Department of
Science & Technology Studies
University College London

Nicholas Kollerstrom's
Flamsteed's 1681 Lunar Theory 

John Flamsteed's Worked Example

In 1681, Flamsteed's only published work in his capacity as Astronomer Royal appeared - De Sphaera, or Doctrine of the Sphere. This contained his polished-up version of Horrock's lunar theory. His worked example, shown in the table below, first computes three 'mean motions' of moon, apogee and node - the solar position having been computed on the previous page. The time is for 6.35 pm GMT 22 December 1680.
Solar Equation

Flamsteed's method involved three steps of 'equation', after the mean motions. First there was the 'annual equation' of the Moon, given an old Keplarian name of 'physical parts', amounting to one arcminute. Then there is the equation of centre. This differs in two important respects from Newton's procedure:

This worked example erred by eleven arcminutes -- rather more than he had in mind. Verify this, firstly by downloading the Flamsteed program (which will show the different stages of his calculations), then download the modern program for comparison (insterting the time Flamsteed was using .

(The correct -- i.e. modern computed -- longitude value, then, for that time was 4  59' 18" Gemini, whereas Flamsteed obtained the value of 5  9' 52" Gemini.)

The contents of this page remain the copyrighted, intellectual property of Nicholas Kollerstrom.  Details. rev: May 1998