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(meteorobs) References & calcs. of lunar meteor impacts



     Yesterday, Ray Sterner added a view of the Moon showing the impact
locations to our Web site on lunar impacts at http://iota.jhuapldot edu
Next week, we will be able to improve some of the impact locations and
will also measure the magnitudes relative to stars that were also
imaged that night - so far, the magnitudes are just eyeball estimates.
The PC-23C cameras that we all used is red-sensitive, so the magnitudes
we obtain may be closer to R than to V.  We will also clean up the Web 
site, providing a menu to access different topics.

     There continues to be some disagreement about the size of the
impacting objects and the craters that they would leave.  Two 
messages below give some details on the subject.  It appears that
the fraction of Leonid kinetic energy that is converted to 
luminous energy during a lunar impact is quite low, implying rather 
large (kilogram-range) objects that would leave craters some tens
of meters in diameter.  But not everyone agrees with that.

David Dunham, IOTA, 1999 Dec. 4
============================================================================

Date: Fri, 3 Dec 1999 14:52:44 -0700
To: Joan and David Dunham <dunham@erols.com>
From: Jay Melosh <jmelosh@LPL.Arizonadot edu>
Subject: Re: News on the lunar Leonids

Dear Joan and David:

I have been following your reports of flashes observed on the moon with
great interest.  I have been curious about the amount of visible light
emitted by an impact for some years now (as well as the infrared signal,
which is much stronger at 2 to 3 microns).  I published an LPSC abstract on
this topic for LPSC XXIV, pp. 975-976 (1993).  Since that time my Russian
collaborators did a much more detailed job of the calculation using the
resources of the FSU nuclear fireball experts.  This work is published in
Solar System Research, vol. 32, pp. 99-114 as "Light flashes caused by
meteoroid impacts on the lunar surface" by I. V. Nemtchinov and a large
number of collaborators.  After all the song and dance they conclude (as we
did in our back-of-the-envelope calculation in LPSC!) that the luminous
efficiency is quite low, not more than .0003 to .00003 of the kinetic
energy of the impactor.  However, since the Leonids are so fast, perhaps
this would be enough to see through a telescope, as you report.

Sincerely,  Jay Melosh
###########################################################################
Jay Melosh                              Tel:   (520) 621-2806
Professor of Planetary Science          Fax:   (520) 621-4933
Lunar and Planetary Lab                 email: jmelosh@lpl.arizonadot edu
University of Arizona
Tucson AZ 85721-0092

============================================================================

Return-Path: <mazur@geo.ucalgarydot ca>
Date: Sat, 04 Dec 1999 08:20:10 -0800
From: Mike Mazur <mazur@geo.ucalgarydot ca>
X-Accept-Language: en
To: Joan and David Dunham <dunham@erols.com>, mazur@geo.ucalgarydot ca
Subject: Re: 2 messages about lunar meteor & crater sizes

David,

With regards to the first note, the easiest way to calculate the crater
diameter
is to use Lampson's scaling law for explosive craters as given in Melosh
(1989)
eqn. 7.2.1. Martin's calculations use a yield scaling relation that is not
necessary for this sort of hand-wavy argument. Also, he must have made an
error
somewhere in his math. Using eq. 7.8.1 which is for craters up to 10m on
the moon,

D_at=0.015*rho_p^0.16666*rho_t^-0.5*W^0.37*(sin(i))^0.66666

where rho_p is the projectile density (~800kg/m^3 is what Martin uses...
600kg/m^3
would be closer to Shoemaker's and others' results), rho_t is the target
density
(3000 kg/m^3), W is the excavation energy (probably about 90% of the total
actually goes into the excavation), and i is the angle of impact (90deg being
vertical.

A 5g projectile moving at 71km/s has a KE of about 1.26e7 J. If 90% of this
goes
into excavation then,

D_at~0.35m

Martin's table should thus be,

Mass (g)    Diameter of crater (m)

5                       0.35
10                      0.46
50                      0.83
100                     1.07

Intuitively, this seems more correct as well. In my original note to you I
think
that I gave you a value of 1/2 kg for the projectile. This I suspect is way
too
large and I think that misread my calculator. Let's work through what I did.

If we are using the standard stellar magnitude system then, m=-2.5log(F*/F_0),
where F* is the flux of the star (or object in this case) being measured,
and F_0
is the flux of a 0 mag. star such as Vega. Recall that F=L/(4*pi*r^2) where
L is
the luminosity of the object and r is the distance. Inserting the luminosity
equation (because we ultimately require L) into the eq. for m gives,

m=-2.5log[(L_obj(r_vega*r_vega)/(L_vega*r_obj*r_obj)]
m=-2.5log(L_obj)-2.5log[(r_vega*r_vega)/(L_vega*r_obj*r_obj)]

r_vega=8.1pc=2.498e17 m, L_vega=2.7295e28 J/s, r_obj= dist to impact site ~
d_moon
- R_moon - R_earth = 3.7586e8m

Now we can solve for L_obj,

log(L_obj)=[(m+2.5(log[((2.498e17m)^2)/((2.7295e28J/s)*(3.7586e8m)^2)]))/-2.5]

L_obj=10^[(m-26.98)/-2.5] J/s

for an m=3 impact,

L~3.9e9 J/s

So if this luminosity was maintained over a period of 1/30th of a second
(probably
much smaller in actuality as I recall someone working out millisecond
durations
based on expected plume size) an upper limit for the energy that went into
producing light is about 1.3e8 J. If 10% of the total energy goes into light
production (probably reasonable based on terrestrial fireball data) then
the total
energy of an m=3 event is about 1.3e9 J. At 71 km/s the mass would
therefore be
about 0.5 kg. So it looks like my mass was what I expected and the diameter
must
have been in error (I think I said about 0.4 m using Snowball test data and
Lamson's eq.). Using Gault's eq. as given at the start of this note, the
crater
diameter for a 0.5 kg leonid is about 1.9 m.

visual mag.    tot. energy (J)   mass (g)   crater size (m)
    3                    1.3e9       500            1.9
    4                    5.2e8       205            1.3
    5                    2.1e8        82            0.96
    7                    3.3e7        13            0.50

At least that's what I get. It all seems reasonable but I would rather use 600
kg/m^3 for rho_p. Originally when I performed this calculation I used Lamson's
equation which simply relates crater diameter to energy using known data (I
used
Snowball) as a comparison. I neglected to include a factor for lunar gravity,
however. Anyway, these are likely upper limits for reasons mentioned above.
Have
fun,

Mike Mazur
p.s. I'm hoping that I didn't miss anything in the above equations when I
typed
them out. It is possible.

Joan and David Dunham wrote:

> -----Original Message-----
> From:   beechm@ureginadot ca [SMTP:beechm@ureginadot ca]
> Sent:   Wednesday, December 01, 1999 1:33 PM
> To:     Dunham, David
> Subject:        Re: Lunar impacts - press release, more flashes, etc.
>
> Hi David,
>
> I have a few comments about the size of crater that might
> be produced by Leonid impacts. They are revised upwards of
> my earlier value of a few meters. Using the experimental
> formula derived by  Gault et al (J. Geophys. Res, 80, 2444,
> 1975 - see also Melosh's book "Impact Cratering" page 120)
> for impacts into a regolith material the following crater
> diameters are predicted for Leonids.
>
> Assumptions:
>
> V = 71 km/s (not really an assumption)
> density of meteoroids = 1000 kg/m^3 - most people use 800 kg/m^3
> but the difference will not be significant as the density
> eneters to the 1/6th power
> density of regolith material = 3000 kg/m^3
>
> Mass(gram)        Dia (meters)
> 5                 18
> 10                22
> 50                35
> 100               42
>
> So, at the upper mass end (more comments later) the crater is
> quite sizeable, but still not visible from Earth.
>
> IF Roger Venable's calculation for the mass is correct (and
> I have to admit I think it is on the very high side), then a
> large ~ 100 m diameter crater will result. It is just possible
> 20 kg and possibly larger mass metoroids exist in the Leonid
> stream (I wrote about this is in a paper in the Astronomical
> Journal 116, 499, 1998), but the observed mass index of visual
> meteors would not support sampling a single such meteor even
> at the very high ZHR's observed. The visual meteor results
> (that is with a mass index of about 2.0) suggest that one 1kg
> meteoroid might strike an area equivalent to the area of
> the Moon's half disk. Hence I am very sceptical about
> associating the impacts with meteoroids any more massive than
> several 100g (but, when it boils down to it, who really knows?)
>
> Ok, I hope this helps.
>
> With best wishes,
>
> Martin
>
> Martin Beech, Campion College, The University of Regina.


Joan and David Dunham
7006 Megan Lane
Greenbelt, MD 20770
(301) 474-4722
dunham@erols.com
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