Orbital Elements-Identification of method

[solarblast]

Orbital Elements--Identification of method

I'm looking at a book that has a method for calculating the six orbital elements. I'm attaching the relevant pages. My knowledge about orbits is limited to knowing the meaning of the six elements. What I'd like to know is where did these equations come from, and is the author right when he says, "e from (87) and (88)" at the bottom of page 39. I suspect he meant 86 and 87.

I've heard of Gauss' and LaPlace's methods for determining orbits. Is the approach given one of those? He notes Herget as a source at the top of page 40. I have access to it, but is not a simple matter to browse through to find the approach on page 40.

 

[solarblast]

Well, for all practical purposes, it looked like I attached 4 jpg files. Guess not, so I'll do it now.

Ah, they were tif files. Invalid. Not quite. I had posted these before with a similar question, and apparently cannot post them again. It's a different question this time.

See <https://www.physicsforums.com/showthread.php?t=556478> Pages 37-40.

 

[Drakkith]

I think it's saying that you need to find p before you can find e, so you would have to do 88 first then do 87. Not sure really.

 

[solarblast]

As it turns out, after really following the text onto page 40, the equations there at the top of the page transform x,y,z in equatorial coordinates to ecliptic coordinates. That paves the way to get omega, capital omega, and the inclination. These are all related to the ecliptic, while the six on the previous page are orbital. If the author had mentioned ecliptic that would have made it clearer. There actually seven orbital elements. q, perihelion distance is mentioned above eq (85), and in (92). We are now getting proper results.

It appears the math here is from the La Place method.

 

[pmacias]

Thank you for providing this information and sharing your interest in orbital elements. The method for calculating the six orbital elements can vary depending on the specific problem and the available data. However, there are a few commonly used methods, including Gauss' and LaPlace's methods, as you mentioned.

Based on the information you provided, it seems that the author is using a combination of these methods to calculate the orbital elements. The equations referenced at the bottom of page 39 may be a combination of equations from both methods. It would be helpful to have more context and information about the equations to determine their exact origin.

As for the source mentioned at the top of page 40, Herget's book "Introduction to Celestial Mechanics" is a well-known and respected resource for orbital mechanics. It is likely that the author is using Herget's approach as a reference or as a basis for their own method.

In general, the process of determining orbital elements involves analyzing observational data and applying mathematical equations and principles to calculate the orbital parameters. It is a complex and specialized field of study, but it is crucial for understanding and predicting the motion of celestial bodies.

If you are interested in learning more about the specific method used in this book, I would recommend consulting Herget's book or seeking out other resources on orbital mechanics. It may also be helpful to consult with experts in the field for further clarification and understanding.