318 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1961 



NORTH POLE 



INTERSECTION OF 

 PLANE OF ORBIT 

 WITH EARTH. 



PERIGEE POINT 



EQUATOR 



Y 



TO VERNAL 

 EQUINOX 



Figure 7. — Diagram of angular orbital elements, fi is the right ascension of the ascending 

 node; w is the argument of perigee; i is the inclination; -y is the vernal equinox. 



would then be a relatively simple matter to define the orbit. The 

 earth, however, is not perfectly spherical, and it is surromided by an 

 atmosphere that produces a "drag" on objects moving through it; and 

 there are other forces at work on the satellite. Consequently, the 

 satellite's orbit is perturbed, and, unless the perturbations can be 

 anticipated, predictions will be in error. 



It cannot be emphasized too much that one of the major reasons 

 for launching artificial earth satellites was to improve our knowl- 

 edge not only of the shape of the earth but also of these other forces 

 that act upon the body as it moves through space. No one could 

 reasonably expect that any program developed before the launch- 

 ing of the first satellite would accurately predict the orbit. Fur- 

 thermore, all estimates of atmospheric density were on the low side, 

 with the consequence that the orbit programs worked out before 

 October 4, 1957, used an inaccurate estimate of this important 

 parameter. 



During the first part of 1957 Dr. Cunningham continued to work 

 on analytical problems of artificial earth satellites. Since, during 

 one revolution, the orbit of the satellite follows essentially an ellipse, 

 he derived a fairly complicated set of equations to compute the devia- 

 tions from, or perturbations of, a perfect ellipse. From the practical 

 standpoint of making predictions, the major term in these equations 

 accounts for the rotation of the orbital plane of the ellipse in space. 



Cunningham's analytical theory could in principle have been used 

 to calculate predictions of satellite positions or satellite transits. 



