Exam%20III%202010%20Soln

# Exam%20III%202010%20Soln - Fall 2010 AAE 532 — Orbit...

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Unformatted text preview: Fall 2010 AAE 532 — Orbit Mechanics Exam III Sol de‘ons Please read the problems carefully. Write clearly and use diagrams when necessary. Note that a table of constants is included. ( 45 Points) 1. Consider the space triangle in the ﬁgure. Assume that a spacecraft Pisces is currently in a circular orbit about the Earth with orbital angular momentum Menage. Pisces departs the current location and will rendezvous with the vehicle Gamma at the indicated position. Consider the minimum energy elliptical transfer arc between the positions. (a) Determine the speciﬁc location of the vacant focus that corresponds to the minimum energy path, i.e., me. Scale F m and add it to the ﬁgure on the next page. (b) What is TA (transfer angle), amm , emin, and bmm ? Determine rdep, vdep, 636.1,, 0;” that is required such that spacecraft is on the transfer path. (c) Add the following to the ﬁgure on the next page: line of apsides, latus rectum, p, minor axis, b, C (center of ellipse), rp, and ra (sketch these to scale as much as possible). Indicate the are for the transfer. ; d o C : TA .270 I 3 Make; Pisces am!“ g 5 Re; Nobe: Y" =a 50 n is at 3R63 endai mmor 0.30.5 9’ gamin‘pi =3R€P=EF 520mm ‘Y‘a. zaRe = PM: 41369 Sum = Chord => Em“ on chord at +hese (X = 513m" /__3__ 2': 120° drstance\$ from Panda £61m!) ﬁ‘WQSin" S-c =48.6L° 0)” Gamma Mn .. (6—Pl {5"}. ~ 0“ .. P - n a: )5m (3(5) ==g> p —- 3.41% _ _ a _ _ r‘p=l-(953’ R69 'P-OLO C) =59 Cm‘n— .447L é ( 15 points) 2. In the previous problem, other options are possible. Instead of a minimum energy solution, choose a value of semi-major axis a 2 4R@ . (a) What are the two values of p that result? (b) If the elliptical transfer type is A, which p is selected? Justify your choice. (at) oé = «23:73 __3_ = /£t0° {zﬁélsmd 3:0— = 4/.4/0 01m M P = 4464636541) Sma< ﬂﬁ> Cl. Sotui’l‘on Space, {elds ehuofvopﬂons acor the: Vaﬂatti as (Ff) TQHJZ 2A : F um um chord, andt 0x0, 80 Vans?» mp2, ‘abovo,’ chord m Soluﬁon Space, (F) Focus F: alumnae between ‘icg’ s gas and prodm“ IN or aceta‘lv‘t'cz'tg‘ SO P=&C“€9“ 7? 1 smaller P T WeF—‘Jlg Select p = ['54‘963 l (40 Points) 3. Assume that a spacecraft (3/0) is returning to Earth and using the Moon to decrease energy. Assume that the lunar orbit is circular and that velocity can be approximated as v‘I = 1.0 km/s. The spacecraft and lunar orbits are coplanar; orbital angular momentum vectors are parallel. At arrival, the s/c velocity M = 2coslS” km/s and is directed such that 7 = -15° . The lunar gravity assist must produce an equivalent A17“ that is directed such that a = —l35“. (a) Determine IAVeq (b) Determine the following quantities associated with the ﬂyby: turn angle 6 , closest approach distance rp . (c) Does the 3/0 pass “ahead” or “behind”? Justify your answer with sketches and vector diagrams. ya: i Kin/S V‘= sleeps/5°: 1.93KM/5 (Mal/«i X‘=15° 5—.— V; =V‘Qa 9.. ‘ _ /a +Va “av 00\$ 3’ I lift. Vac/a = I KM/s I l. 2 X? any 5 = 1:5? ==a7 [5 =00“ I50 guttch s s - @ v ’ g; r w (5:150" Va = V00 run; 7315" (also note: veg/aﬂaﬂ is isosceles ’___. __ 3‘1 53,. 'tr‘i'ang IL Kg) 2 M .9, my: 49mm 71 (11a! 3%: VeH =£> WW 3;, = [Mm-I) ‘9 Q =490a'9m ‘ =Q.8&Ra ...
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## This note was uploaded on 12/22/2010 for the course A&AE 532 taught by Professor Kathleenhowell during the Spring '10 term at Purdue.

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Exam%20III%202010%20Soln - Fall 2010 AAE 532 — Orbit...

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