Preliminary Orbit Determination - Gauss Method

[Echulion]

Hey @jasquier,

I saw earlier that you’ve started translating the code, its wonderful news! I will try to do my best and address your questions now.

@jasquier

Why did you chose to do that and not follow Vallado suggestion to try to use Gibbs or Lambert methods to find v2 ?

Actually, I implemented both Lambert’s and Gibbs methods at the end of the code as Vallado suggests. The v2 result we get after applying Gibbs method perfectly matches with what Vallado provided in his example.

@jasquier

Inversely, what not use Curtis algorithm the all time ?

I cannot rightly remember now but I think that the data Vallado provided in his example was really on point to follow (in terms of verification at every step). So I started with his work. At some point in his example, he mentioned that the Gauss method formally ends once we found slant ranges. And since I’ve also found his v2 result applying Gibbs method, I wanted to see the v2 results of Algorithm 5.5 provided by Curtis. Long story short, I did not have any particular reason to switch between books, but you have every right to question this odd behavior. I would do the same tbh It would also be interesting to see the results following Algorithm 5.5. from start to end.

@jasquier

Second i see that you truncated the Taylor serie function of f and g at the first order. Is it approximated like this in Vallado and Curtis but because it seems easier by hand.

Yes, well Curtis ended up with the first order truncation of the series expressions, as he pointed out that if consecutive time intervals of observations are small enough, just first two terms could be retained. He also states that “we want to exclude all terms in f and g beyond the first two so that only the unknown r2 appears in equations”. So this first order truncation greatly reduces the computational work, and you can check it in the section “5.10 Gauss method of preliminary orbit determination” of Curtis.

@jasquier

We could expand the all Taylor serie, or as Vallado suggests “that f and g functions should be used instead of the series coefficients”. What do you think of this ?

Lastly, I couldn’t understand what you mean by this though, I am sorry.

Maybe you could also end the code translation once you found the slant ranges, as Vallado pointed out in his example. I think it makes sense that users ending up with slant ranges (or taking one more step, position vectors) using IodGauss class, since continuing further with velocity requires other IOD methods in play such as Gibbs or Lamberts methods.

Finally, it is wonderful to see that you are also improving the code by including 3 different observation positions! I thank you sincerely for your contribution

Regards,
Baris