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On 01/04/2008 01:42 PM, Ludwik Kowalski wrote:
But why should the 149.1 m/s and not 357.36 (satellite) be perturbed?
Several answers:
1) You should definitely explore perturbing each and every
relevant number. I picked on 149.1 as a place to start,
because it "looked" like it had been more brutally rounded
off.
Since the uncertainty in these numbers was not explicitly
stated, I had to guess.
(Don't get me started about "significant figures" and
their meaning or lack thereof.)
http://www.av8n.com/physics/uncertainty.htm
2a) If you typed in the initial condition as "149.1", and
used that as the initial condition in the program, then
you have *already* perturbed things by rounding off.
Do not think for a moment that roundoff errors on the
order of parts in 10^4 are negligible. It is characteristic
of unstable systems that the outcome is exponentially
sensitive to small changes in the parameters.
2b) If on the other hand you calculated the initial
condition algebraically *within* IP then the roundoff
error is probably much less, on the order of parts in
10^15 rather than parts in 10^4.
In this scenario the idea is that the numbers used
by the program are good to parts in 10^15 and only
the email (*not* the program) used numbers rounded
off to parts in 10^4.