[meteorite-list] Typical large meteoroid entry angle

From: Sterling K. Webb <sterling_k_webb_at_meteoritecentral.com>
Date: Thu, 20 Dec 2007 21:39:01 -0600
Message-ID: <00e101c84383$076eae50$b64fe146_at_ATARIENGINE>

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." <ROBERT.D.MATSON at saic.com>
To: "Sterling K. Webb" <sterling_k_webb at sbcglobal.net>; "Jason Utas"
<meteoritekid at gmail.com>; "Meteorite-list"
<meteorite-list at 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
Received on Thu 20 Dec 2007 10:39:01 PM PST