Newton and his Fudge Factors

Newton remarked to Halley that lunar theory gave him a headache. In particular the calculation of the motion of the lunar apsides frustrated Newton (an apse is an endpoint of the major axis of the ellipse defining the orbit of a body). The lunar apsides rotate approximately 3 degrees per month, but Newton’s calculations only showed half of this amount, leading Newton to say that the problem was “too complicated and cluttered with approximations.” In this talk we will examine Newton’s lunar theory, his failures and successes, and his occasional use of a fudge factor to get the theory to align with observation. Newton’s biographer, Richard Westfall, once commented that “no one can manipulate the fudge factor as the master mathematician himself.”