Orbital insertion: getting captured

A ranar 10 ga Maris, 2006, bayan watanni bakwai a sararin samaniya, Mars Reconnaissance Orbiter na NASA ya kashe manyan injiniyoyinsa shida na minti 27. A wani yanki na wannan lokaci, ya kasance a bayan Mars, ba tare da sadarwar rediyo ba: babu wanda zai iya sanin ko ya yi aiki. Idan an yi asarar wuta, jirgin sama zai yi tafiya a kusa da Mars kuma ya shiga cikin wani orbit mara ƙarewa a kusa da rana.

Kuma bã ya isa ya isa. Sai a kama ku.

Look

Wani jirgin sama na sararin samaniya ba zai “tsaye” a wata duniyar ba. Yana faɗuwa zuwa gare shi, ya kara sauri kamar yadda yake kusa, a kan wani launi mai buɗe wanda ake kira hyperbola. Idan an bar ta da kanta, zã ta yi gudu a kusa da duniyar kuma ta tãka zuwa wani wuri mai nisa.

Domin ya zauna, yana bukatar ya rasa gudu a lokacin da ya dace, da ya fi kusa:

1. Kafar cece-kuce. Maɓallan wuta suna da alaka da hanyar motsi. Wani burn mai ƙasƙanci yana juyawa da ƙura mai buɗe zuwa wani tsawo, ya ɗaure ellips.
2. Aerobraking. A maimakon yin amfani da karin man fetur, masu kulawa suna rage matsakaicin matsayi na orbit zuwa cikin mafi girman sama na yanayi. A kowace tafiya, wani ƙaramin jujjuyawar iska yana rage gudun jirgin sama kuma matsakaicin matsayi na ƙasa.
3. Science orbit. Bayan daruruwan wucewa a cikin watanni biyar, MRO ya kai wani ƙananan, kusan tsawo na 250 km ta hanyar 316 km, kuma zai iya fara yin maɓallin Mars.

Understand

Da yake zuwa daga ƙasa a kan hanyar Hohmann-like, jirgin sama ya isa Mars game da 2.65 km/s mai sauri fiye da Mars. Daga ma’anar Mars, wannan shine “saurinta a ƙarƙashin iyaka”, v∞. Ya fadi zuwa 426 km a sama da ƙasa, yana sauri har zuwa

v = √(v∞² + 2μ/r) = √(2.65² + 2 × 42,828 / 3,822) ≈ 5.4 km/s

A kan wani ellipse daga 426 km zuwa 44,500 km, gudu a matsakaicin wuri dole ne ya zama 4.56 km/s (vis-viva). An yi amfani da wannan a cikin 0.87 km/s. A gaskiya 27-dakika na wuta ne mafi ƙarancin inganci saboda shi ne ya watsa a duk faɗin curb; MRO’s da sauri jirgin sama ta hanyar kusan 1 km / s.

Kashewa kai tsaye cikin wani orbit na tsawo zai kashe kusan 2 km/s (ka duba Shirin shi). Aerobraking yana adana mafi yawan wannan bambanci, kuma mai da aka adana ya zama jirgin sama na sararin samaniya da kimiyya.

Master

A hyperbola yana da rabin-masu girma axis a = −μ/v∞² da eccentricity e = 1 + r_p v∞²/μ. Lokacin tafiya daga wuri mai nisa zuwa periapsis an tsara shi ta hanyar daidaiton Kepler na hyperbolic M = e sinh F − F.

An kama Δv a periapsis r_p cikin wani ellipse da apoapsis r_a

Δv = √(v∞² + 2μ/r_p) − √(2μ r_a / (r_p (r_p + r_a)))

wanda yake mafi ƙaranci ga wani ellipse mai tsawo sosai (r_a → babba): an yi kama da jirgin sararin samaniya. Wannan shi ne dalilin da ya sa masu zuwa farkon shiga cikin wani loose orbit, kuma me ya sa aerobraking ko wasu ƙananan burns bi. Ga Mars da aka yi aiki, aerocapture (ɗaukaki mai zurfi ta hanyar yanayi a bayan wani ɓoyayyiyar zafi) zai iya maye gurbin ƙonawa na ɗaukar hoto gaba ɗaya.