$ 2s6j Variation of tfie Elements 303 



in an elliptic orbit. For wherever a planet may be and 

 whatever (within certain limits *) be its speed or direction 

 of motion some ellipse can be found, having the sun in 

 one focus, such that the planet can be regarded as moving 

 in it for a short time. Hence as the planet describes a 

 perturbed orbit it can be regarded as moving at any instant 



FIG. 81. A varying ellipse. 



in an ellipse, which, however, is continually altering its 

 position or other characteristics. Thus the problem of 

 discussing the planet's motion becomes that of determining 

 the elements of the ellipse which represents its motion at 

 any time. Euler shewed further how, when the position 

 of the perturbing planet was known, the corresponding 



* The orbit might be a parabola or hyperbola, though this does 

 not occur in the case of any known planet 



