DOUBLE STARS 135 



A particular simple case of the problem is represented 

 in fig. 12 (p. 162). A and C are two stars. In conse- 

 quence of their mutual attraction and the motions that 

 they possess independently of it, they describe similar 

 orbits, which are in this case circles, about O, their centre 

 of mass. If their masses were equal the point O would 

 lie midway between their centres, but in the case repre- 

 sented it is assumed that A has twice the mass of C, and 

 in consequence, the point O divides the line joining their 

 centres, so that its distance from the centre of A is one- 

 half its distance from the centre of C. A consequently 

 describes a small orbit round O, while C, always lying 

 upon the opposite side of O, describes a larger one. The 

 case is precisely analogous to that presented by the Earth 

 and Moon. Under the controlling influence of the Earth's 

 attraction, the Moon is commonly regarded as describing 

 a circular orbit round the centre of the Earth. This 

 however is not a complete statement of the fact. The 

 Earth attracts the Moon, but the Moon must necessarily 

 attract the Earth with equal force. Consequently, both 

 Earth and Moon describe orbits in the same time round 

 their centre of mass. Since the mass of the Earth is 

 eighty times that of the Moon, the centre of mass of the 

 pair is quite close to the centre of the Earth, and the 

 orbit described by the Earth is very small. In this case 

 the orbits are not true circles, but are slightly elliptical. 

 They are however precisely similar in form. 



A case in which the ellipticities of the orbits are very 

 pronounced is illustrated in fig. 4 (p. 139). Here .5* and Z 

 are two stars, describing, in consequence of their mutual 

 attraction, similarly elliptical orbits round their centre of 

 mass O. The mass of ,S is twice that of Z, and conse- 

 quently OS is one-half of OZ. As the revolutions 

 proceed the line SZ continually passes through O, and 



