RE: How to determine N-dot from two values of N?

From: Ted Molczan (ssl3molcz@rogers.com)
Date: Mon Nov 08 2010 - 07:15:20 UTC

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```Bram Dorreman wrote:

> As with Skymed 4 rocket the N-dot value from the TLE I used to find
> it, had a small negative value. Just as the day before when I was too
> late to have a search action. I was thinking: If one has two values of
> N it should be possible to calculate the N-dot value from them. My
> only question is: What is a suitable algorithm for this.

You can calculate the mean ndot/2 between a pair of elsets from their values of epoch (t) and mean
motion (n):

ndot/2 = (n2 - n1) / (t2 - t1) / 2

Some judgement is required to select suitable elsets, especially soon after launch, when they may
not yet have settled down to realistic values. It is best to avoid using erratic-looking elsets, and
to consider spans of at least one day.

Looking at all of the data of 10060B / 37217, up to and including the epoch 10312.07014429 elset, it
appears that a realistic ndot/2 is about 0.003 rev/d^2. Finding ndot/2 will be sufficient for the
older SGP model, but nearly everyone has adopted the current model, SGP4, which requires the B*
decay term. For the elset and mean ndot/2 in question, I estimate a corresponding B* value of
33702-3, expressed in TLE format.

There is a simple equation relating B* and ndot/2, which can be added to SGP4 with a bit of surgery:

http://www.satobs.org/columbia/SGP4decayterms.pdf

Ted Molczan

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