The article “The location of Planet X” was written by Dr. R.S. Harrington, of the US Naval Observatory in Washington. In this article he calculated several parameters of Planet X and its orbit. Harrington started from the perturbatians in the orbits of Neptune and Uranus, knowing that Pluto could not be responsible for them. The observations he used were supplied by the Nautical Almanac Office of the US Naval Observatory and go back as far as 1833 for Uranus and 1846 for Neptune. A weight was assigned to the data because later observations were more accurate than earlier ones, but he still thought it important to give enough weight to the early data, in order to be able to give them some significance in a solution for long period effects.
To calculate the position of Planet X, the following formula was used:
This equation therefore gives the equation of motion of the perturbation vector. There is no need to explain all the calculations he did here, but I also want to mention that he also took into consideration the complete Lowell Planetary Survey. It was at this Observatory that the astronomer Clyde Tombaugh discovered Pluto in 1930. After that he continued to look for any additional planets for another 13 years, covering a good portion of the northern sky down to approximately the 16th magnitude. Of course he could have overlooked Planet X, but according to Harrington the search was quite thorough. The probability that the planet is in the north is therefore quite low. Eventually Harrington came up with the following results, not as a best solution, but as a typical good case:
|Perihilion Epoch T:||6 August 1789|
|Semimajor axis a:||101.2 AU|
|Period P:||1019 yr|
|Argument of perihelion w:||208.5|
|Argument of node omega||275.4|
|Mass m:||4 Me|
|Absolute magnitude V(1,0):||-6 (assumed)|
The parameters give the positions in the 1930′s, now of course its position has changed, but the change can be calculated.