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# hw3 - 28 cHAprER 2 RELATIvIsrrc MEcHANrcs 2.47 o o l newl a...

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28 cHAprER 2. RELATIvIsrrc MEcHANrcs 2.47 oo lnewl (a) The radius of the satellite's orbit is .R : h+R.:2.6bgxl0? m. The orbital speed is determined by the condition mu!/R-- GMrnf R2, whence o, : ./dMn: E = gS,?0 -/;1. (b) The error in calculating r as uo At is dr : lu" - clAt x a"hf c: 1160 ;-l 2.48 or [new] (a) As in Problem 2.47,u" :3870 m/s. Hence 7 : lt - (as /c)21-L/2 x 1 + !(u"/c)2. The time for one orbit (measured on earth) is e = 2rr/u": 43200 s. Since e, : 7[, the dference between these is about (error in time) : 2i 3.59 x 10-6 s -7" x (.t - r)r. - ;\;) ,": 2.49 rr [new] (a) As in Problem 2.48, the time for one orbit is T:43200 s. The ftactional shift in frequency is Lf .fsdh l(GM/r2)dh GM / t t\ T:--7_=----_7-=-7-\&-El where .R : 2.658 x 107m, as in Problem2.47. Putting in the numbers, Af /f :5.27 x l0-ro. Thereforetheerrorinthetimefromignoringthisshiftis(A'l/flr (b) Error in position : c x (error in time) : l?8rffi]. 2.50 oo [new] (b) Error in position : c x (error in time) : llO8ffil ,h= Y ''t" a _ u 5 m C

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8.29 ooo [new] (a) Under the suggested "radical assumption," with all molecules having the same lu,l and h;11 of iirem moving eu.ct *ay, the number density of molecules moving to the right is ,rn,. in a time At, thesemolecules move a distance u,At to the right. Therefore the molecules that hit the right wall are precisely those right-movingmolecules in the volume to the right of the dashed
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hw3 - 28 cHAprER 2 RELATIvIsrrc MEcHANrcs 2.47 o o l newl a...

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