51613 uw astr 323 sp13 eric agol 2013 5 magnitude

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Unformatted text preview: ; Δpy≈mvy≈ m v b y x M 5/16/13 UW, ASTR 323, SP13, Eric Agol ©2013 4 ScaYering of small bodies •  By energy conserva8on: v M m b 1 21 1212 2 mv = m(v − Δvm ,x ) + mvm ,y + MvM ≈ 2 2 2 2 •  By conserva8on of momentum, large mass is decelerated by a velocity: ΔvM ,x = −Δvm ,x !! 5/16/13 = UW, ASTR 323, SP13, Eric Agol ©2013 5 Magnitude of dynamical fric8on •  Par8cles between b b+db pass at a rate 2πnvbdb, so the force on mass M is: fd = M dvM ,x dt =−∫ bmax bmin 2G 2M 2 2π bnmv 2 3 db = bv •  C=ln(bmax/bmin)≈10- 20 typically •  Note: this is independent of m; just depends on mass & velocity of larger body & ________ of small bodies •  If larger body moves slowly, fric8on is larger - if too slow, then scales with velocity of small bodies 5/16/13 UW, ASTR 323, SP13, Eric Agol ©2013 6 Origin of dynamical fric8on 5/16/13 UW, ASTR 323, SP13, Eric Agol ©2013 7 Consequences of dynamical fric8on Mergers are _____________ Satellites/clusters sink to ________ Supermassive black holes __________ ______ _______...
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This document was uploaded on 04/05/2014.

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