RE: how useful are these old elsets?

Ted Molczan (molczan@fox.nstn.ca)
Tue, 14 Jan 1997 10:51:56 -0500

Ryan Rudnicki asked the following, regarding the
many "old" elsets that appear in the *.n2l file:

>My question:  Why are the elements below in the .tle file?  

These objects are in the file because certain
observers are interested in them.

Referring to the list appended to his message,
Ryan asked:

>Are the objects 
>whose elset age is over 1000 days still in orbit?  

84122A is not in orbit, and should not be in the
list. It is there by mistake, so I will remove it. 
All of the others are in orbit.

>Are these orbits stable 
>enough that they don't need refreshing too often?  

Some yes, some no. USA 86 and 116 make orbit-
maintenance manoeuvres 2 or 3 times annually.
They experience considerable drag, which 
creates prediction uncertainty as the elements
age. In the N. hemisphere, we lose these objects
for 6 months centred on the winter solstice, so
by the spring, an effort has to made to recover
them. This is a test of observing and analytical
know-how, but not all that difficult.

>Is it a case of too many 
>satellites and too few refreshers?  

Correct!

Finally, here is some advice to help you cope with
old element sets, taken from a message I posted
to SeeSat-L on 23 Sep 96:

In the olden days, which for the purpose of this discussion ended 
about 1990, most orbital elements were available only by snail mail, 
and very few people had access to more than about 20 object's elsets.
It was common to have to use 2+ week old elsets, even for mundane 
stuff like Mir predictions, which meant prediction uncertainties of 
at least several minutes. Today, elements for all non-secret objects 
are available via the Internet or dial-up lines, so millions of people 
have access to almost all elsets in near-real-time. But for the 
infrequently updated secret spysat elements, and non-secret objects 
near decay, observers need to be able to cope with the prediction 
uncertainty that arises from the uncertainty in the rate of orbital 
decay.

About 10 years ago, I derived the following simple formula which helps 
me to cope with old element sets of decaying objects:

UNC = 864 * %UNC * ndot/2 * dt^2
      --------------------------
         n0 + 2 * ndot/2 * dt

where:

UNC    = the uncertainty of the time of the satellite's passage, seconds

%UNC   = the uncertainty in the rate of decay, expressed as a percentage

dt     = the time elapsed since the epoch of the elset, days

ndot/2 = one half the rate of change of the mean motion with respect
         to time, as it appears in the NORAD elset, rev/d^2

n0     = mean motion at the epoch, as it appears in the NORAD elset, rev/d

The constant 864 is simply the number of seconds in day, divided by
100. It enables UNC to be expressed in seconds of time, and converts 
%UNC into a fraction.

The original message is available from the SeeSat-L home page. It 
includes a worked example, and considerable commentary. It also includes
a slight error in the formula, which I have corrected in the above
excerpt.

Ideally, I believe that ephemeris generators should include some means
of estimating prediction uncertainty, like the one above, and perhaps 
indicate whether or not an object manoeuvres, instead of simply discarding 
old elements.

Clear skies!
Ted