Iindawo zokutshintshiselana ngeeHohmann: ukutshintsha iimijikelezo

Apha kukho imithetho enomdla kakhulu yokuhamba ngenqwelo-moya: ukutsala ukhawuleze, kwaye ukuba uhambe phezulu ukhawuleze, emva koko uphele uhambe phantsi. UWalter Hohmann, umyili waseJamani wedolophu, wasebenza ngo1925 indlela ekhawulezayo yokuqhuba phakathi kweendawo ezimbini ezijikelezayo. Imalunga nesatellite nganye ekwi orbit yendawo ehlala kuyo i-geostationary yafika apho isebenzisa le mbono.

Yiya phezulu ukunyuka, kwaye ufike ngokucothayo kunokuba washiya.

Bona

1. Gcina 1, phambili. Isantya esithe nkqo asiyi kwenza i-satellite ihambe ngokukhawuleza ngaphezulu kojikelezo lwayo: iphakamisa ujikelezo lube yi elipsis. Inqanaba eliphantsi lihlala apho ukutshisa kwenzeke khona; icala elincinane linyuka ukuya kwinqanaba elifanelekileyo lobude.
2. Ilwandle. Ingxenye ye orbit ngaphandle kwenjini. I-satellite inyuka kwaye, njengebhola eqhutywa phezulu, ihamba ngokucothayo njengoko ihamba.
3. Gcina 2, iqhubekeka phambili kwakhona. Kwisiphelo sendlela ngoku iyacotha kakhulu ukuba ihlale apho kwaye izakubuyela umva. Uxinzelelo lwesibini lusenza i-orbit ijikeleze kwinqanaba elitsha lobude.

From 300 km to geostationary orbit the two burns add up to about 3.9 km/s, and the trip takes about 5 hours 17 minutes.

Ukuqonda

Isantya kwindawo naliphi na le orbit ivela kwi-vis-viva: v = √ (μ(2/r − 1/a)). I-Hohmann transfer ellipse iqhatha zonke izijikelezi, ngoko ke umgca wayo ophakathi mkhulu yi a_t = (r₁ + r₂)/2.

	Umda (km)	Isantya (km/ s)
Ijikeleza kwi 300 km	6,678	7.73
Unikezelo, incopho ephantsi	6,678	10.15
Unikezelo, incopho ephezulu	42,164	1.61
Ijikelezayo, 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. Ilwandle liphesenti yexesha lokudlulisela i-ellipsis: π√(a_t³/μ) ≈ iiyure ezili-5.3.

(Izithuthi ezihlala zijikeleza ihlabathi kufuneka zitshintshe ubukhulu bendawo ejikelezayo ukusuka kwilayini ye latitude ukuya kwi-equator, oku kuthatha ixesha elide; ukuthutha kufutshane ne-equator kukhusela ifuthe.)

Umphathi

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

Uthutho lweHohmann luyimfuneko yothutho olunoxinzelelo olubini phakathi kweendawo ezijikelezayo zeplanethi, kude kube r₂/r₁ < 11.94. Ngapha koko uthelekiso bi-elliptic lokudlulisa (ukutshisa okuthathu, ukudlula kwinjongo yokuqala) iindleko ezincinci Δv, ngexabiso lexesha elininzi.

Ukutshisa kwindawo ephantsi kulapho kusebenza khona kakuhle ukudibanisa amandla: i-Oberth effect ithetha ukuba u-Δv onikezelwe utshintsha amandla okujikeleza kakhulu apho inqanawa yendawo yokuhamba ngokukhawuleza, kuba Δ ≈ v·Δv.