Hohmann transfers: na-agbanwe orbits

Ebe a bụ iwu nke dị iche iche nke ụgbọelu orbital: iji hụ na ị na-akwụsịla, ma ọ bụ ka ị gaa elu ị ga-agba ọsọ, mgbe ahụ ị ga-aga n’ihu na-akwụsịla. Walter Hohmann, onye injinia obodo German, rụrụ ọrụ na 1925 n’ụzọ dị ọnụ ala iji gaa n’etiti orbits abụọ. O doro anya na ihe niile dị n’eluigwe bụ ihe ndị a kpọrọ ihe.

Nnọọ n’elu ka ịga elu, na ị ga-abịakwute n’ụzọ dị mgbagwoju anya karịa ka ị nọchiri.

Nlegharị anya

1. Bọ̀rọ̀ 1, n’ihu. Oge okporo ụzọ nke ọzọ anaghị eme ka saịtịlụ gaa n’ụzọ ngwa ngwa n’ụdị ellipse ya: ọ na-akpụgharị ellipse ahụ n’ime elupụ. N’ebe ala nke ebe ọbụla ebe ọbụla ebe ọbụla ebe ọbụla ebe ọbụla ebe ọbụla ebe ọbụla ebe ọbụla ebe ọbụla ebe ọbụla ebe ọbụla ebe a na-edebe ya.
2. Coast. N’elu ala nke orbit na-enweghị engine. Saịtịlaịt na-agbago ma, dị ka bọl a kpụgaara elu, na-akwụsịla dịka ọ ga-aga.
3. Banye 2, na-aga n’ihu ọzọ. Na elu ọ bụ oge a dị ngwa karịa ka o bido ebe ahụ ma ga-apụ azụ. Pịa nke abụọ na-eme ka orbit kpụga n’elu ọfụụ.

Site na 300 km ruo geostationary orbit ndị abụọ na-ebu ibu ruru ihe dịka 3.9 km/s, na njem ahụ dị ihe dịka 5 awa 17 nkeji.

Mara

N’ebe ọ bụla n’ime orbit, ọsọ na-abịa site na vis-viva: v = √(μ(2/r − 1/a)). Hohmann transfer ellipse na-adọta etiti abụọ ahụ, yabụ axis nke ya bụ a_t = (r₁ + r₂)/2.

	Radius (km)	Nhazi
Oge 300 km	6,678	7.73
Ntụgharị, ebe ala	6,678	10.15
Kpụga, n’elu	42,164	1.61
Oge	42,164	3.07

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

(N’ihi na ọ bụ ihe dị mkpa ka a gbanwee ntụgharị orbit site na latitude nke ebe a na-adọta gaa na equator, nke nwere ọnụ ahịa karịa; ịmalitegharị nso na equator na-echekwa mmanụ.)

Onyenwe

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

N’ihe banyere ntụgharị Hohmann, ọ bụ ihe dị ala nke abụọ-impulse transfer n’etiti coplanar circular orbits, ka ogologo dị ka r₂/r₁ < 11.94. N’ebe dị anya nke ahụ ratio a bi-elliptic transfer (ọbara atọ, na-aga n’ihu ihe mbụ) nwere ọnụ ahịa dị ala Δv, na ọnụahịa nke oge dị ukwuu.

Ọrụ na-agbanye n’okpuru ebe ahụ bụkwa ebe kachasị mma iji tinye ike: Obụla mmetụta Na-ekwu na Δv a ga-enye gbanwere ike orbital kasị ukwuu ebe spaceship na-aga n’ihu ngwa ngwa, n’ihi na Δε ≈ v·Δv.