z-earth-moonsyst - RE LE −rot Earth –Moon System 2π =...

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Unformatted text preview: RE LE −rot Earth –Moon System 2π = IEωE = IE ( ) TE LM −orb = IM −orbωM −orb = mM R 2 ( 1 day 2π TM −orb ) 27 days R very small (neglect) IE = 2 MER 2 E 5 constant K E −rot = Ltot=LE-rot+LM-orbit+LM-rot Ltot = IE ( 1 1 2π IE ωE 2 = IE ( )2 2 2 TE 2π 2π ) + mM R 2 ( ) TE TM −orb solid Earth – rotates under ocean tidal budge - frictional energy loss ∆EE= ∆KE-rot =-Wtidal-friction Earth’s rotation slows with time (2π ) 1 1 TE (later ) > TE (earlier ) =[ IE ]( − ) 2 TE (later )2 TE (earlier )2 2 −Wtidal = ∆K E −rot constant Ltot = IE ( 2π 2π ) + mM R 2 ( ) TE TM −orb decreases moon moves away Ltot with time = IE (2π TE increases (2π )2 3 T= R GME 2 L transferred to moon ) + mM GME R1/ 2 m3 =G s 2kg T-2 = GME (2π )2 R3 GM E 1 1 = T (2π ) R 3/2 (2π )2 3 T= R GME 2 RE R=rRE TM-orbit = 27 days = TE-rot27 ( now ) TM-orbit = τ TE-rot (now ) (2π )2 RE3 3 τ2 = r 2 GMETE R=rRE τ 2 = [0.003584] r 3 distant future moon-orbit at 91 RE τ 2 = [0.0033375] r 3 day’=month’=51 days (current) distant past moon- much closer day shorter very small (neglect) Ltot=LE-rot+LM-orbit+LM-rot Moon orbit RE TM-orbit = 27 days = TE-rot27 ( now ) R=rRE M mM = E 80 Earth rot. IE = LE -rot LE -rot 2 MER 2 E 5 2π = { I} TE 2 2 ME RE 2π =[ 5 TE TM-orbit = τ TE-rot (now ) τ = 27 (now ) 2π L M-orbit = m M R 2 ( ) TM-orbit L M-orbit = ME 2π ) ( r R E )2 ( 80 τTE-rot L M-orbit r 2 M E R E 2 2π = [ 80τ TE TE-rot (at other time) = t TE-rot (now ) LE -rot 2 M R 2π = [E 5t TE 2 E L totM-orbit = L E-rot + L M-orbit L totM-orbit 2 r 2 M E R E 2 2π }[ ={ + 5t 80τ TE fE-rot =1 day fM-rot =1/27 days RE= 3.7RM E R=Earth-Moon Distance M RM RE 60RE = REarth-Moon ME = 80mM IE = 2 MER 2 E 5 IM = IM = 2 2 mM R M 5 2 2 ME R E 2 2 mM R M = ( ) = (0.000913)IE 5 5 80 3.7 L M-rot = I M (2π f M-rot ) LE-rot= IE (2πfE-rot) L M-rot 1 = (0.000913)I E (2π f E-rot ) 27 L M-rot = (0.0000338)L E-rot Earth F= GMM m (R + RE )2 RE F= GMM m F= R2 F= GMM m (R )2 GMM m (R − RE )2 Moon ...
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This note was uploaded on 04/03/2012 for the course PHY 1020 taught by Professor Kodera during the Spring '11 term at University of Florida.

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z-earth-moonsyst - RE LE −rot Earth –Moon System 2π =...

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