{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PS5_2010_Soln[1]

PS5_2010_Soln[1] - ”/75(32 P55” Prat/ml 5/02 MAM/3...

Info iconThis preview shows pages 1–14. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 14
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ”/75 (32 P55” Prat/ml 5/02 MAM/3% M#/97 ({QMM’ E = 970M; «SW/5;; AM M 01M [swmgm V7, = 4/9/7252): +4.9 7/; km/ WM“ 40 7/» 2:, MJW? gig, f, A, f, 6,923 Ea,(zé«t,o)? Y A é I‘ = _. v; = 0,707] 7 A ‘a ? 1‘ gm): / C VJ/l/‘l= '/ )ga_X// c7am7y V1? V5 45/ r a”, h = 23:1 [fi'nu (mil/1 If 11’) Xy W) \; WMmi=r§mZ 15%,? [5XEI é: AAXIQ" K/‘ig'PX/ZE/ Me WWI/e 70 = 11°F 4. vgoé ‘ If? * C‘QQ 4 = (\’/_0';‘); r (170 'é)9 = msl’hrr‘ * vamflgé Vr.‘ gm". = 4.40795- km/ (yr v9.= 170-9“ = 9.23/20 5% a W 27: fM"(K;:) = “Mam" m. Mam)” i=1? ‘4. = 47.4w: aw “ : ”ll/25 = /(7/M,?7 ém [P = Zr”; : /0/s'7./$ 5a (2.92M) A = ”WU = mum/z M/sec P : by“ = 89%,” A“ a 2 'z//' [042‘ = 0.374397 Ea = ws"((;—”a)/a) = “313m” 3% 1755M? 9’; = Zia/[W WW4» = 4/4,??77’ WM ' “(L/opt/ia @(‘E9” 65in ’a) = “bl-1936 {g5 (ti/(913m). [Ir/W 7’6 /WIW5L ) 5) Wat z‘z'm, 23” if ”am/w m 7% Mg (£"tf) '7 (fit/J) +ZCW‘M‘AZS :ys’zp/qfec ’ W 7 m'm/eo "> Since (hi/jam /l7 3 Mn /)//§1Y 16 /J.e,/w7r/€ 2‘: MM; Mary?! 6077/ M26 M? Mfr» [9W /.fl/y.a7vx€ Pw’n Wat 29’ nun/M55 5511 57C “177/ (/05) WM 07% ./ 7,001 a, Mr fizz/mu 5/2 35M; WW fa //w[/c»/ r,’ =,H 75,7)7/j‘a7 = 3/ZM” \\) Air; A9 = 9”” 9.," = Mrrré m4 = AI; = 6, ' 60 = Um; rml ‘ 77. ML fmJW/m [M r,=a[/racwE/)) f: /’/://”ng(9*)= /’7// CoSAE) = ~a/00é35937 fl? = raga/me" = {t/‘ ")to )—,/“7: [AE 972415): 37 fifé/Zé gee ' 79 a a ’ fl * = P7; ‘7“ WM) “51/”? ""49: g‘m‘w = ’0 (MN/7&3”??? sec” , __ f g .. I Fem/wag“) ={}«,¢(: CosAE)> = "003/010;on F. = zen/3.722; + [fin/94; km ‘7, = 41762534,: ‘ 5 479292 )7 bag C) 130% WWW farm/V7 WCW in [4) flaky/Kw W M j) Daily/5% 21/121 M f. M 50 W// 5/2 ”:54? J /\/o. affix: 3% W/ 74 x/MZZZ’Z’W M W ff:a[/va): Qé7¥,32? 4.4, 994% /Z M WM (0/ W’flg" ZMw A ,%%WM é% [oz/W SW A MM {‘0' a: ?,7 K6}? C‘) 5 /Zflo L : Z8" {ft/F mp; = 36000 sea a’ z’Crwrp) = 52.67/33: @= I- 0/“ = @.駒7/¢/3 5% “flaw = ’577r/W 2,3 5 f5 2/7 7/66/14 ._ é'dfiafx/fl‘psec /é 739W 4/; ’> flfV/j ”7wa f/x/gg 2274(1’ 5) <1!) wLWMM/fifl My wwiy/éw W Mayra Ha: (;"£f)‘/‘IZS7 = 37/?27‘5vl’w/ fl/fla/E,MWZ4/W/5/W , mmb/M/ M fiWWMW/Mfifljfl/M flag/7M, M/%/m)4w[/ww/’EM 5m =En- {En-asr’~E~ ) WW/MMLM MM 6 my >/6fl°/ 2% 57/ A). W”. {M26 M (1M m 4% 50: 4442/47“) %r/ 4/ and/Jr é/AIZJ 9,:5)‘€f:~5‘a?2790 ”K211“WQWWWWZZWMWWWWWWWWW.WWWWWWWW /.;= a{/~ awn) = €7/7/, w; 4m = 5% 97693757; = / (a? 5% 1% W?) = izé'zmi wag/Mg; MM W2 @1meWWWWWWIW.WW_¥MWA.MW“WAKWWV “WKWMWW’WMDw,gramWWW.“W«WmamVWMWW-a.wwmwmxwwwmwww‘WWWWMWWW”,mWWW.MWWMW.MMW W: = F. I" = 5-9/9/.fi?b’:€«1 F iv; = was/nae); + was(fl)é = ~o. 4/77/75”; +/é%75’7é Aug/g 1.,WW.WWM,..wwmwwmW.WMWMMWMWWW.“ WWW, awww.mw,“MWWWMWW M. ._ A x fl 5:; ca Hm egg new/g +0». C/ ca *5» 5/ Z S: 59 5; 69 C J = 0. mm mgr/u 3 (9,259 776 4271577 dam/27 .. myoés’W/ ’0. 34797.4 0,2757% 1%? :2 748 WgWWMWWWWWKWWdWVMWWWW; a }F = :62 gs’yf/WEM : 4/37/971sz —/$‘0?3y{; ;-/9757,9£ kh/ V MMWaMmNWWMMW”WWWMWWWMW '1‘ M ‘ in ['94 .m.WWW.Wmflw”MEAN.”WW,Ma,”MWWWWMWW,M,WM,WNWWWM”u,«MM..W,.VMWWMWMMWNWMMWWWWMwmwnmnwmwmwmnm.wmwMWWWDMMWMWM if .3 I z w o. ‘i‘H / 135‘ _ n A ' V, = C E fwwnywj ~ 01/1790»: HJJMZéfmaéL/Hflz k; g . 0 F A L) m few/”q Wm MW; at my,» 7/“. x” 3,22 m/ mu {é,—17)=(éo-é,,)4 m = m, = 4/2005“ flax/3MMW/wm fWM m m'// Crm fax/2178 A My ,4». My we WM (z‘,~£,,)= x7444" = Z/9.‘/%3.rec ff: (left/J” = é.30§f0/rd= Jé/Z’zs'epz’ m’l/ M #275702" flaflWé/WIU MW 4% M, = Azmvoz" a 94/19; 5M; Wm 5; En 3.7772 4% m 45 = M-W’ = zyéZ/x/m/ [W nwwfiv fMfiWm) M V',= “(/rgasé) F = aCI-e‘) gun/2%» fi=(I-%(2—wo5))fi + ((f,—fa)"7/fd7(05‘5/%AEB>E 0,17%“ m/MWI + //-' i’ffl-MMUVZ rt r0 = -M/mw + 2747.575; *L/ZW‘Z/7 g A. = flier/WK)? «w $717751? ' 2.0974932“ 5/5. gov/W IC‘ ”Li/441 W flew/a] /g/ 7%f/UZ W 9, :w+19;*J wéze 297*:me ’mfwflv V) ’92760330 ‘9 ICR ° ‘d.5’6’3/0‘/ - 0.4/0é23s’ 0. 239734 a Mai/09‘ — a. no 275' » 0. am 775/ 0, 3689/ - 0. 270377 0, $73 z ‘77? a VW/ 33 —— =~ 571‘ = //rze.37f~ 4.. (+09“ +04) I u VRVTC‘ 0,43372ww75's377fé /c»«/ K o A?) 0/1497 /'5 P2710313 MW fi= ‘c" E} E ‘F, = Mumg + am”; +02 47 m: E 1 W47“ "LC/(£97? V 17, =»og;5'7&r22 +?r37M/’;+ 0+2 A? Mi.” (alum i w E, WWW”W“WW“?WWWflMMWNWMWWMMWMWNMMwWam.MWNWNMWWVMM.mmwwmmm“m‘iwmmw ,L/, = - flame/0 [74“ A 4/3er ,V/fé’fl/MW 9;: 65457 e )= 1/702992 5= Zsflfl) m 56% 1/505 /,[e7Z M/ / rf= {200b, *ng? (—1 {79) = “3,4” fi—Mswggc, ’11, 7% A 61 QWA 5 5:1,,_i“:iiififi;i:i:ifi:,_,iiii:::iii;ffii: ,, g L7’2 ”/3?77‘/Z Am/ :’ ”/é/g, : ~/§’ :24), W“) km, {ZIP/4 = / 5” M 1 Z 3 A/ 7//s (z; 2}, ) = ”Z/Wé‘m’ (fly/”Mic Va“; ’on [xi/few, ) M5 w mm 55W {3; we 0% M ; Lam/V a 2% Wat-W15 71 ”/5 : zvfm'W QM (”7))= —//7 m) (PM Wu Mai/0M 7 777 ”WWW" %” 7'” ” 257 4/3/0 My; 5 M Mb/mce M 54 m UMM fixa/Nfim/MM W& %%Wi%/fl‘7/fl/fl77 "Emu W‘wm’rz é /a/fiu/z72é Wang. 5 [Z 25411 g/W 712?? Am 5.1%wa 0M [My/1 721/% Mm x/zm 711,591,, ,4, .7 %mfiw // Wk MM a/W/W / vp/ 14,]? :9 g Z (L? P>:L/é29‘/%é’%; 1’) f4 %f€/ wflaé flm Ma ,fl/w/gz/ Wfiwfi %rfl/{(;/é Wéfifh/W/ 19/75 afar»: M u, ; M/I/ V‘ W “W 14/ Magyueyfi MMgZ/Mcfiéfln Jaw/W/ figwwgm’ady/IngM/ecfim (fr/72 a VW 002mm 71/ WWW 144 14 VP 147 W; M. 7/11/1411 /1«WW \7’0 + . V ‘ ' , a [7: . é/ fM/ff [05/ W a" Xx M 11 @1557 @fié MW Elnce f’afla/fl%—WW/ % /C W/fl/ MAM VS!“ ”/6 % W/ a/%/LW 5” V3542?“ VS’A/fléé km amw/ M w % 5/: am: owém 2/ alma/Mm 90/75 54”: / 070047051: (fa: Mme) ”9111:117le m} fibrin/756, r“ r], 7% WWI/7‘ 50 I)": r, / /fl¢r/'677§€ 961‘fo 000! WWW ”AW 73 AV: V”=v/}’ = 9,4 279% ém/ ¢w AV: ”Hf/KM M/Kc %% 4%)? \f,*‘7/Z("zflze + “‘79) v+= ‘flZaéflV [mg AV=V*~V” = ~fl,423/‘7’Z ,ém/ {M #424 Mac/a. firm/6m A” We, é ;% 55/922 Mn of V? - //11 rym/M WAMW 74 W a/aye MVM .7 as: (’ “Zia: r5: aE(/+ a) = 962/29 A" 74 W My“ W £29206 1m WM W % fl 7AM; ,. W§%%' ifl%’ WW, fifl @WM’mM‘é/jw %5M%r Myfifjp. c) 6r Ww flue ./ %rfi7/ ,Jfi mafia/M f, m M/flfm ”’7’“ v”: LUZ 5% gay“) $1? W M¢ %s¢’»/Z7V5 : fl? 5 9.3/47??sz flaw rum} MW VA, >Vgsc éfl/ML /Me5// Mam % Ago 160,925? 5% ”V5 M 5W“ % yfl/‘r/M‘C/M M M Wm (24/ A47 /4 mmc 0’» MM gage/Ma! / , w‘ = _ - r é;— /z~/"¢,, a W5,” af/ a, w,” = V5,, = & w/ww ,ém/ / Q; = (057%,) = 1/?6’739 5 W 4 A”? 96 MW 6c fill/l I 4%Jgf ('ZZ’OfZ/wgyw W4/MV;;%%2 H“ cm //27 V25] ‘/ WW7 Z . II 2 7%»W ém {iii )= /3 (6’5/0AH’H) p ”(jg—fl ZL/‘K'XJJW f // )%Mf/é ! W ’T W fl /C W//%é gI/i'a fl/fi ?a%rx/MW/ y 29 W a M 4%; / \l “ Problem Set 5, Problem 3 STK/Astrogator output Data taken from the Initial State to confirm calculations of part (a): Astrogator MCS Segment Summary Astrogator MCS Initial State Summary MCS Segment Type: Initialstate Name: Initial State User Comment: Initializes state data Oct 2010 18:30:00.000 UTC Julian Date: 2455474.27083333 Time past epoch: 0 sec (Epoch in UTC Gregorian Date: 4 Oct 2010 18:30:00.000) Parameter Set T oe: Keolerian sma: —l5320.0089501865130000 km RAAN: 0 deg ecc: 1.3000122268l7l548 n. - .-. inc: 0 deg TA: 240.3145813164251 deg Mean Anom= —67.534l8l70313844 deg Long Perl: 0 oeg Arg. Lat: 240.3145813164251 deg True Long: 240.3145813164251 deg Vert FPA: 162.4959371078869 deg Ang. Mom: 21277.95282703191 kmA2/sec - ' ' “ 2.795584000018654 kmAZ/SecAZ 4.6294763330089665 km/sec : 4596.19 : — a. I 1.672000000005578 km/sec Values for semi-major axis, energy, eccentricity, initial true anomaly, flight path angle, and periapse velocity all agree with what was computed for this orbit given radius at periapse, 170°, and the time of (to-tp) = -3 hrs. Values for semi-minor axis, flyby angle, and true anomaly at infinity could not be found. Note that a value for "Eccentric Anomaly” is given in terms of degrees. The calculated value of Hyperbolic Anomaly was H = -1.455240. Though, this is not an angle, if we were to mistakenly treat it as an angle given in radians and then convert it to degrees we would get —83.36911 deg., exactly as the Astrogator output lists for "Eccentric Anomaly.” Since the value is actually the Hyperbolic Anomaly and not the Eccentric (which does not really exist in this case) and since it should not be listed as an angle in degrees but rather as a dimensionless quantity, then Astrogator is in error in the way in which it reports this value, though it appears it has nonetheless computed a correct value in some sense. Astrogator output does not list a 1700 value by that name. Instead it refers to the quantity as ”Excess Velocity.” That’s a standard term for the same thing. The terminology is indicative of the fact that it may be thought of as that velocity which is in excess of the amount necessary to escape at any given point since it can be shown that 2 __ 2 2 v — 17esc'ape + ”on STK / Astrogator output from the New Hyperbola Propagator model used Mars_Point_Mass (Simple numerical twobody) Stopping Condition Information (Gregorian Date '.. I. 29 Oct 2010 08:23:16.493 [2455498.84949645]: Stopped on: R Magnitude; Run Sequence STOP UTC Gregorian Date: 29 Oct 2010 08:23:16.493 UTC Julian Date: 2455498.84949645 Julian Ephemeris Date. 2455498. 85026247 Time past epoch: 2.1236e+006 sec (Epoch in UTC Gregorian Date: 4 Oct 2010 18:30:00.000) State Vector in Coordinate System: Mars Inertial Parameter Set Type: Keplerian sma: —1.6515083633450835e+006 km RAAN: 0 deg ecc: 1.0027830255674237 w: 359.9999999999823 deg inc: 0 deg TA: 171.1316118847977 deg Parameter Set Type: Spherical Right Asc: 171.1316118847799 deg Horiz. FPA: 86.59240087335036 deg Decl: 0 de- Azimuth: 90 deg Mean Anom: 11.80388354966251 deg Long Peri: neg Arg. Lat: 171.13161188478 deg True Long: 171.13161188478 deg Vert FPA: 3.407599126649435 deg Ang. Mom: 19855.54080007465 kmAZ/sec p: 9205.1713142896660000 km C3: 0.02593288223774801 kmA2/sec“2 Energy: 0.012966441118874 kmA2/secA2 ‘ . : 0 de Vel. Peri: 4.3200000000129890 km sec Excess Vel: 0.1610368971315208 km/sec 'c.l' " 3 sec 4596.1900000034602000 km Time Past PeriapSls: The highlighted quantities verify that for the given rp and vp, the expected 1700 (listed as Excess Vel.) is achieved. Also note that propagation out to R=1000000 km produces the expected time past periapse and Hyperbolic Anomaly H = 1.047809, though here Astorgator incorrectly states the Hyperbolic Anomaly quantity is the Eccentric Anomaly and gives it as 1.047809*(18O deg/n rad)=60.035044 deg. Green: Original Blue: New, after periapsis misfiring ...
View Full Document

{[ snackBarMessage ]}