t2_FA05_KEYr - l. [25 peinta] A spacecraft {sic} has an...

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Unformatted text preview: l. [25 peinta] A spacecraft {sic} has an initial orbit with at = EUDGG km and e; = 11?. a) [3 pta} Calculate the flight—path angle 951 when the aft: reaches a true anemaly §=290 deg. ¢ 1 *l‘ 505*l[bl_ H}; : a, (he?) 1? lSSUG km. I '7 nu ‘ 1m film = Mamba ma. El : _72&C:1: “é.‘;Ll'3 lira/g" r 2 L— : emaaz am ' Ham-5 we waited“ Ur = 1) 2(3 + %)=7.az Jame. E‘Dfiflfitk eff-Ir -i. ‘7’ f 2 “C95 [miewfififlkmfiirazemlfll ¢E ': "‘ b] {9 pta) Calculate the dc; needed to change the flight—path angle R) d»; = —2 deg and the He’s specdteV2=4kml$ M: Ag: 9;. $3: :'-ch3 *(‘27'q59l3) U! : u Ax] : 1i “1+ 113.. Zviulcaael a. a] e 7. la 1 Jan}; UL : LH-flel'i. A AU :W ‘5‘}: Bl‘lflfz ldmlsg e) [3 pte} Explain what is meanl by impulsive apprmimarian. The Search admit; fl‘” ’3‘ “fgflé’m‘flyi PDSi'llm-m {EMMM' cwrexim 2. [25 points] A communications satellite is supposed to be transferred from a low Earth orbit {LED} to geosynchronous equatorial orbit {GED} using a Hohmann transfer. The two corresponding circular radii are rm = TTGU km, raga = 4223! km. a} [9 pts} During the first bun], the engine stops too soon, producing a aw = 1.5 k11th {parallel to the initial circular velocity vector}. The transfer orbit will therefore have insufficient energy to reach mm. Calculate the radius of the outer circular orbit that can now be selli'eyed. _ F : rmqg LN: LEJ: “ r“ Lea flu : LEM-his. - e-r a _. LEI: whey _ uLEG 4— 3w : 8.015 kmis. rise '1 : U 'Pfil' _ ‘ *' I; m1. 1' Egg“ if a; c 15.99): a “Les smear : Eb 1 res-11.3% Jen. at nf+r~ =2a~xg~ear Earl-Let“ =2ex£reflaa b.) {8 pts] When the satellite reaches a radius of areas km, the remaining prope ants onboard explode in a colossal, Visually satisfying fireball, with some fragments of the satellite achieving very high speeds. 1|What minimum speed is needed at that radius for a fragment to escape from Earth? (recall that escape requires orbital energy = CI]. ,r-x L I.d-" U k" = D = as: _ - an: '2'.“ AP .491)”; :- Edit; I'" @ new. c.) (8 pts} Some of the fragments from the explosion end up in an orbit with a = Elfltlfl Inn, .2 = 13.1, f = 2!] deg. Calculate how long it will take for this ol'bit‘s ascending node to change by 133 deg. {because of Earth—oblateness effects} a. , (pill. : Hgfifizk$ Cast. -7 (lug, ifL€qu1)1 in: E : (iii):ng 3. (25 points} Consider an Earth orbit with a = ESGDU km and e = 13.3. a.) [12 pts] At time t = Cl, tracking facilities determine one satellite to he at t? = 15 deg. Calculate the time Tnet which this sfc passed through perigee. E : Z'i'dflF" PE“ fan-g] : “036 A?‘ :L oJ‘tht FIJ- l+a h) {13 pts} Another satellite on the same orhit passes through perigee at T9 = 85H s. Using an},r fomi of numetical iteration, calculate this slc‘s eccentric anomaly E at time I] = mm s. Use an initial guess ot‘Et} = M: «Jello: [it] # 1'73) and tolerance to. = {LUL Show the steps in each it : 1%? 0:. In.) -: 0.2 Fag». iteration. The process will converge in a few iterations. E as c.3721: ml. :msz 4. (25 points) If a satoflito has principal moments of inortia I; = 19, I; = 23, [a = 31 (kg-ml}, a.) {8 pts] Calculate the rotational kinetic energy when the angular ureiomilyr is (a = 0.253, —fl.?52 4.333 (mars) . T: Llolu = é: $5 = gin-2 -n "v" -D 31 4“ (L3 Wu) 4L3 : 14mm W‘) E. T: 7 LH ij‘sh # b.) (3 pts) Coloulalotheungie between u": ondtho £33 axis. m 5.1;: “Hwy: momma a I; -.- _ '2- m: Lb}:- (0.1)14 ['I:u.":']"+{4i:u.3)1L ’13-- caga = “0'7 : as 35‘: c.) (9 pts) Calculate the torque requirod to produce a new angular velocity (T3 = 21de + Asin Rib: + 5M3J , whero A and 21 are constants and 1‘ is the tilno. M: : 1—10.61 + Quagc—L'S'Il) ‘33: z k 2 II x +0;qu (SAVE-.52) M2,; IZLE1+ m3"f":’r(H1——1‘I:5) Lida: canst u I Mm H +435; 1%)(17HI3) M1 7' 23 AXE-s -—(;D x a M3 ; T5333»? audio—I.) L03 1 a +_:- : {j + ASInH)(IE-'IF) M3: LIL“: Amsffl ...
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t2_FA05_KEYr - l. [25 peinta] A spacecraft {sic} has an...

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