Science & Technology Studies
University College London
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.
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 .
In Figure 1 his eccentricity is given, not by the line TF
but by its projection onto TB, so that the two quantities differ by cos
It has a slightly smaller epicycle CF, Flamsteed's equation
of apogee being half a degree smaller than Newton's.
(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