orbital period calculations: which is "better"?

From: wkitty42_at_gmail.com via Seesat-l <wkitty42_at_gmail.com>
Date: Wed, 09 Apr 2014 12:22:09 -0400
yes, "better" is subjective but i'm curious about other's thoughts and methods...

using only the data contained in a TLE, is it "better" to calculate an object's 
orbital period by

1. simply dividing minutes per day (1440.0) by the object's TLE mean motion

OR

2. work kepler's 3rd law by calculating the semi-major axis of the orbit via the 
mean motion in the TLE

for kepler's 3rd law, i'm currently using the WGS'72 value of 398600.8 for 
earth's gravitational constant... this is also the value that TS' routines 
use... would it be better to use a/the newer WGS values? i've not found an 
update for the routines that uses anything other than WGS'72 values...

so, back to the orbital period calculation... there is a slight difference in 
the results but they generally start in the 4th or 5th decimal place of the 
resulting minutes... mostly the 5th...

eg:

COSPAR        Perigee KM x        Apogee KM x      Inclination  SemiMajorAxis KM 
          MMPeriod         SMAPeriod
--------------------------------------------------------------------------------------------------------------------
72023E      206.56106474 x    3190.47187333 x      52.09280000     8076.65146903 
      120.39445477      120.39447252
98067A      413.34288340 x     416.33722680 x      51.64930000     6792.97505510 
       92.86445208       92.86446577


granted, we're talking about only a few hundred-thousandths of a second but over 
time, they do add up and can lead to predictions being off by X amount of 
time... especially with older TLEs...

in all cases, my SMAPeriods (SemiMajorAxis) are longer than my MMperiods 
(MeanMotion)...

so, i'm curious which method(s) others use when they calculate the orbital 
period of an object and why they chose the method they use...

FWIW: originally i decided to use both methods as a way of verifying and 
validating that my math was right and that i was getting the proper answers... 
when comparing with other's results, mine are pretty much spot on with some 
slight variance on some values but "close enough for gov't work" as they say ;)
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Received on Wed Apr 09 2014 - 11:23:17 UTC

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