PS6_Soln[1] - W A45 932 WM& WM fl Www/mpm WW 5 WWJR Wafer MA [email protected]/W 4:3,“:0, flame/My 4f 4&9 =e=oi(r= 2 PM/54 W Z/Whvw>M%MVW6

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Unformatted text preview: W/ A45 932 WM & WM»; fl Www/mpm WW 5 WWJR Wafer MA% dawn/M7 @Km/W): 4:3,“; @:0,§ flame/My -' 4f 4&9 =e=oi (r= 2%) PM (/54 W Z/Whvw%/>M%%MVW6 22M : __ V 1. 473,4: 9* w" 3 => mm W M; M 74" 7“ =0" €41 .. 7144‘/H~7’6wvm/fl W/cauw r,“ &6m 7/? /‘% I! m_/4W/N/W//‘/, M 17/12?“ /¢7V/Ué”%2m/z'/J 0M xéi 72mm 925/ % %/rx/ air/2’. [“9 < WM (fix: 854/.b/775” WWII/M (me/fi/m'yx'flha/ fl/ ___,.,—«—~. WV ,Z/e mid; 7553 2r" £ 9“ 5 2M. 9775’” Z) ff} % W (92‘ //§4/{1f5 9“: EM, L/77f" ,2 Why/M?) W %IX/7/7WI I": Co” = V'= fl/gir-éz) = é.4/r77fl Mg 2”” “(34344 = r imp?” m/ 9”” “212%?” W% asf'WW%M/W€ / m 2% m 05;? WV“ r=fPN=ZK+ 3;; W = Mme/é A4; 7 =0” (If/0330'»? (57¢ afl/mfw f/vz %‘; 0014; _ /—I—T“M"‘ / [Av/=74” +V' ’va'ws AT {In Q = v* MM AV Us 7 = 0wz— Iv-f- 15/1) ‘ZIWIAVI ,o<= Moo-Q (/AV/= 72,7// M}: o< = 73.57.?” K y [RE] Iqm.mwwm mom Iww.mmwu Qmo +\Io.oowommm Q0“ m Pg: xa\m mw.mom amo M M' M / / fl. MI: W W .M./0WW Mr W //%2 W #7.? fl M) face: 6%» fl /W an 0/ *W%~’ M IX X / /. s; 6min S g}. ax 74" i HM 7% ' 4 d / W fiA'Vne/M/r/S' Wu pg .5 ~ X ' 0 W WM 1‘- / 9 *1 I27 >0 <0 120 140 160 180 200 220 240 260 280 100 J V N C [Wu] IA VI 100 120 140 160 180 200 220 240 260 280 80 120 140 160 180 200 220 240 260 280 9 ' [deg] 100 80 r"= MW} :mwh Val/J: #34,- - 1a) = /.azs*7z by; 44w NKrV/ywvr’ WWW: 5’ ’ 0 (armba- néfi’) a * = V‘ * = r” = 79’772. 3 in r"= /‘*=75’77Z«3/M W; 7//“/,+'= 2.293979 ém/s V+=z9° a %W , \7- 721% )AW=Z\7*/‘/l7'/‘ MW”? ” w F o< : 0° @5/ iom :3 flow = 3. 30/Md 11%; = s 3,023? $04 ‘WW n/x/ : army? 4/ r) //~(} a,*’/“”= 1”: 39/912 M a+=0 39/912 kw 4H =1/j/i, + : 1/97/‘7’ ff 2: é/lé‘WM' => 00/301? , IKE/1.390275 k 5 (x: H.453" View in: iom Vamp. 3 Gwen [aka/wa M {/M flax/{*V/JW/ «24/64, M a cum Mxfld‘f 24m ,' C ‘K@ v ‘/§‘/ 5/; t, aiww‘ WW?) 4, 4,135, mama", {Ma Jim, .1 92‘ i0 (My) 92" = firYAWMnV‘ 5"”? ’Mfi) ’MWV 642W 93030:) 5135051)? r) fl 9;&MW~M~W&M-WMW »»»»»»»» ....._..M_\.. ___.._.".._4m.4.._._mum“..__«..__g“, § H 2‘ “i “i \A: Ni, NR§ Vi N‘ \A 2a 5 “5.3/777éh75‘ rp;a((,g) $//7flZ-éé4‘2 ‘ manna) :éjZf/QAM E z 4%” 457;”) r 1* (gay/“6;” ‘ ¢ - azaww (*c'z‘pF/gj’ (Ec'flS/flgc) : '5’e’&3,.§;gc = ~ /. S'za’ZZ/lp E / E g7: e 7220q3m =2a.asz75%r E = a E E c i 5) d W /r f A xwz/M ?%wrr. 5/4/44 fl W-w/anflc; 41/,” )C.‘ ,1, 7,6; .7 _ , I!“ F = h- My gm ’éthgh = fl (frvt'f) affix f’fl/wrén Mal/m = M? 3334ij W P wag-WNMM "w «WWW ,Auflmw.ww.mmwwnwfl‘_fl.,wW...” 27" “YA—«V “M” ) = 239/477“ WWWWMMwwww.mfimeWWmmwwmg R WQM //’L/jo¢£o¢ /’(Z’§)($WVM oi) {M A) W5 1% may" i? Mm UL}; f," = fiaJ/W/ ,4” VJ= 2,922“ #4 n"=3'$i/L/eza %f mi: 6% 3 " 35'— b‘fla‘z ’ '2‘ 1;, “f ‘ “fl/(Z ’ = W, /ég¢ y a” a = : ywm, 2,7- 65)“ "=/3‘7a/Z5 : 39,7311 4/ fink/$77 a?” 437.47%; 3 Am 7/ééi? 6" £4». a 030 f 8+) : - 017M“- * a I = 695 Ta”? 0) — map/M (W) 4 air = ziffié “7%”‘9 nun—u. usual-.— :83 H... on." 3.8 Hana-"8.98 1' «I! 26.8 non Egan... in 9.? Egg in 9.? Problem 3 e) The new orbit’s apoapse distance is over 91000 km. That’s fafinough that Luni-Solar perturbations may be significant. Using an STK propagator that includes point mass Earth Moon and Sun gravity models and comparing the resulting state after a revolution or two may prove enlightening in deciding how good our 2 body assumption is. State immediately after the maneuver: sma: 58166.8519429708030000 km RAAN: 0 deg ecc: 0.5764548676696663 w: 148.9491023156693 deg inc: 4.251582469653128e—015 deg TA: 128.1468142171284 deg Rad. Peri: 24636.2870034244990000 km Vel. Peri: 5.0503564503631972 km/sec Rad. Apo: 91697.4168825171070000 km Vel. Apo: 1.356876073621066 km/sec State after three periapse passages using the Sun + Earth + Moon model: sma: 58159 1174610350210000 km RAAN: 125.9238909873654 deg ecc: 0.5769286935017606 w: 23.03093385103763 deg inc: 0.04445498369534009 deg TA: 2.127346758410093e—008 deg Rad. Peri: 24605.4538090246530000 km vel. Peri: 5.0542791672048120 km/sec Rad. Apo: 91712.7811130453920000 km Vel. Apo: 1.356003286317135 km/sec A plot included here would show no difference from the previous plot, the changes are too small to easily visualize at the scale that shows the entire orbit Immediately after the maneuver, the inclination was zero, so actually RAAN and argument of periapse were not well defined. Yet, later on the inclination has changed. Granted, the original problem did not state what plane the orbit was in, but the point is that the plane arbitrarily chosen was the inertial XY plane and then after several revolutions, the perturbations have begun to pull the orbit out of its original plane (whatever it may have been). Also, some small changes have been made in orbit size and shape so that periapse has been lowered by 31 km and apoapse raised by 15 km. These may or may not seem significant in terms of the original orbit characteristics, yet over longer and longer periods such variations may increase. ® 3k H ‘B K S H M 3 9 g V. . .\§ \_, r = [email protected])/[I+ew€*‘) = 9M/ 2.4 ,1,” g = W‘Yg‘g = Zfifl-xqg" : ~ZXMJ” M —_ 1:”,é5mg = ~577ZJ§§9 =- 7mm?” = ~330,/,9[$;ec W + #70321“ 1/ = ’7,“ (Z/r ‘ ’m} 2 7-57747/1émfl = m" v/lMU-e‘) rv) 3 “427965” . WWW,“ gamma;anflfi.‘“wwwmmmw.” H Mae f (Cm. C9 ’5nC/59))4< 4‘ (551C; “ CnC/Jg); 4' 5/59; 9 = (1,159 111069)»? 4' (4mg + CozC/Cg); + and WWymwwww Wmmmmmmfiw;W».WWMWWW,W~WMWWwwmmflmwmwmv w.wa MK 26 ,fi A». 4510.73»? » $7122 ; ~9320.é3 :3 fl» W\ n u gammymmwxmmm { : ~73 may 7% f + 7. gram/é mg &.?Z(o?39£ I 0,/$'47zz;> « ZL/mw 2 16% an 'S—rx: 1L) AV 5 “WV?” ’> ¢= “+2’= [7/fl.72€}fo fl 2 +300 1» 417 A17: AV(Op5¢ I5" 4' apt—4:5 4— 5/52,) AV = 0,427”in f 437577 é #4 A ’11,; M W/h’ 2/1””; {fl/‘f/g/Xflll/Alf A [(1449 $5.315; X ’CAS; y" + C)? LWMMJL §K WMWW;; «3 [017 = age/57¢“? «9453751; —4905’;=/z é /+ .- V gr”? = 7‘! 372200’)? —/./zm;29y" 4.707497% [pk/5 m i. u 3 n i w “9 P \9 sq, k3 \ ~‘J “1 \n >0 N N \x i \b :3 § m u x» V“ Q3 ,"\ \ ~N _R é‘n» I“ = 11"} W =wa /m w =117+/ = 3,3312??? my; @75 V'F=*/0’7’ >0 my 7”; m“ ( $3.7 ) = 0J7FL/7" .1 A+ '~ A“ ram , 4 Wm»; = azmwkwMY/O’?WWW“ (n+9 ‘ U ‘ _\ N , ( 3.; >~‘§\N 2 4:1 I' n §~\A $8“ w§ SQ: K“ 0x3 A, , fl" 3“ 4’7"” w "MW } f .y .9 = A“; —> J2 = 129‘. 571/0 2 = fvé «r 9” 4/2/3720 0, 229.17%”J ’9+=—/3/.;7427° ; 9+' 9,)”- : -/33’ ?L/?9 W: 4- w M 7. 9’ h» z e*-€, " 02””: = 1+ ,L- = ~Z. 572W” 9 ‘ flu “Q = fl 4. 32892 a" = ar— 0 :~’1?C{?Z§D z €+fl 0 : ’ngéryéjp 5 i WmvM“,WWWMNN.WWW,“WWWWWWNMWW WWW mm M ,, __ ,. _, i g E E Problem 4 d) From the STK/Astrogator maneuver summary: Astrogator MCS Segment Summary Astrogator MCS Maneuver Summary DeltaV vector with respect to Earth J2000 axes: X: 0.6455563944729605 km/sec Y: —0.9633579004505282 km/sec Z: -O.3085425370911121 km/sec Azimuth: —56.17353919564506 deg Elevation: —14.89916922511487 deg Magnitude: 1.199999999999999 km/sec State Vector in Coordinate System: Earth J2000 Parameter Set Type: Cartesian x: —3500.9780019654509000 km vx: 6.7267382408867711 km/sec Y: —7599.2252702991045000 km vy: —0.1567218213762097 km/sec Z: —4830.6324773768929000 km Vz: —3.4990952794242363 km/sec Parameter Set Type: Keplerian sma: 15945.3499999715500000 km RAAN: 30.00000832815135 deg ecc: 0.3999999999993747 w: 239.9999882248199 deg inc: 45.00000200562691 deg TA: 344.9999970985265 deg Parameter Set Type: Spherical Horiz. EPA: —4.270653729293734 deg IRI: 9661.2670913543698000 km |V|: 7.5840119241199044 km/sec other Elliptic Orbit Parameters . Ecc. Anom: 350.1480651437454 deg Mean Anom: 354.0694487195192 deg Time Past Periapsis: 19708.24802527709 sec Satellite State at End of Segment: 1905+”4V State vector in Coordinate System: Earth J2000 Parameter Set Type: Cartesian X: -3500.9780019654509000 km Vx: 7.3722946353597321 km/sec Y: —7599.2252702991045000 km Vy: —1.1200797218267384 km/sec Z: —4830.6324773768929000 km Vz: —3.8076378165153479 km/sec Parameter Set Type: Keplerian sma: 32114.8032305598060000 km RAAN: 25.67108194561948 deg ecc: 0.6992316369895842 w: 226.2527027987534 deg inc: 42.17290332160273 deg TA: 1.884538321115084 deg other Elliptic Orbit Parameters . Arg. Lat: 228.1372411198685 deg new WW um um é— flv‘fwéy MM ‘ Md! The two orbits before and after the maneuver are in very nearly the same plane: mam: ...
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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 University-West Lafayette.

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PS6_Soln[1] - W A45 932 WM& WM fl Www/mpm WW 5 WWJR Wafer MA [email protected]/W 4:3,“:0, flame/My 4f 4&9 =e=oi(r= 2 PM/54 W Z/Whvw>M%MVW6

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