No evidence for Planet X
Finally in 1993 an article was written in which it is shown that the possibility of the existence of Planet X is negligible. In "Planet X: No dynamical evidence in the optical observations" the author E. Myles Standish Jr of the California Institute of Technology gives two arguments, with which he shows that the alleged "unexplained anomalies in the motion of Uranus" are simply not there. Those anomalies were used to predict the existence of Planet X and without them no evidence for it would remain.
The first argument he uses involves the observational data of the orbit of Uranus used to calculate the position of Planet X by authors such as Harrington in 1988. Harrington and other authors used data provided by the US Naval Observatory, going back as far as 1830. This set of data however, is far from complete, because it contains no Greenwich data and only a scattering of Paris data, which are needed for accurate corrections.
The second argument uses the fact that by now corrections have been made to the masses of the Jovian planets, determined by the data provided by Voyager, a spacecraft sent into space to collect information about the solar system. Especially the mass of Neptune is important, as it was adjusted by 0.5%, which is quite a lot. These new masses were used to calculate the orbit of Uranus again and the residuals already disappeared nearly completely by this adjustment alone.
Figures 1a and 1b below show the residuals in the orbit of Uranus in Right Ascension (a) and Declination (b) in arcseconds as received from the US Naval Observatory. In Right Ascension there is a clear negative slope visible in the twenieth century (marked by two red lines) and a rather large negative bias in the nineteenth century (shown by the two vertical green lines).
Fig 1. Residuals of Uranus in Right Ascension and Declination as received directly from the US Naval Observatory.
Taken from Standish: Planet X: No dynamical evidence in the optical observations.
Figures 2 a and b show the residuals again, but now after having accounted for the correct masses of the outer planets (especially Neptune's mass) and after correcting the observational data, by weighing them according to the apparent scatter in the observations.
Fig 2. Residuals of Uranus in Right Ascension and Declination as in Fig 1, but now reduced for an adjusted orbit of Uranus and after having accounted for the new masses.
Taken from Standish: Planet X: No dynamical evidence in the optical observations.
Both the negative slope and the negative bias are almost completely gone in figure 2a. The difference may not be very clear, but by looking at the difference of the red and green lines of figures 1 and 2 the difference is eminent. Minor systematic errors do remain, but they are very small in the twentieth century and are easily explained by a number of uncertainties in the observations themselves. The fact that there are still large residuals before about 1920 is almost certainly due to observational errors.
Because no significant residuals in the orbit of Uranus are left, the author concludes that there is no evidence for the existence of a tenth planet at all, and probably Planet X will never be found. After all, you cannot find what isn't there.
Original article