Leonhard Euler’s early lunar theories 1725–1752

Abstract

Leonhard Euler (1707–1783) published two lunar theories in 1753 and 1772. He also published lunar tables in 1745, 1746, and—anonymously—in 1750. There are notebook records, unpublished manuscripts, and manuscript fragments by Euler reflecting the development of his lunar theories between about 1725 until about 1752. These documents might be used to reconstruct Euler’s theory on which he based his calculations of those lunar tables and to analyze the development of his lunar theories within this time span. The results of this analysis will be published here in three parts representing three stages of Euler’s research on this topic: First approaches (about 1725–1730), developing the methods (about 1730–1744), and the breakthrough (about 1744–1752). In this part, I analyze Euler’s manuscripts and, predominantly, Euler’s records of his first two notebooks written between 1725 and 1730. I found that his early theoretical approach is coined by his development of analytical (rational) mechanics of punctiform bodies moved by central forces. He tried to describe the Moon’s motion in terms of two simultaneously acting centripetal forces, Huygens’ centrifugal theorem, and associated osculating radii.