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(meteorobs) Re: References & calcs. of lunar meteor impacts

Just a short note to say that Mike Mazur is absolutely
right about my maths! For some reason I thought the equation taken from
Jay Melosh's text was in cgs units - apologies for a stupid
mistake.

Martin Beech

On Sat, 4 Dec 1999, Joan and David Dunham wrote:

>      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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