On the Stability of Spinning Asteroids

Abstract

Abstract Most asteroids with a diameter larger than $$\sim 300 \ {\mathrm{m}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>300</mml:mn> <mml:mspace/> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> are rubble piles, i.e., consisting of more than one solid object. All asteroids are rotating but almost all asteroids larger than $$\sim 300 \ \mathrm{m}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>300</mml:mn> <mml:mspace/> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> rotate with a period longer than $$2.3 \ {\text{hours}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2.3</mml:mn> <mml:mspace/> <mml:mtext>hours</mml:mtext> </mml:mrow> </mml:math> , which is the critical period where the centrifugal force equals the gravitational force. This indicates that there are nearly no adhesive interaction forces between the asteroid fragments. We show that this is due to the surface roughness of the asteroid particles which reduces the van der Waals interaction between the particles by a factor of 100 for micrometer sized particles and even more for larger particles. We show that surface roughness results in an interaction force which is independent of the size of the particles, in contrast to the linear size dependency expected for particles with smooth surfaces. Thus, two stone fragments of size $$100 \ {\mathrm{nm}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>100</mml:mn> <mml:mspace/> <mml:mi>nm</mml:mi> </mml:mrow> </mml:math> attract each other with the same non-gravitational force as two fragments of size $$10 \ {\mathrm{m}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>10</mml:mn> <mml:mspace/> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> .

Topics & Concepts