The rediscovery of neptune

Abstract

The methods used by Adams and Le Verrier for the prediction of the position of Neptune led to extremely extensive calculations, and the question still remains open whether any much simpler approarch is possible that could have led to comparably accurate prediction with much reduced effort of calculation. Such a method is presented. It turns out that the time of conjunction with Uranus can be derived with very little calculation using only elementary considerations applied solely to the (observed) discrepancies in heliocentric longitude. The instant so found is only about six months later than actual value. On the basis of a circular orbit for the unknown planet, its position at discovery (25 years later than conjunction) even using Bode's law for the size of orbit is then only some 13° away from the actual position, and in fact within the zone that Challis began to search, and so probably sufficient for ultimate discovery. However, the distance appropriate to a best-fit of the observations can also be found, and this makes a considerable improvement in the predicted position. By suitably combining the equations of condition, the number of unknowns associated with the necessary correction of the orbit of Uranus can be reduced from four to two, and with any assumed radius for the (circular) Neptune orbit only the mass of the planet is unknown. Thus the number of unknowns can be reduced to three (for each assumed mean distance) compared with eight in the original methods. Even with the extra work of calculation of the coefficients in the perturbations for a sufficient number of assumed mean distances, there results an enormous reduction in the amount of calculation. For the demonstration of the method, further economy of arithmetic has been achieved by making use only of part of the observational material that was actually available at the time (the so-called “modern” observations). Nevertheless the procedure succeeds in predicting a position of Neptune (in 1846) with the same accuracy (1°) as Le Verrier and more accurately than Adams ( 2 1 2 ° ).