Meam motion mystery

Allen Thomson (thomsona@netcom.com)
Wed, 30 Aug 1995 16:45:15 -0700

   Does anyone know why the mean motion given in the "NORAD" two line 
element sets should be different from the rate of change of the 
revolution number calculated by taking the differences of revolution 
number and epochs and dividing them: (R(n) - R(n-1))/(E(n)-E(n-1))?  
Looking at a collection of over 800 element sets for Cosmos 1833, Norad 
17589, I find a fairly constant (but not entirely so) difference of 
0.00417 revolutions per day. For two successive element sets, for 
example, the mean motion as given in the later one might be 14.1234, 
whereas the calculated number would be 14.1192. 

   Put another way, if you integrate the mean motion from time of launch 
to come up with a total number of revolutions, the result diverges 
linearly from the number in the TLEs, and now amounts to some 13 
revolutions difference for Cosmos 1833. 

   I assume this has to do with measuring revolutions in two different 
coordinate systems -- inertial vs earth-fixed, for example -- but it's 
not obvious to me which systems are involved, or why NORAD should use 
different ones for different parts of the element sets (if that's what 
is going on).  One thing which may speak against this simple 
interpretation is that the difference between the given and calculated 
mean motion values isn't quite constant, but wanders around the average value 
in a somewhat complex but apparently real way with a characteristic time 
of many months and an amplitude of perhaps 0.00003 revolutions per day.

   Pointers to an explanation of this minor mystery will be gratefully 
accepted.