Àwọn ìjánu-ìṣàfarawé Hohmann: àwọn ìjánu-ìṣàfarawé orbits

Nínù yìí ní àwọn ìṣẹ̀dà tí a fi gbọ́dọ̀ kọ̀ǹpútà: láti gbá, o lè rọ́ọ̀nù, láti lọ́wọ́lọ́wọ́ o lè rọ́ọ̀nù, láti sé bẹ̀rẹ̀ o lè rọ́ọ̀nù. Walter Hohmann, a German ilu engineer, ti wa ni ṣiṣẹ ni 1925 ọna ti o kere ju lati gbe laarin meji circular orbits. Bibẹẹkọ, gbogbo awọn satẹlaiti ni orbit geostationary ti wa nibẹ nipa lilo imọran rẹ.

Lati oriṣii 300 km si oriṣii geostationary, 35,786 km lọ́wọ́lọ́wọ́: awọn iyẹ̀wu meji, 5.3 iṣẹ́ju. Tí a fi àwọn ìṣàmúlò-ètò vis-viva pọ̀.

Fi ààyè-iṣẹ́ hàn láti pọ̀, ki o si dé ní ìgbà tí o tì kù.

Wo

Ṣẹ̀dá 1, lọ sílẹ̀. Ìjánu-ìsẹ̀ àwọn ìṣàmúlò-ètò kò mú sáàtìlì lọ sílè nípa ààyè rẹ̀: ò fi ààyè náà pamọ́ sí ẹ̀yàn-ìtàn kan. Àwọn ààyè-iṣẹ́ ìsàlẹ̀-ilà tí a fi pamọ́ nínú àwọn àgbékalẹ̀.
Ìwọ̀n. Ààyè-iṣẹ́ kan àti ìpàsẹ̀. Sáàtílẹ̀tì náà tí wọ́n lọ, bí aago tí a fi pamọ́ lọ́wọ́lọ́wọ́, àtí òkùn-un nígbà tí o bá lọ.
Ṣẹ̀dá 2, lọ sílẹ̀ lẹ́nú. Nínú àwọn ìsàlẹ̀-ilà níbẹ̀ náà o tí kù jú láti wa níbẹ̀ lọ́wọ́lọ́wọ́. Ìpàsẹ́ kejì náà náà mú àwọn ìṣàfarawé ààyè-iṣẹ́ lọ́wọ́lọ́wọ́ nínú ìpele tuntun.

Lati 300 km si geostationary orbit awọn meji burns fi kun soke si nipa 3.9 km/s, ati ti irin ajo gba nipa 5 wakati 17 iṣẹju.

Àwọn ààyè-iṣẹ́

Akoko ti o wa ni eyikeyi aaye ti orbit kan wa lati vis-viva: v = √(μ(2/r − 1/a)). A Hohmann fipamọ ellipse ta awọn meji Circles, ki o si rẹ semi-major axis ni a_t = (r₁ + r₂) / 2.

	Radí (km)	Ìjánu-ìṣàmúlò-ètò
Circular at 300 km	6,678	7.73
Àwọn ààyè-iṣẹ́	6,678	10.15
Àwọn ààyè-iṣẹ́	42,164	1.61
Àwọn ààyè-iṣẹ́	42,164	3.07

Burn 1 = 10.15 − 7.73 ≈ 2.43 km/s. Burn 2 = 3.07 − 1.61 ≈ 1.47 km/s. O ni awọn agolo mẹrin: Agbegbe Ilẹ-ilẹ (Ile-ilẹ) - 5.3 km².

(Awọn ifilọlẹ geostationary gidi tun ni lati yipada titẹ orbit lati aaye ifilọlẹ lati equator, eyiti o jẹ idiyele diẹ sii; fifiranṣẹ ni ayika equator ṣe iranlọwọ fun awọn ohun elo.)

Àwọn àyọkà ìṣàmúlò-ètò

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

Iyipada Hohmann ni iyatọ ti o kere julọ laarin awọn orbits coplanar, titi di igba ti r₂/r₁ < 11.94. Àwọn ààyè-iṣẹ́ àwọn ìṣàfarawé Ìjáde (àtí àwọn ìpàlẹ̀ mẹ́tà, tí wọ́n lọ́wọ́lú nínú ibí tí a fẹ́) jẹ́ àwọn owó tí kò ju Δv lọ, nínú iyé igbà tòjú.

Ìpàdé nínú àwọn ìṣàmúlò-ètò kejì jẹ́ ààyè tí o dara jú láti fi agbara mú: Àwọn ìṣàfarawé àwọn ìpéwọ̀n sọ pe Δv ti a fun ní yìí yipadà si agbara orítọ́lì tí o jú lọ níbí tí ọkọ oju-omìláàyè náà bá gbè ní ìpelé, nitori Δε ≈ v·Δv.

Wá

Ló àwọn ìṣàfihàn láti ṣayẹwo ààyè-iṣẹ́ nínú ojú-ìwé tí a fi pamọ́: μ = 398,600 km³/s², r = 42,164 km, a = 24,421 km. Lọ́wọ́lọ́wọ́ lọ́wọ́lù náà nínú 42,164 km. Àwọn ìyatọ̀ ní ìpàsẹ̀ kejì.

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Àwọn ìjánu-ìṣàfarawé Hohmann: àwọn ìjánu-ìṣàfarawé orbits

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