An Excess Motion of the Ascending Node of Mercury in the Observations Used by Le Verrier

Abstract

We have reexamined the twenty-one observations of second and third contacts during transits of Mercury across on the disk of the Sun — the same Le Verrier used himself (Le Verrier 1859) — to check the reality of the excess of the observed motion of the longitude of the ascending node of Mercury’s orbit over the theoretically predicted on. To this, we numbered these observations chronologically from 1 to 13 for the transits on November and from 14 to 21 for those on May. The results are as follows:

• (1) An initial analysis showed that three of the observations (Nos. 2, 8 and 21) might have been erroneously recorded. If the signs of observations Nos. 2 and 8 are changed and if the value for the observation No. 21 is changed from - 1.“03 to - 2.”52, the sum of the squares of the residuals is reduced by almost 60%.

• (2) Leaving out these observations altogether, as well as observations Nos. 10, 17 and 18 - which leaves us 15 observations to analyze - the sum of the squares of the residuals is drastically reduced to 5% of its original value (but now, there are of course also fewer observations contributing to this sum), and we obtain an excess motion of 16.“7 ± 3.”4 (s.e.) per century. This shows, that the appropriate choice of observations will indeed produce an estimate for the excess motion of the node which exceeds its formal standard error by a factor of 5.

• (3) Eliminating eight additional observations and thus utilizing only the seven observations, viz. Nos. 1, 9, 13, 14, 16, 19 and 20, the least squares adjustment of the remaining seven condition equations in the six adjustment unknowns produces an estimate for the excess motion of the ascending node of Mercury’s orbit. This time, it gives 15.“2 ± 0.”1 per century, with the sum of the squares of the residuals now reduced to the order of 10^-5, even with only even summands contributing, clearly an unrealistic result in view of the precision of observations attained in Le Verrier’s time.