Computing Atmospheric Trajectory of Meteor

[solarblast]

I'm trying to understand the mathematical methods of computing the atmospheric trajectory of a meteor for two or more stations. Ceplecha wrote a rather complete description of this in around 1987. See <http://adsabs.harvard.edu/abs/1987BAICz..38..222C>. Something of a simpler version meant for students can be found with Google using "ceplecha meteors" and look for "exercises in astronomy" about 8 to 10 entries down the page. He gives details from the reduction process, finding ra/dec on a photographic plate for a point, x-y, all the way to orbital calculations. He works out the material from 2 stations to N stations. I pretty well understand the reduction process. It's detailed in books such as Astronomy for Personal Computers, complete with computer code. Use of least squares is regularly used in these methods, and I'm quite familiar with them.

What I am not comprehending fully is what happens immediately after the reduction process, is the trajectory computation. That's his section 5 of the 1987 paper. There he starts talking about the intersection of planes of the trajectory from two stations. At this point, I'm not sure what the planes are and how they intersect with the meteor (fireball). It's not even clear to me what trajectory he's computing. It doesn't seem to be a fit or an equation, but there may be a twist that I'm not getting.

The paper is described in the link above, but I'm not sure if it's available for free there. I have the paper (pdf), and it shows the source as the NASA Astrophysics Data System.

The explanation may be a bit hard to describe by text in this forum, but perhaps their are web sites and references that might help. I've really collected a lot of stuff of the web. If paper and pencil drawings are needed, I might be able to suggest temporary web posts for images files of such materials. In any case, we can begin by continuing with text message exchanges and see how it goes.

Ah, I see I can attach a pdf. I'll do that. If you do start into the article, you can assume the fisheye lens is linear. Know to that I'm working wide a video camera. He used emulsion based photography.

 

[AndyW]

Hello, thank you for reaching out and providing the link to the paper and your understanding of the reduction process. It seems like you have a good grasp on the initial steps, but are struggling with the trajectory computation portion.

To better understand this, let's break it down into steps. The first step is to determine the position of the meteor in the sky from each station. This is done by using the x-y coordinates on the photographic plate, as you mentioned. These coordinates correspond to the meteor's position on the celestial sphere (the imaginary sphere surrounding the Earth on which the stars and planets appear to be located).

Next, we need to determine the trajectory of the meteor. This is essentially the path it takes through the sky as it travels through the Earth's atmosphere. To do this, we need to find the intersection of the planes formed by the meteor's position at each station. These planes can be thought of as slices of the celestial sphere, with each station's position marking the center of the slice. The intersection of these planes gives us the trajectory of the meteor.

Now, the intersection of these planes may not be a perfect fit or equation, as you mentioned. This is because the meteor's path is not always a smooth, straight line. It may have curves or bends due to atmospheric conditions or other factors. However, by using the positions from multiple stations, we can get a more accurate representation of the trajectory.

I hope this helps clarify the concept of trajectory computation for multiple stations. I would also recommend looking into resources on celestial mechanics or orbital calculations, as those fields deal with similar concepts and may provide additional insights. Best of luck with your research!