“Lowell saw in advance that the perturbations of the latitudes of Uranus and Neptune (from which alone the position of the orbit plane of the unknown planet could be calculated) were too small to give a reliable result and contented himself with the prophecy that the inclination, like the eccentricity, would be considerable. For the other four independent elements of the orbit, which are those that Lowell actually undertook to determine by his calculations, the agreement is good in all cases, the greatest discrepancy being in the period, which is notoriously difficult to determine by computations of this sort. In view of Lowell’s explicit statement that since the perturbations were small the resulting elements of the orbit could at best be rather rough approximations, the actual accordance is all that could be demanded by a severe critic.

“Even so, the table does not tell the whole story. Figure 1[49] shows the actual and the predicted orbits, the real positions of the planet at intervals from 1781 to 1989, and the positions resulting from Lowell’s calculations. It appears at once that the predicted positions of the orbit and of the planet upon it were nearest right during the 19th century and the early part of the 20th, while at earlier and later dates the error rapidly increased. Now this (speaking broadly) is just the interval covered by the observations from which the influence of the planet’s attraction could be determined and, therefore, the interval in which calculation could find the position of the planet itself with the least uncertainty.

Predicted and Actual Orbits of PLUTO

“In the writer’s judgment this test is conclusive.”[50]

Later observations, and computations of the orbit of Pluto, do not vary very much from those that Professor Russell had when he wrote. Two of the most typical—giving more elements—are as follows:

Predicted Nicholson and Mayall F. Zagar
Period 282 years 249.2 248.9
Eccentricity 0.202 0.2461 0.2472
Longitude of perihelion 204.9 222° 23′ 20″ .17 222° 29′ 39″ .4
Perihelion passage 1991.2 1889.75 1888.4
Inclination about 10° 17° 6′ 58″ .4 17° 6′ 50″ .8
Semi-major axis 43. 39.60 39.58
Perihelion distance 34.31 29.86 29.80
Aphelion distance 51.69 49.35 49.36

Except for the eccentricity, and the inclination which he declared it impossible to calculate, these results have proved as near as, with the uncertainty of his data, he could have expected; and in regard to the position of the planet in its orbit it will be recalled that he found two solutions on opposite sides, both of which would account almost wholly for the residuals of Uranus. The one that came nearest to doing so he had regarded as the least probable because it placed the planet in a part of the sky that had been much searched without finding it; but it was there that Pluto appeared—a striking proof of his rigorous analytic method.

But the question of its mass has raised serious doubts whether Pluto can have caused the perturbations of Uranus from which he predicted its presence, for if it has no significant mass the whole basis of the calculation falls to the ground, and there has been found a body travelling, by a marvellous coincidence, in such an orbit that, if large enough, it would produce the perturbations but does not do so.[51] Now as there is no visible satellite to gauge its attraction, and as it will be long before Pluto in its eccentric orbit approaches Neptune or Uranus closely enough to measure accurately by that means, the mass cannot yet be determined with certainty. What is needed are measures of position of the highest possible accuracy of Neptune and Uranus, long continued and homogeneous.

The reasons for the doubt about adequate mass are two.[52] One that with the largest telescopes it shows no visible disk, and must therefore be very small in size, and hence in mass unless its density is much greater, or its albedo far less, than those of any other known planet. The other substantially that the orbits of Uranus and Neptune can be, and are more naturally, explained by assuming appropriate elements therefor, without the intervention of Pluto’s disturbing force. This is precisely what Percival stated in discussing the correctness of the residuals—that it was always possible to account for the motions of a planet, whose normal orbit about the sun is not definitely ascertained, by throwing any observed divergencies either on errors in the supposed orbit, or upon perturbations by an unknown body.