Hohmann kutumira: kuchinja orbits

Heano muenzaniso wechirevo chinokosha chekufamba mumigwagwa: kuti uwane mukana unoramba uchinonoka, uye kuti uende kumusoro unoenderera mberi, mushure meizvozvo unotanga kunonoka. Walter Hohmann, muEngineer weguta reGermany, akawana mu1925 nzira yakachipa yekufambisa pakati pezviviri zvemaorbit. Anenge ese ma satellites ari mugeostationary orbit akasvika pano achishandisa chirongwa chake.

Kukurumidza kusvika kukwira, uye iwe unosvika zvakaoma kupfuura wakanga wakasiya.

Ona

1. Burn 1, forwards. Iyo yakakura kupfuura iyo yekutanga simba haiite kuti saiti iende nekukurumidza pamusoro pechiso chake: inosimudza chiso kuita ellipse. Iyo yakaderera nzvimbo inogara panzvimbo iyo burn yakaitwa; iyo yakadzika-pasi inobva yakwira kusvika pakusvika kwechinangwa.
2. Kubva panzvimbo. Half an orbit without engine. Satellite inokwira uye, sebhola rakasviba, inononoka sezvairi kuenda.
3. Burn 2, forwards again. Pamusoro pechidzitiro ichi, zvino iri nyore kugara pano uye ichadzokera kumashure. A yekutanga kumanikidza inoita orbit circular patsva hurefu.

Kubva pa300 km kusvika kugeostationary orbit, zviviri izvi zvinowedzera kusvika pamamiriyoni mashanu emadhora. 3.9 km/s, uye chitima chinotora pamusoro 5 hours 17 minutes.

_Zvinyorwa

Kufamba kwechiedza kunogona kutaurwa sezvimiro zvemasimba emagetsi: v = √(μ(2/r − 1/a)). Hohmann transfer ellipse inobatawo macircles maviri, saka iyo semi-makuru axis i a_t = (r₁ + r₂)/2.

	Radius (km)	Speed (km/s)
Circular pa 300 km	6,678	7.73
Kutumira, pasi penzvimbo	6,678	10.15
Kutumira, yakakwira point	42,164	1.61
Geostationary	42,164	3.07

Burn 1 = 10.15 − 7.73 ≈ 2.43 km/s. Kupisa 2 = 3.07 − 1.61 ≈ 1.47 km/s. The coast is half the transfer ellipse’s period: π√(a_t³/μ) ≈ 5.3 hours.

(Zvinoitika kuti ma satellite anotanga kutenderera panyika achibva panzvimbo yekutanga anofanirawo kusarudza nzvimbo yekutanga, izvo zvinoda mari yakawanda.

Munyori

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

Hohmann kushandura ndeimwe yezvishoma zviviri-impulse kushandura pakati pe coplanar circular orbits, sezvar₂/r₁ < 11.94. Pashure peiyo ratio a bi-elliptic kushandura (matanhatu burns, kuenda kunze kwetarget yekutanga) inodhura zvishoma Δv, pamitengo yenguva yakawanda.

Kupisa panzvimbo yakaderera ndiyo nzvimbo ine simba kwazvo yekuwedzera simba: Oberth effect inoti Δv inochinja zvakanyanya orbital energy apo chikepe chepasi chiri kufamba nekukurumidza, nekuti Δε ≈ v·Δv.