Published online by Cambridge University Press: 12 April 2016
SALE and ELP, analytical theories of the main problem of the Moon, are developed by Henrard (1979) and Chapront-Touzé (1980), respectively. Both theories are compared with numerical integration over one year, which covers about 13 revolutions of the Moon’s orbit. The root-mean-square residuals in the distance of SALE truncated at 10−5 arcsecond is about 10 cm for series truncated at 10−5 arcsecond and 1.2 cm for series truncated at 10−6 arcsecond. ELP is also compared with 20 years of numerical integration and the root-mean-square residuals in the distance is about 1.5 cm.