## [meteorite-list] Spherical Shapes of Planets, Asteroids.- Mail actions: [ respond to this message ] [ mail a new topic ]
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From: almitt <
almitt_at_meteoritecentral.com>
Date: Thu Apr 22 09:48:14 2004 Message-ID: <3BDB1321.8B2F9226_at_kconline.com> Dear list, Here is a discussion on shapes of the minor planets and so forth. Thought it might be relevant to this group. Comes from THE MINOR PLANET MAILING LIST. I have included credits and subscription information to those interested. Best! --AL >During some discussion on 2001 KX76, the question arose as to what
size an object would have to be before you could reasonable assume that its gravity was sufficient to assure that it would have a spherical shape due to gravity.> >Can anyone assist on this question?>
Dear Larry, My mentor and thesis advisor, William Kaula, put the answer to this in terms of gravitational harmonics, in what has sometimes been referred to as Kaula's rule. The basis of his rule is simply the following. On Earth, we see deviations from the equilibrium figure of the planet of the order of one part in a thousand. That is, the Earth has a radius of 6378 km and we see mountains and ocean trenches around 6 km from equil- ibrium "sea level". Since the force of gravity is proportional to the dimension of the body, you can stack rocks twice as high on a body half as big with the same stress (pressure) at the base. So assuming rocks on other bodies (Mars, moon, asteroids) have the same strength, the maximum height or depth of deviations from figure should be inversely proportional to the dimension of the body, or expressed as a proportion, inverse with the square of the dimension. For the Earth, deviations are one part in a thousand. For a body sqrt(1000), or about 30 times, smaller, deviations reach the level of order unity, thus the body is no longer "spherical" in any sense. So at r = 6000/30 = 200 km, or diameter around 400 km, rocky bodies should take on close to arbitrary shapes rather than spherical. However, as deviations from "equilibrium" shape become very large, the"equilibrium" gravity field itself distorts in the direction of the deviation, so the non-equilibrium stresses are not so great as you would estimate by not accounting for this effect. Allowing for this, one would expect asteroids as large as 500 or so km to be able to sustain fairly major deviations from equilibrium. Observation is the final arbitor of nature, of course. Looking at actual lightcurve amplitudes, we see that the very largest asteroids (Ceres, Pallas, Vesta) have fairly modest lightcurve amplitudes. About the largest large-amplitude asteroids are 87 Sylvia and 15 Eunomia at around 250 km diameter. But these are fairly fast rotators so their irregular shapes are partially equilibrated by centrifugal force. You have to go down to around 200 km before you find really irregular shapes with no significant compensation by rapid rotation. This would suggest that asteroids are somewhat weaker than terrestrial (and lunar and Martian) rocks and have a bit less ability to sustain non-equilibrium shapes, but only by a factor of 2 or so. Regards, Alan **************************************************** Alan Harris Senior Research Scientist MS 183-501 Phone: 818-354-6741 Jet Propulsion Laboratory Fax: 818-354-0966 Pasadena, CA 91109 email: Alan.W.Harris_at_jpl.nasa.gov **************************************************** ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ NOTICE: Material quoted or re-posted from the Minor Planet Mailing List should be proceeded by the following attribution: FROM THE MINOR PLANET MAILING LIST [date]. For the full text or tosubscribe, please visit: MPML Home page: http://www.bitnik.com/mp MPML FAQ: http://www.bitnik.com/mp/MPML-FAQ.html MPML's Yahoogroups page: http://www.yahoogroups.com/group/mpml To unsubscribe from this group, send an email to: mpml-unsubscribe_at_yahoogroups.com Received on Sat 27 Oct 2001 04:03:45 PM PDT |
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