Hohmann transfers: ngowahi orbit

Dina orbit ieu, éta bakal ngaleuwihan laju angin anu dihasilkeun ku pesawat, sareng dina waktos anu sami, éta bakal ngaleuwihan kecepatan angin. Walter Hohmann, insinyur kota Jerman, ngarancang dina taun 1925 cara anu paling murah pikeun pindah antara dua orbit bulat. Saben satelit ing orbit geostasioner bisa digawé nganggo idené.

Nalika lajeng katarik, éta bakal ngaleuwihan lajuna.

Lihat

1. Burn 1, forwards. Kacepetan tambahan ora ndadekake satelit luwih cepet ing sakiwa-tengené lingkaran: iku ngencengi lingkaran dadi elips. Titik paling handap tetep di mana kebakaran lumangsung; sisi jauh naék ka tingkat target.
2. Coast. Setengah orbit tanpa mesin. Satelit naek, sarta, saperti bal anu dicokot, naék nalika ngaleuwihan.
3. Burn 2, forwards again. Di luhureun éta ayeuna teuing lambat pikeun tetep di dieu sarta bakal turun deui. Saben orbit iki diwiwiti saka titik paling dhuwur ing orbit.

Saka 300 km kanggo orbit geostasioner loro burns tambah nganti kira-kira 3.9 km/s, lan perjalanan njupuk sekitar 5 jam 17 menit.

Ngerti

Kecepatan ing titik-titik orbit asale saka vis-viva: v = √(μ(2/r − 1/a)). Sacara umum, sumbu semi-mayor ellips Hohmann nyambung ka dua lingkaran, jadi a_t = (r₁ + r₂)/2.

	Radius (km)	Cepat (km/s)
Circular ing 300 km	6,678	7.73
Transfer, titik ngisor	6,678	10.15
Transfer, titik dhuwur	42,164	1.61
Bunder, geostasioner	42,164	3.07

Burn 1 = 10.15 − 7.73 ≈ 2.43 km/s. Burn 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.

(Saben titik dina orbit bumi diwangun ku sababaraha lapisan, anu disebut lapisan luar; lapisan jerona diwangun ku lapisan jero.)

Master

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. Luwih saka rasio iku a bi-elips transfer (tilu burns, ngaliwatan target kahiji) biaya kirang Δv, dina harga leuwih loba waktu.

Burning at the low point is also the most efficient place to add energy: the Oberth effect says a given Δv changes the orbital energy most where the spacecraft is moving fastest, because Δε ≈ v·Δv.