Ukudluliswa kuka-Hohmann: ukushintsha ama-orbit

Lapha imithetho ethakazelisayo yokundiza kwe-orbit: ukufinyelela phezulu uhamba kancane, futhi uhambe phezulu uhamba ngokushesha, ngemuva kwalokho uphela uhamba kancane. UWalter Hohmann, umnjiniyela waseJalimane wedolobha, wasebenza ngo-1925 indlela elula kakhulu yokuzulazula phakathi kwezinkanyezi ezimbili ezijikelezayo. Kuyinto encane kakhulu.

Ukhawulela ukunyuka, futhi ufika ngokucophelela kunalokho okwenzekile.

Bona

1. Bhekisa 1, phambili. Isivinini esingeziwe asikwenza isibhakabhaka sihambe ngokushesha kakhulu ngaso lonke ikhanda: liwumisa uhlangothi lwekhanda libe yi-ellipsis. Ingxenye ephansi ihlala lapho umlilo usuvele ukhona khona; ingxenye esenyakatho ikhuphuka iye kuphakame okuzofinyelelwa kulo.
2. Isiqhingi. Ingxenye ye-orbit ngaphandle kwenjini. I-satellite ikhuphuka futhi, njengebhola elithunyelwe phezulu, ihamba kancane njengoba ihamba.
3. Bhala 2, uqhubekele phambili futhi. Ephezulu manje kunzima kakhulu ukuhlala khona futhi kuzobuyela emuva. Ukucindezela okulandelayo kwenza i-orbit ibe yi-circular kuphakame okutsha.

Kusuka ku-300 km kuya e-geostationary orbit, izidleke ezimbili zihlanganisa cishe 3.9 km/s, futhi indiza ithatha cishe 5 amahora 17 imizuzu.

Ukuqonda

Isivinini kunoma yisiphi isiqephu se-orbit sivela e-vis-viva: v = √(μ(2/r − 1/a)). I-Hohmann transfer ellipse ithinta izingqimba zombili, ngakho-ke umcibisholo wayo omkhulu ophakathi u_t = (r₁ + r₂)/2.

	Umzila (km)	Isivinini (km/s)
Ijikeleza ku-300 km	6,678	7.73
Ukudluliswa, indawo ephansi	6,678	10.15
Ukudlulisa, indawo ephezulu	42,164	1.61
I-geostationary	42,164	3.07

Umlilo 1 = 10.15 − 7.73 ≈ 2.43 km/s. Umlilo 2 = 3.07 − 1.61 ≈ 1.47 km/s. I-coast iyingxenye yesikhathi sokuguqulwa kwe-elips: π√(a_t³/μ) ≈ amahora angu-5.3.

(Izindiza ezihamba nge-geostationary zidinga futhi ukushintsha i-orbit’s tilt kusuka esiteshini sokuqala se-latitude kuya kwe-equator, okubiza kakhulu; ukuqala eduze kwe-equator kulondoloza isithako.)

Umphathi

Δv₁ = √(μ/r₁)·(√(2r₂/(r₁+r₂)) − 1),   Δv₂ = √(μ/r₂)·(1 − √(2r₁/(r₁+r₂)))

Ukulungiswa kwe-Hohmann kuyindlela encane yokulungiswa kwezingcindezi ezimbili phakathi kwama-orbit ajikelezayo, kuze kube yilapho i-r₂/r₁ < 11.94. Uma kuqhathaniswa nenani elifanayo, ukudluliswa kwe- bi-elliptic (ukulahleka okuthathu, ngaphezu ko target lokuqala) kuthatha isikhathi esincane Δv, ngentengo yesikhathi esiningi.

Ukudlidliza endaweni ephansi kuyindawo engcono kakhulu yokufaka amandla: Imiphumela emibi ithi Δv enikezwe ishintsha amandla okuhamba ngamandla lapho isithunywa sezulu sihamba ngokushesha kakhulu, ngoba Δε ≈ v·Δv.