Jan (and Bill),
There is a good explanation in A. D. Dubyago, THE DETERMINATION OF ORBITS
(Macmillan, 1961): Chapter 7, "Determination of an Orbit by Two
Observations." First he covers a circular orbit, and then a Vaisala orbit,
with numerical examples for each. (There are a few typos in some of his
numbers, which I discovered in programming these methods, so if anyone is
interested I can point them out.)
Roger
-----Original Message-----
From:
find_orb@yahoogroups.com [mailto:
find_orb@yahoogroups.com] On Behalf
Of Bill J Gray
Sent: Wednesday, March 02, 2011 1:52 PM
To: jan vales;
find_orb@yahoogroups.com
Subject: [find_orb] Re: method of Vaisala
Hi Jan,
For some reason, your message didn't make it onto the list. I only got
it because it was cc'd to me... I'm posting it on-list in hopes that
somebody can provide better references for the method of Vaisala than I can:
jan vales wrote:
> Dear Find Orb group!
>
> I am Jan Vales and I am studying physics at Faculty of mathematic and
> physics in Ljubljana ( Slovenia ). I am writing the seminar on how
> determine the orbit from the observations only, that is on Ra and Dec.
> I found that the MPC uses methods like Gauss and modified Vaisala method.
> In some books I found nice description of Gauss method, but I couldn't
> find anything about Vaisala method. I tried to find anything about
> Vaisala method and how to derive it, over the web and in the books and
> I couldn't find anything. At your web page
> http://www.projectpluto.com/vaisala.htm you are describing that
> method, and I was wondering if you have anything more about that
> method and its derivation.
> I thank you in advance.
>
> Jan Vales
I haven't actually found much about the Vaisala method either. All the
comments on my Web page were derived from basic principles, based solely on
the knowledge that a Vaisala orbit assumes the object is at perihelion or
aphelion, and at a guesstimated distance from the sun.
Given those two constraints, I came up with the math at 'vaisala.htm',
plus a couple of minor improvements that allow it to use more than just two
observations.
Maybe somebody else on this list has seen a good exposition of Vaisala
orbits?
There are two other methods that you might want to consider
investigating, depending on how much depth you want to go into in this
seminar: the method of Herget and the "downhill simplex" (DS) method. You
probably saw my page about the method of Herget at
http://www.projectpluto.com/herget.htm .
I have never seen anything written about the use of the downhill simplex
method for orbit determination. It's widely used in finding the minimum
value of N-dimensional problems; in this case, you'd be looking for a
minimum in the sum of the squares of the residuals. Its advantages are that
it's very easy to understand what it's doing, it's not hard to implement,
and you can set it up so that the results are unlikely to diverge and cause
some sort of wacky orbit. More about DS at
http://www.projectpluto.com/herget.htm#simplex
Hope this helps.
-- Bill
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