Hohmann ya canja: canja orbits

Wannan ita ce ƙa’ida mafi ban sha’awa ta jirgin sama na orbital: don ka samu ka daina, kuma don ka kai mafita ka yi sauri, sa’an nan kuma ka ƙare da yin sauri. Walter Hohmann, wani injiniyan birni na Jamus, ya yi aiki a cikin 1925 kan hanyar da ta fi sauki don motsa tsakanin orbits biyu masu juyawa. A kusan kowace salula a geostationary orbit samu zuwa nan da amfani da tunaninsa.

Ka yi sauri ka hau, kuma za ka isa cikin sauri fiye da yadda ka bar.

Look

1. Burn 1, forwards. Saurin da aka kara bai sa tauraron dan adam ya yi sauri ba a cikin ɗaurewarsa: yana shimfiɗa ɗaurewar zuwa ellipse. Maɓallin ƙananan yana zaune inda ƙonawa ya faru; gefen da ke kusa yana tashi zuwa tsayin maɓallin.
2. Coast. Half an orbit without any engine. Sataiti na tashi kuma, kamar yadda aka yi wa kwallo, ya daina yayin da yake tafiya.
3. Burn 2, forwards again. A sama yanzu yana da sauri sosai don ya zauna a can kuma zai iya faɗi baya. A na biyu ya sanya orbit da ke cikin wani tsawo.

Daga 300 km zuwa geostationary orbit biyu burns kara har zuwa kusan 3.9 km/s, da tafiyar take kusan 5 hours 17 minutes.

Understand

A cikin wannan littafin, an yi amfani da kalmar “a” a matsayin ma’anar “a” (a cikin Littafin 1:2). Wani ellipse na canja wurin Hohmann yana shafar daruruwan biyu, don haka maɓallinsa mai girma shine a_t = (r₁ + r₂)/2.

	Radius (km)	_Saurin (km/s)
Cire a 300 km	6,678	7.73
Transfer, low point	6,678	10.15
Transfer, high point	42,164	1.61
Geostationary	42,164	3.07

Burn 1 = 10.15 − 7.73 ≈ 2.43 km/s. Burn 2 = 3.07 − 1.61 ≈ 1.47 km/s. An yi amfani da wannan tsari ne a cikin tsarin lissafi na zamani (5.3).

(A gaskiya geostationary launches kuma dole ne su canza da orbit’s tilt daga launch site na latitude zuwa equator, wanda farashin fiye da; launching kusa da equator tsare mai.)

Master

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

Canja wurin Hohmann shine mafi ƙarancin canja wurin motsi biyu tsakanin coplanar circular orbits, har sai r₂/r₁ < 11.94. A baya ga wannan adadin bi-elliptic canja wurin (uku burns, tafiya a kan gaba da manufa) farashin kaɗan Δv, a kan farashin lokaci mai yawa.

Burning a kan kasa point ne kuma mafi kyau wuri don ƙara makamashi: Oberth tasiri ya ce da aka ba Δv canja orbital makamashi mafi yawan inda jirgin sama yana tafiya da sauri, saboda Δε ≈ v · Δv.