Inclusion of the third zonal harmonic in an accurate reference orbit of an artificial satellite.

Abstract

The previous pape r gave the ge ne ra l theory and phys ica l princ iples involved in so modifying the author's s phe roidal potential for an ob late plane t as to pe rmit exact inc lus io n of the e ffects of the third zonal harmonic of the pl ane t's gravit ati ona l fi e ld. The present pape r ca rri es out the computationa l details necessary to de rive the res ulting orbit , whi c h now corres ponds t.o a pote nti a l fitte d exactl y through the third zona l ha rmonic and to a bout two·third s of th e fourth . The accuracy of the orbit it self, as a so lution fo r the give n po te nt.i a l, depends o n the acc uracy of so lutio n of a ce rtain c ubi c e qu a tion. T he pa pe r wo rks out thi s so lution t hrough te rm s of the thi rd orde r in .f" the coe ffi c ient of the seco nd zo na l ha rmo nic, but it s acc urac y, a nd thus tha t. of t.h e sec ula r te rm s, may be inc reased a t. will. Pe ri odi c te rms a re ca rried t.hrough the seco nd o rde r, but the ir ac· c uracy may a lso be in c reased. An o bvious ad va nt age of accounti ng for I . in thi s way is the absence of s ma ll deno min a tors in e o r sin J tha t occur in a pe rtu r ba tio n theory. Anuthe r is the res ult.in g inc rease in acc uracy, through te rms in i i, of t. he long·pe ri od ic third ha rmo nic te rm s.