34 LUNAR THEORY. SECT. V. 



SECTION V. 



Lunar Theory Periodic Perturbations of the Moon Equation of Centre 



Erection Variation Annual Equation Direct and Indirect 

 Action of Planets The Moon's Action on the Earth disturbs her own 

 Motion Excentricity and Inclination of Lunar Orbit invariable 



Acceleration Secular Variation in Nodes and Perigee Motion 

 of Nodes and Perigee inseparably connected with the Acceleration 

 Nutation of Lunar Orbit Form and Internal Structure of the Earth 

 determined from it Lunar, Solar, and Planetary Eclipses Occulta- 

 tions and Lunar Distances Mean Distance of the Sun from the Earth 

 obtained from Lunar Theory Absolute Distances of the Planets, how 

 found. 



OUR constant companion, the moon, next claims our attention. 

 Several circumstances concur to render her motions the most in- 

 teresting, and at the same time the most difficult to investigate, 

 of all the bodies of our system. In the solar system, planet 

 troubles planet ; but, in the lunar theory, the sun is the great 

 disturbing cause, his vast distance being compensated by his 

 enormous magnitude, so that the motions of the moon are more 

 irregular than those of the planets ; and, on account of the great 

 ellipticity of her orbit, and the size of the sun, the approximations 

 to her motions are tedious and difficult, beyond what those un- 

 accustomed to such investigations could imagine. The average 

 distance of the moon from the centre of the earth is only 238,793 

 miles, so that her motion among the stars is perceptible in a few 

 hours. She completes a circuit of the heavens in 27 d 7 h 43 m 11 8 *5, 

 moving in an orbit whose excentricity is about 12,985 miles. 

 The moon is about four hundred times nearer to the earth than 

 the sun. The proximity of the moon to the earth keeps them 

 together. For so great is the attraction of the sun, that, if the 

 moon were farther from the earth, she would leave it altogether, 

 and would revolve as an independent planet about the sun. 



The disturbing action (N. 101) of the sun on the moon is 

 equivalent to three forces. The first, acting in the direction of 

 the line joining the moon and earth, increases or diminishes her 

 gravity to the earth. The second, acting in the direction of a 



