-analytical lunar ephemeris adequate for historical times". Astronomy & Astrophysics. 190: 351. Bibcode:1988A&A...190..342C.
The periods are calculated from orbital elements, using the rate of change of quantities at the instant J2000. The J2000 rate of change equals the coefficient of the first-degree term of VSOP polynomials. In the original VSOP87 elements, the units are arcseconds(”) and Julian centuries. There are 1,296,000” in a circle, 36525 days in a Julian century. The sidereal month is the time of a revolution of longitude λ with respect to the fixed J2000 equinox. VSOP87 gives 1732559343.7306” or 1336.8513455 revolutions in 36525 days–27.321661547 days per revolution. The tropical month is similar, but the longitude for the equinox of date is used. For the anomalistic year, the mean anomaly (λ−ω) is used (equinox does not matter). For the draconic month, (λ−Ω) is used. For the synodic month, the sidereal period of the mean Sun (or Earth) and the Moon. The period would be 1/(1/m−1/e). VSOP elements from
Simon, J.L.; Bretagnon, P.; Chapront, J.; Chapront-Touzé, M.; Francou, G.; Laskar, J. (February 1994). "Numerical expressions for precession formulae and mean elements for the Moon and planets". Astronomy and Astrophysics. 282 (2): 669. Bibcode:1994A&A...282..663S.
