Hohmann amasintha: kusintha kwa orbits

Munkhaniyi tikambirana za malamulo osiyana kwambiri a ndege yoyenda pa orbit: kuti upite patsogolo, umathamanga, ndipo kuti upite pamwamba, umathamanga, kenako umathamanga. Walter Hohmann, a German city engineer, worked out in 1925 the cheapest way to move between two circular orbits. Zina mwa satellites za ku orbit ya satellite zimagwiritsa ntchito ma satellites a GNSS.

Kufulumira mpaka kugwa, ndipo inu kufika mofulumira kuposa inu anasiya.

Onani

1. Burn 1, forwards. Kuthamanga kwapaderaku sikungapangitse kuti satellite ipite mofulumira kwambiri m’mphepete mwake: kumatenga m’mphepete mwake kukhala elipse. M’mbali ya nyanja, kuwala kwa dzuwa kumatsika kwambiri; kuwala kwa mwezi kumakwera kwambiri.
2. Coast. Half an orbit ndi palibe injini. Sateliti imakwera ndipo, monga mpira wothamanga, imakhala yofulumira ngati ikuyenda.
3. Burn 2, forwards again. Pamwamba pano ndi pang’onopang’ono kwambiri kuti ikhalepo ndipo ingawonongekenso. Kuthamanga kwachiwiri kumachititsa kuti orbit ikhale yozungulira pa kutalika koyamba.

Kuchokera pa 300 km mpaka ku orbit ya geostationary, ma burns awiri amawonjezera mpaka pafupifupi 3.9 km/s, ndipo ulendowu umatenga pafupifupi 5 hours 17 minutes.

Kumvetsa

Kutalika kwa mtunda pakati pa mapiri ndi dziko lapansi kumawerengedwa ndi mfundo ya: v = (1 − r)/2. A Hohmann transfer ellipse touches both circles, so its semi-major axis is a_t = (r₁ + r₂)/2.

	Kutalika (km)	Kuthamanga (km / s)
Chigawo pa 300 km	6,678	7.73
Kusinthanitsa, pansi pa gawo	6,678	10.15
Kusinthanitsa, phokoso lalikulu	42,164	1.61
Kuzungulira, geostationary	42,164	3.07

Kutentha 1 = 10.15 − 7.73 ≈ 2.43 km/s. Kutentha 2 = 3.07 − 1.61 ≈ 1.47 km/s. M’madera ena, nthawi ya kuwala kwa mwezi ndi pafupifupi maola 5.3 (omwe ndi nthawi yotentha kwambiri).

(Malo ozungulira mapiri a ku Africa amatchedwa mapiri a nyanja, ndipo malo omwe ali pafupi ndi nyanja amatchedwa mapiri a m’mphepete mwa nyanja.)

Woyang’anira

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

The Hohmann transfer is the minimum two-impulse transfer between coplanar circular orbits, as long as r₂/r₁ < 11.94. Kuposa kuti khalidwe a bi-elliptic kutengerapo (maphikidwe atatu, kupita patsogolo pazolinga zayamba) mtengo wapatali Δv, pa mtengo wa nthawi zambiri.

Kutentha pamalo otsika ndi malo abwino kwambiri kuti muwonjezere mphamvu: Oberth zotsatira Malinga ndi lamulo la Newton, mphamvu yamagetsi yozungulira dziko lapansi imasintha kwambiri pamene chowombera chimayenda mofulumira kwambiri.