The sine wave oscillation in the amplitude of apogee 
and perigee, in phase with the precession of perigee, clearly shows 
that the orbit behaves differently depending on whether perigee 
occurs in the northern or the southern hemisphere. This is a 
striking illustration of the existence of a north-south dissymmetry 
in the earth - the famous "pear-Shaped" term in the expansion of 
the earth's gravitational field, first deduced by O'Keefe from 
Vanguard data. It is, of course, possible to confirm, quantita- 
tively the value of Jx> the "pear-shaped" coefficient in the expan- 
Sion of the gravitational field of the earth in spherical harmonics. 
in fact, from this data for TRANSIT 1-B together with similar data 
for TRANSIT 2-A, R. R. Newcone- has improved on the value for J3 
and also obtained values for Je and Ja; the next two odd-order 
coefficients beyond Jo: 
Not all of the long term effects shown in Figs. 2 through 
9 are understood. For example, the very small but clearly signifi- 
cant increase in the inclination of the orbit through May and June 
has not been explained to date. 
The day-to-day consistency of the Kepler orbit elements 
is not the best way of judging the accuracy of the tracking and 
could indeed be misleading since there has been perforce some 
smoothing of data involved in the very act of describing the orbit 
by means of Kepler elements. Actually the true orbit, obtained by 
a numerical integration of the full equations of motion, departs 
from a Kepler ellipse (even with allowance for precession of perigee 
and the line of nodes) by one or two tenths of a mile. Obviously 
the "smoothness" of parameters which, at best, can only approxi- 
mately describe the orbit, cannot accurately indicate the precision 
of the system. 
3/ 
—R.R.Newton, "Odd Harmonics of the Earth's Gravitational Field" 
(to appear) 
111 
