## February 27th, 2011

A Quandary

Today I am considering an important problem concerning the algorithm I use for determining the height of the flares of a Leonid. My original, and deeply flawed method was to apply simple plane geometry based on the assumption that every Leonid first begins to emit light at a height of about 119 km. This means that the first flare will be at 119 km; combining this with the angular altitude, it is trivial to determine the distance to the Leonid. But this approach suffered from a nasty flaw: the earth isn’t flat. I had always thought that, for meteor work, the curvature of the earth isn’t important, and it isn’t when you’re looking at most meteors that are fairly close. But many of the Leonids in this dataset are very low and therefore quite far away; the curvature of the earth is indeed a significant factor. So I began using a better algorithm taking that into account; it is explained here.

But I was bothered by another problem: how do I know that the first recorded flare actually represents the first instant that the Leonid entered the atmosphere and began glowing? Many of these Leonids are quite distant; the likelihood of seeing their true first flare is reduced. The first flares recorded in my data might well represent the Leonid at some deeper point in the atmosphere. So I tried a completely different algorithm. We know the linear velocity of the Leonids quite accurately: it is 71 km/sec. If we contrast the linear velocity of the Leonid with its angular velocity, we can calculate its distance. It doesn’t matter if we catch the entire Leonid or just part of it; so long as we get enough data to give a reliable indicator of its angular velocity, we can reliably calculate its range. Here’s the actual code I use: