Re: [find_orb] Orbit determination exercise

Dave Herald Jan 29, 2011

I fully agree with Andy re the zero residuals.

An upsides of the ready availability of software to do complex tasks such as orbit determination is that it enables anyone who is interested to do the calculations. However the downside is that typically the user has little appreciation of the mathematical and physical issues involved in the solution. Possibly the most significant issue (but it is a while since I wrote code to do orbit solutions) is that the reliability of the solution depends upon the extent to which the motion deviates from great circle motion, combined with an understanding of the role of numerical precision in the calculations. In this regard (and taking a _very_ simple approach):

a. the time intervals of the observations are 0.04167 and 0.04143 days - that is, a numerical precision of 4 digits.
b. The RA change is -49.71s and -49.51s. A numerical precision of 4 digits. The departure from uniform motion of 0.09s - a numerical precision of 1 digit
c. The Dec change is 158.3" and 155.3". A numerical precision of 4 digits. The departure from uniform motion of 2.4" - a numerical precision of 2 digits.

What this tells me is that the numerical precision of the sample data limits the accuracy of any solution to about 2 digits at best. Added to this is the typical interdependency of the solution for longitudes of the ascending node and of perihelion - such that an 'error' in one is balanced by an equivalent offset in the other - and you might be able to see that you cannot expect to derive an orbit that exactly matches the elements used to generate the positions used. And it is for reasons such as this (combined with measurement uncertainties) that leads to a process of continuing orbital refinement as more observations become available.

Dave Herald
Murrumbateman, Australia


----- Original Message -----
From: Andy Puckett
To: find_orb@yahoogroups.com
Cc: find_orb@yahoogroups.com
Sent: Sunday, January 30, 2011 4:54 AM
Subject: Re: [find_orb] Orbit determination exercise


I believe that 3 points is the minimum to determine an orbit. (3 observations * 2 coordinates each = 6 = number of orbital parameters.). So Find_Orb plots an orbit exactly through all 3 points, and RMS would be 0 because there is no difference between the original points and the resulting curve.

Andy

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Andy Puckett, PhD puck@...
Director - Planetarium & Visualization Theater
Asst Professor of Astronomy 907-786-1838
Univ. of Alaska Anchorage CPSB 202P
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On Jan 29, 2011, at 12:45 AM, "Alessandro" <alessandro_odasso@...> wrote:

> Here is a newby question for people who are interested in orbit determination.
>
> Let's imagine that an object MYOBJ has been measured only three times, according to this hypothetical MPCReport:
>
> MYOBJ C2011 01 11.43745 11 05 20.01 +38 02 33.7 17.00R 857
> MYOBJ C2011 01 11.47912 11 04 30.30 +38 05 12.4 16.58R 857
> MYOBJ C2011 01 11.52055 11 03 40.79 +38 07 47.7 17.93R 857
>
> Based on these three observations, what would you say about the orbit of such an object ?
>
> I tried to use the program FIND_ORB on this example but I am not yet able to use it understanding what it finds out.
> For example: when I press the autosolve button, the program determines an orbit with RMS error = 0 ?
>
> Here is what I find:
> MYOBJ
> Perihelion 2010 Nov 18.173749 TT = 4:10:12 (JD 2455518.673749)
> Epoch 2011 Jan 12.0 TT = JDT 2455573.5 Earth MOID: 0.2550
> M 72.84720 (2000.0) P Q
> n 1.32869204 Peri. 9.25958 0.59463100 0.39030866
> a 0.81944503 Node 301.60625 -0.78034732 0.06968394
> e 0.8931816 Incl. 55.62134 -0.19357690 0.91804318
> P 0.74/270.94d H 18.7 G 0.15 q 0.08753180 Q 1.55135825
> From 3 observations 2011 Jan. 11 (2.0 hr); RMS error 0.000 arcseconds
>
> Thanks,
> Alessandro
>
>


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