## The Problem of N Bodies in General Relativity Theory in Proceedings of the Royal Society of London A 166, 1938, pp. 465 – 475

London: Royal Society, 1938. 1st Edition. FIRST EDITION OF THE FIRST CORRECT “SOLUTION TO THE MANY-BODY PROBLEM IN CELESTIAL MECHANICS UNDER EINSTEIN’S THEORY OF GRAVITY FOR THE SPECIAL CASE OF POINT MASSES” (History of Physics: The Wenner Collection). Eddington and Clark’s equations “are now frequently used for high precision tracking of planetary orbits and spacecraft movements within the Solar System” (ibid).

“The problem of the secular acceleration of the center of mass of binary systems has a checkered history. Levi-Civita (1937) first pointed out that general relativity predicted a secular acceleration in the direction of the periastron of the orbit, and found a binary system candidate in which he felt the effect might one day be observable. Eddington and Clark (1938) repeated the calculation using de Sitter’s (1916) n-body equations of motion. After first finding a secular acceleration of opposite sign to that of Levi-Civita, they then discovered an error in de Sitter’s equations, and concluded finally that the secular acceleration was zero” (Israel & Hawing, General Relativity, 84).

In the confrontation between gravitation theory and experiment, Eddington and Clark’s work here provided the first “approximate solution to Einstein’s field equations for the case of a massless particle moving in the gravitational field of n massive bodies” (Israel & Hawing, General Relativity, 84).

Sir Arthur Stanley Eddington (1882-1944) was an influential astronomer, mathematician, and writer. Among other things, he led the 1919 expedition that provided the first evidence supporting Einstein’s General Theory of Relativity by showing that the sun’s gravity caused curvature of starlight consistent with Einstein’s prediction. Eddington was particularly well known for his ability to explain the concepts of Relativity in lay terms as well as scientific. He included original thinking in Mathematical Theory of Relativity, and Einstein suggested this work was the finest presentation on the subject in any language.

George Norman Clark (1890-1979) was the most significant member of the large group of students whom Eddington worked to train. Item #1581

CONDITION & DETAILS: London: The Royal Society. Complete volume. 4to. 9.75 by 7 inches (213 x 138mm). [4], 589, [4]. Ex-libris with markings limited to spine and a bookplate on the front pastedown. Bound in tan buckram; black lettered at the spine. The volume is illustrated throughout with in-text figures and 16 plates; the Woolfson paper has many in-text illustrations.

**
Price:
$275.00
**