t2_FA04_solns

# t2_FA04_solns - t{25 paints A satellite has an initial...

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Unformatted text preview: t. {25 paints) A satellite has an initial drbit with m = 1130a km and e. = (i=1. When it reaches a true anomaly 5'] = 12:3 deg, it perfomts an impulsive velocity changes placing it em a new orbit with peﬁgee and apogee radii aft-P; = TEDG km and rag = 1465!] km. [,u= 3.9315 x 105 km3i‘s3} a} {3 fits} Calculate the possible values of the new ﬂight—path angle it}: {immediately after the div neeurs}. 2 __ 02: GJE+FEJL : {D425 is” ?Z: alﬁleeljzcl’éﬁéQELi-L 2" r“? [’1 11—7 (—2 as a 1 T- : - 5- “52—13152” 0.3% l Kr; St “MA” {2,2, +rthl E; = 7;— : elem Ice/r: Ital : ext-ref): Create/cm. r——-1 E K! : 2 +15; “7 1 ' - tzsmtsfm l U (Ea r' l+erce5t9i - :1 3.38 )6me F :I’“ teler ﬂu) Cass 53L: he - L l a, -: a. 2 :er‘ (a ) velar-we) W p t : 25a (ma-"+1 = 5:512”; LIL D{alcmi2 I # .... b) [9 pts} Calculate the required 4' v, aside the value of Q; that ives the smal M: as warm“ .2; Wat-25 : ARES” 9; £51,952" n T__‘—_"**--——ﬁ-“I AU + w Raf-Jr silk aujuleejgp’ Q93 =—t/<¥z° uiﬁlﬂ 5M JW-ML __ A“: RU: C), #21; king}: " e] {3 pts} Calculate the new 1.Jalue afﬁne annmaly t3; {immediater after the div eeeurs} Mg] 95; 3 H353“ bafﬂe)“ Au) was a .r a . ' ‘I 7. I ._ “‘1 -— — 62, * ("‘35 aria-(\$1; 0d ! M21555“ 5 ELIE; 2. [25 points} A mission from Earth to Jupiter will use a Hohrnann transfer. Assume that only the Sun‘s gravitational force acts on the spacecraft. The transfer begins at Earth’s circular orbit with radius from the Sun oft-e. = 1.4913 x 11313 l-tln= and terminates at Jupiter‘s circttlar orbit with radius from the Sun oft}: ?.?834 x 1'03 km. The Sun‘s gravitational constant is its =1.32? a 1ft” kin’i’sz. a.) {12 pts) Calculate the time required for the transfer. 3 [at I LT : Til-Ln” Xjér ‘ A VIEW f: 5842/ i [:3 + E 2._ A‘i‘kgr : EMEE XIUTSH, (: : teammate lo.) {13 nts} Calculate the total at: required for the transfer. V, s “at 7' inf: : 2.3.7513 belt. 3.1[25 points) cm. it eg. a.) {13 pts) Determine an expression for the location ofthe eenter of gravity,r tog.) ofhodgir B with respeet to bod},r A, using the coordinate system shown. Eddy B is modelled as a pair of masses 2m and iii. separated by a massless rod of length d. 4 M it | r. l d 1 F : ‘szmﬁl 6”” t TeT Ll" (mat); : *GMH 3; l 3 L I; — “GM 3 A E Jr‘l_"o"t" E- M) L “'33 2 HGMﬂni‘ F _ ___.___._—-—-—T—""" C — - 2, j 41%? J‘” {La-ML) 13.} {12 pts} ‘ g are monitoring a space probe that is orhiting asteroid X. The navigation team has determined that the orbit has i = 12 deg, a = 4130' km, e = Uni. It is estimated that X has an approximate radius RX = 3th} km and a gravitational constant it. = 2.53 x 10'2 krnEi’sz. After an interval ofohservatiort, it is determined that the orbit’s aseending node is regressing at an average rate {driftith = -2.9 degfsidereal day, where sittereal day = as | rid see. Determine the value of J; for this asteroid. 4. (25 points) If a satellite has the mass inertia matrix in the principal axis system 1? o o g: o 23 o (kgmzl GU31 a.) (3 pts} Calculate the angular momentum vector for the case where the angular velocity is r?) = 413.61 +l .4152 - ELSE); traits). ti = .I. a : [iii] (agar/5) 124, E" eta '-..—-— It" 2 6.11.. +32.2’E;,_L2‘t+6’£3 (kg-W's) b.) [8 pts] Calculate the angle between H and (I: from part a.) at. 2 H M“ _! awake/H = (35" (O.‘l'3"ta) : 3.9!? (er OJ??? ML) e.} (9 pts} Calculate the torque required to produce a new time—varying angular trelocity of: = plil + gt")? + {I — t?"th3 , where p, q, and k are constants. Mi : Ittial + DLHSCIEF 2F):tf)+ clone—EX?) : E; (leaf-H Ml: ragtime, (II#13):0+ (t- *%)P(—tr)ect%_-E (FEM) M3 : Iéﬂaﬁ t— [A‘t’él (IL-:10 : T3 (leagidrli’ <6) M5 1 Tﬁlcefbi— *i‘é f; ...
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t2_FA04_solns - t{25 paints A satellite has an initial...

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