Hi, Rob, Jason, List, I meant angles to be referenced to the horizon. Zenith = 90 degrees; Horizon = 0 degrees.
I also mean a local polar coordinate system with 0, 0 at ground level, crater center. Probably a flat Earth too, while we're at it. "If it was good enough for..." Rob, I'm assuming here that the degeneracy you're referring to is "areal" or should that be "area-al"? You divvy the sky up into patches of equal area rather than "square degrees" (which start out large and almost-square trapedezoids at the horizon and end up as tiny elongated triangles at the pole), and assign an equal probability to each equal area. Hmm... Just discovered there's a word for that: "symptetic." Never did find "area-al" or "areal;" too confusing to use, I imagine. For those not annoyed but intrigued by symptetic maps, go to this URL and look at Jupiter: http://www.physics.drexel.edu/~goldberg/projections/ Or see all the different ways of trying to preserve areas (or distance) here (applet requires Java): http://www.btinternet.com/~se16/js/tissot.htm Rob wrote: > this is a common misconception... Every physicist I ever knew does it. I pulled out my favorite textbook, 783 pages, 1995, on the solar system by a man that I took courses from... well, never mind how long ago. Right there, 45 degrees is described as the "average" incidence of meteoroids and later it's called "typical," more of an intuition than an assertion, but he always uses 45 degrees; everybody does. I even said that to Jason in my Post -- "That's what everybody does." And that is a true statement; it IS what physicists do, just like we generalize everything to the spherical case. But it's obviously dead wrong, once you think about it. The problem is... you never think about it! I even went and did a proof to be certain. This has been my religious moment for the day. Sterling K. Webb ------------------------------------------------------- ----- Original Message ----- From: "Matson, Robert D." <[EMAIL PROTECTED]> To: "Sterling K. Webb" <[EMAIL PROTECTED]>; "Jason Utas" <[EMAIL PROTECTED]>; "Meteorite-list" <meteorite-list@meteoritecentral.com> Sent: Thursday, December 20, 2007 6:08 PM Subject: Typical large meteoroid entry angle Hi Sterling and Jason, (I'd say "List", too, but I'm pretty confident that this won't get through to the list from my work e-mail.) Haven't really been following your discussion in detail, but the entry angle issue deserves a comment or clarification: Sterling writes: > As for the angle of an impact, that is a datum obscured by the event. > There is no way to derive the angle of impact from the resulting crater > in any except the smallest and weakest events. Any angle of incidence > over 15 degrees produces a round, level crater. At 15 degrees or less, > elliptical craters are produced. That has been my understanding as well; that the entry angle has to be quite shallow in order to produce a non-circularly-symmetric crater. Jason wrote: > the likelihood of an impact occurring at an angle of ~30 degrees or > less is simply unlikely. Possible, but unlikely - as in odds are that > it would not occur this way. I'm not an idiot. I e-mailed him privately last night inquiring as to whether this 30 degrees you guys were talking about was measured from horizontal or vertical -- makes a huge difference to the correct answer, and I was hoping that he could save me some time digging through the archives to find out which was meant. However, based on your comments below I now assume that the 30 degrees is measured from horizontal, in which case Jason is mistaken. Sterling writes: > ANY angle of incidence with the surface of the Earth is totally > random and ANY angle of incidence is as equally likely as ANY other. > Basic knowledge. Look it up. Here, Sterling, you're also mistaken. Not all angles of incidence are equally likely. All *azimuth* angles are equally likely, but spherical coordinate system degeneracy means that there are more ways to come in shallower than 45 degrees than steeper. > If you average all the directions together, you get 45 degrees, > just because you have to pick some direction! No, you don't, though this is a common misconception. The correct answer is exactly 30 degrees. Half the possible entry angles are shallower than 30 degrees, half are steeper. So you actually had the right answer when you typed "30" instead of "45". ;-) --Rob ______________________________________________ http://www.meteoritecentral.com Meteorite-list mailing list Meteorite-list@meteoritecentral.com http://six.pairlist.net/mailman/listinfo/meteorite-list
