MAE 4410: Fundamentals of Astrodynamics Exam #1 Part A: 60 pts Due: 1905, February 21 st, 2012

Transcription

1 MAE 440: Fundmntls of Astodynmics Exm # Pt A: 60 ts Du: 905, Fuy st, 0 Cicl th ll of th coct nsws, fill in ll lnks, o ifly nsw ch qustion. I. (5ts) List th 5 ssumtions usd in diving th stictd two-ody qution of motion nd susquntly th tjctoy qution: II. (5ts) Th sc vlocity fo 00 km Mcuin oit is: III. (t) Kl s nd lw stiults tht th lin joining th sun nd th lnt sws out qul in qul IV. (ts) Ths mts constnt thoughout n ity oit of sccft:. Altitud. Vlocity c. Mchnicl ngy d. Flight th ngl. Angul momntum f. Tu nomly g. Position V. (ts) Th tnsf tim fo Hohmnn tnsf twn two cicul oits is qul to:. th iod of th lg cicul oit. th iod of n lliticl oit with qul to hlf th sum of th cicul dii c. th iod of th smll cicul oit d. hlf th iod of n lliticl oit with qul to hlf th sum of th cicul dii. th iod of n lliticl oit with qul to th sum of th cicul dii VI. (ts) Which of th following oits hs th most scific mchnicl ngy:. A cicul oit ound Eth with n ltitud of 00 km. An lliticl oit ound Eth with mjo xis qul to 4,4 km c. A cicul oit ound Pluto with dius of 4,4 km d. An lliticl oit ound Juit with smi mjo xis qul to 4,4 km. A cicul oit ound Eth with dius of 4,4 km

2 VII. (ts) Th Univsl Gvittionl Constnt is qul to: 6.674x0 - m 3 kg - s -. Clcult th foc of gvity twn two 000 kg sccft std y km. VIII. (ts) In od to tnsf fom on oit to noth, wht ky lmnt is quid of th two oits? IX. (ts) Which of th following is not chctistic of o duing hyolic oit:. Th tuning ngl, δ. Th symtot ngl, ρ c. Th hyolic xcss ngl, d. Th tu nomly t infinity, θ. Th flight th ngl, β X. (t) Kl s st lw stiults tht th oits of th lnts in th sh of (n) with th sun t (n)(th) XI. (ts) Stllit A is 000 kg nd stllit B is 000 kg. If oth stllits in 00 km cicul oits ound Eth, wht is th tio of th iod of stllit A s oit to tht of stllit B s? XII. (ts) Wht is th lin momntum of 000 kg sccft tvlling t 8 km/s? Wht is th ngul momntum of this sccft if th tjctoy is cicl of dius 0,000 km?

3 XIII. (ts) In th tingl low, giv th ltions fo: sin(θ), cos(θ), tn(θ), sc(θ), csc(θ), nd cot(θ). XIV. (ts) Wht is th scific mchnicl ngy of sccft in 0,000 km ltitud cicul oit ound Ntun? XV. (ts) Wht, if ny, is th significnc of ch of th following sttmnts (individully): uv i = 0 u v = 0 XVI. XVII. (t) Accoding to Nwton s nd lw, Foc is qul to th tim t of chng of (ts) If I ws to clcult th oit of th lnt Mcuy which vlu of th stndd gvittionl mt, μ would I us?

4 XVIII. (ts) If I ws to clcult th oit of th lnt Juit which vlu of th stndd gvittionl mt, μ would I us? XIX. (ts) How mny volutions dos th th mk in y, i.. how mny tims dos th th ott though 360 in th intil fnc fm? XX. (ts) Fo which conic sctions is th following two qutions vlid: μ ε = μ μ v = XXI. (5ts) List th fou conic sctions nd thi ngs/vlus of ccnticitis, ngis, nd smi-mjo xs: Conic Sction Eccnticity Engy Smi-mjo Axis XXII. (ts) Wht is th gumnt of isis if fstst oint of you oit hns t th scnding nod?

5 XXIII. (ts) Wht dfins th (ngl) tu nomly of sccft in n oit nd fo this clss wht is its symol. XXIV. (ts) Wht dfins th (ngl) inclintion of n oit nd fo this clss wht is its symol. XXV. (ts) In od to fom siml ln chng nd ott you ight scnsion of th scnding nod, wht ty of oit must you in? XXVI. (ts) How mny uns fomd in i-llitic tnsf, wh thy loctd, nd in wht diction is th dlt v vcto?

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7 MAE 440: Fundmntls of Astodynmics Exm # Pt B: 00 ts Du: 905, Fuy st, 0 Fo ch olm, list ll of you ssumtions nd show you wok.. (75ts) Assum sccft is in givn oit such tht its gocntic qutoil osition nd vlocity vctos givn low. Now ssum tht th sccft mnuvs such tht it ccomlishd 30 inclintion duction nd nlgs th oit to nly cicul ccnticity of 0.0. Giv th COEs immditly ft th un. Assum tht th mission commnd is doing minimum Δv singl un to gt fom his cunt oit to his dsid. Wht is th Δv of th mnuv? Body Cntic (IJK) Position [km] = Body Cntic (IJK) Vlocity [km/s] =

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9 . (5ts) Th Sc Shuttl oits th th in out 90 minuts. In fct, low-ltitud oit ound Mcuy nd Vnus is lso out 90 min. Evn low-ltitud oit ound Ms is clos to ½ hous. Why ths oit iods ll out th sm?

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11 3. (5ts) Wht is th Δv nd tnsf tim quid to is stllit fom 000 km qutoil oit to sttiony oit ound Vnus using Hohmnn tnsf?

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13 4. (75ts) Aft ys of witing, you y of sccft hs finlly ivd ound Ntun. Th lnty instion tm ots th vlocity t th sh of influnc (infinity) s.7475 km/s nd th imct mt s km. Should this ot woy you? If nothing is don, how much will th tjctoy of th sccft dflctd y Stun? You ultimtly wish to in cicul oit with n ltitud of.5 lnty dii. You hv 3.5 km/s of ful onod; ssum tht to nt this oit two mnuvs fomd, on t infinity nd on to ciculiz th oit. Is th nough ful on od?

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15 Symol Constnt Vlu Units Rf. G Univsl Gvittionl Constnt (67)x0 - m 3 kg - s - () μ L Gvittionl Pmt Eth (8) km 3 s - () μ s Gvittionl Pmt Sun 3.74 x0 9 km 3 s - () c 0 Sd of Light in Vcuum m s - (3) u Astonomicl Unit (30) x0 M (3) Minut (tim) 60 S (3) Hou (tim) S (3) Dy - Sol(tim) S (3) ( ) ( ) ( ) ( ) ( )

16 MERCURY VENUS EARTH MARS JUPITER SATURN URANUS NEPTUNE PLUTO SUN Mss (0 4 kg) ,989,00 µ (0 6 km 3 /s ) ,7 Equtoil Dimt (km) 4879,04, ,984 0,536 5,8 49, ,000 Dnsity (kg/m 3 ) Sufc Gvity (m/s ) Smi-Mjo Axis (0 6 km) N.A. Oitl Eccnticity N.A. Oitl Inclintion (dgs) N.A. Oitl Piod (dys) ,747 30,589 59,800 90,588 N.A. Pihlion (0 6 km) N.A. Ahlion (0 6 km) N.A. Avg. Oitl Vlocity (km/s) N.A. Esc Vlocity (km/s) Rottion Piod (hous) Lngth of Dy (hous) N.A. Axil Tilt (dgs)