Ukufaka i-orbit: ukuqwalaselwa

Ngomhla we-10 kuMatshi 2006, emva kweenyanga ezisibhozo kwisithuba, i NASA’s Mars Reconnaissance Orbiter yatyhila iinjini zayo ezine ezinkulu zemizuzu engama-27. Kwinxalenye yexesha yayisemva kweMars, ngaphandle koqhagamshelwano lweradiyo: akukho mntu emhlabeni owaziyo ukuba yasebenza na. Ukuba ukutshisa kwakungaphumelelanga, inqwelo-moya iya kuba ifile ngaphezu kweMars kwaye ifike kwindlela engapheliyo ejikeleza ilanga.

Ukufika akuyonto ilungileyo. Kufuneka uthathelwe ingqalelo.

Bona

Iinqanawa zokuhamba ngenqwelo-moya aziyi “kuyeka” kwiplanethi. Iwela kuyo, ihamba ngokukhawuleza njengoko ifika phezulu, kwigophe elivulekileyo elibizwa ngokuba yi hyperbola. Ishiyeka isolo, iya kutyhala ijikeleze iplanethi kwaye ikhuphe kude kwakhona, ngokukhawuleza njengoko yafika.

Ukuhlala, kufuneka ilahle isixa-mali kwimo yexesha elifanelekileyo, indlela efutshane:

1. Ukufumana umlilo. Iinjini zityhila ngokuchasene nendlela yenkqubela phambili. Umlilo ophantsi uguqula igophe elivuliweyo libe lide, livale elilipse.
2. Ukukhawuleza kwenqwelo-moya. Ngelixa ukutshaya ifuthe elininzi, abalawuli bakhupha indawo ephantsi ye orbit kwinqanaba elincinci phezulu kwimozulu. Iintsuku zonke, uxinzelelo oluncinci lwemoya lukhawulezisa inqanawa yenqwelomoya kwaye indawo ephezulu ihla.
3. I-orbit yesayensi. Emva kwamawaka eentsuku ezidlulayo ngaphezulu kweenyanga ezintlanu, iMRO yafikelela kwinqanaba eliphantsi, elijikelezayo elimalunga ne-250 nge-316 km phezulu, kwaye yaqala ukudwelisa iMaphu yeMars.

Ukuqonda

Ukusuka eMhlabeni kwindlela efana neHohmann, inqwelo-moya ifika eMars malunga 2.65 km/s ihamba ngaphantsi kweMars. Kusuka kwindawo yokujonga yeMars leyo yi “santya esingenakuphela”, v∞. Ihla ukuya kwi-426 km phezulu komphezulu, ihamba ngokukhawuleza ukuya

v = √(v∞² + 2μ/r) = √(2.65² + 2 × 42,828 / 3,822) ≈ 5.4 km/s

Kwi-ellipse ukusuka kwi-426 km ukuya kwi-44,500 km, isantya kwisiqithi esiphantsi kufuneka sibe yi-4.56 km/s (vis-viva). Ilungele, ukufakelwa okukhawulezayo kokutshisa ngoko kumalunga ne 0.87 km/s. Imizuzu engama-27 yokutshisa incinci kakhulu ngenxa yokuba iyasasazeka ngaphaya kwegophe; MRO’s yakhawuleza inqanawa yendawo engaphandle nge 1 km/s.

Ukutsala ngokuthe ngqo kwi orbit ephantsi ejikelezayo kuya kubiza malunga ne 2 km/s (bona uPhinda). Ukumisa ngenqwelo-moya kukhusela uninzi lwesiphelo, kwaye ifuthe eligcinwe liyinxalenye yenqwelo-moya kunye nesayensi.

Umphathi

I-hyperbola ine-semi-major axis a = −μ/v∞² kunye ne-excentricity e = 1 + r_p v∞²/μ. Ixesha lokuhamba ukusuka kude ukuya kwi-periapsis limiselwe yi-hyperbolic Kepler equation M = e sinh F − F.

Ukuqwalaselwa Δv kwi-periapsis r_p kwi-ellipsis ene-apoapsis r_a yi

Δv = √(v∞² + 2μ/r_p) − √(2μ r_a / (r_p (r_p + r_a)))

encinci kakhulu kwi-ellipsis ende kakhulu (r_a → enkulu): iinqanawa zesithuba zinzima ukuqwalaselwa. Le nto ibangela ukuba izithuthi ziqale zingene kwimo ye-orbit ekhululekileyo, kwaye kutheni ukutshisa ngemoto okanye umlilo omncinci olandelayo. Kwimisitho yeMars eqhutywa ngumqhubi, ukubamba ngenqwelo-moya (ukudlula okunzulu olunye kwimozulu ngasemva kwesikhuselo sobushushu) kungatshintsha ukubetha ngokugqithiseleyo.