tokens: elements of Mercury given by the DEA431 analytical series and by DE431 numerical ephemerides. Table 2. Maximum differences between orbital elements of Venus given by the DEA431 analytical series and by DE431 numerical ephemerides. Table 3. Maximum differences between orbital elements of the Earth–Moon barycentre given by the DEA431 analytical series and by DE431 numerical ephemerides. Table 4. Maximum differences between orbital elements of Mars given by the DEA431 analytical series and by DE431 numerical ephemerides. Table 5 gives the number of terms in the DEA431 analytical series, that is, the value of j i in equation ( 8 ) for the i th orbital element of every terrestrial planet. Table 5. Number of terms in the DEA431 analytical series. We also made a comparison of planetary heliocentric distances R , ecliptic longitudes L , and ecliptic latitudes B calculated using the DEA431 analytical series with those obtained from DE431 numerical ephemerides. Tables 6 – 9 present the maximum deviations between the two sets of spherical coordinates for every terrestrial planet over the total time interval of 30 000 yr covered by DE431. For comparison, some corresponding data available for the VSOP2013 theory from Simon et al. ( 2013 ) and a description of the theory's files on ftp 2 are given. In the case of VSOP2013, the numerical ephemerides INPOP10a (Fienga et al. 2011 ) extended to the time interval [−4 000, 8 000] were used as a reference. Table 6. Maximum differences between the spherical coordinates of Mercury given by the analytical series and by numerical ephemerides. Note. the coordinates R *, L *, B * are related to VSOP2013 planetary theory; the corresponding differences are taken from Simon et al. ( 2013 ). Table 7. Maximum differences between the spherical coordinates of Venus given by the analytical series and by numerical ephemerides. Note. the coordinates R *, L *, B * are related to VSOP2013 planetary theory; the corresponding differences are taken from Simon et al. ( 2013 ). Table 8. Maximum differences between spherical coordinates of the Earth–Moon barycentre given by the analytical series and by numerical ephemerides. Note. the coordinates R *, L *, B * are related to VSOP2013 planetary theory; the corresponding differences are taken from Simon et al. ( 2013 ). Table 9. Maximum differences between the spherical coordinates of Mars given by the analytical series and by numerical ephemerides. Note. the coordinates R *, L *, B * are related to VSOP2013 planetary theory; the corresponding differences are taken from Simon et al. ( 2013 ). Tables 6 – 9 show that the VSOP2013 theory better predicts the motion of terrestrial planets over 100 yr or so, but that the DEA431 solution performs better over long-term intervals such as thousands and tens of thousands of years. From Tables 1 – 4 and Tables 6 – 9 it can be seen that the DEA431 development has a rather stable accuracy over approximately 24 000 years centred at epoch J2000. In
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