Fara tagogi: hanyar zuwa Mars

A watan Yuli na 2020, ayyukan uku sun bar ƙasa zuwa Mars cikin kwanaki goma sha biyu: United Arab Emirates’ Hope orbiter, China’s Tianwen-1 da NASA Perseverance rover. Wancan bai zama kamã ba. An iya isa Mars da sauƙi kawai idan taurãri sun daidaita daidai, kuma wannan yana faruwa kusan kowace wata 26.

Ba ka mai da hankali ga wata duniyar ba. To, a inda yake shi ne kake mai dãko.

Look

Kuma, lalle ne, hasken rana yana tafiya a cikin wata, kuma hasken wata yana tafiya a cikin wata. Wani jirgin sama na waje da ke barin ƙasa ba ya tashi a cikin layi madaidaici: yana bin orbit ɗinsa a kusa da rana, wani rabin-elipsis wanda yake farawa daga orbit na ƙasa kuma ya ƙare a kan Mars.

• 259 days ne tafiyar take kaiwa a kan hanyar da ta fi sauki.
• A wannan lokaci Mars motsa a kan, kuma, don haka ya kamata a game Digiri 44 gaba Na ƙasa a lõkacin da suke tafiya.
• Earth overtakes Mars and the same lineup repeats only every 780 days, about 26 months.

Ka rasa tafarkin da makonni kaɗan kuma tafiyar tana buƙatar man fetur mai yawa, ko kuma ya zama ba zai yiwu ba ga roket ɗin da kake da shi. Ka yi jira, kuma tebur na gaba shi ne shekara biyu daga nan.

Understand

Da ake yi wa orbits biyu kamar darabkai (Dukkiya a 1 AU, Mars a 1.524 AU) da amfani da μ na rana = 1.327 × 10¹¹ km³/s²:

• The transfer ellipse has a = (1 + 1.524)/2 = 1.262 AU; half its period is 259 days.
• A lokacin da yake tafiyar da duniya, jirgin yana bukatar 2.94 km/s fiye da na duniyar 29.8 km/s a kusa da rana.
• Yana zuwa cikin orbit na Mars 2.65 km/s da sauri fiye da Mars kuma dole ne a kama shi (darasin gaba).
• A gefen lokaci: a cikin kwanaki 259 Mars ya rufe 360° × 259/687 ≈ 136°, don haka dole ne ya fara 180° − 136° ≈ 44° gaba.

A gaskiya, orbits ne kaɗan elliptical da tilted, don haka kowace taga ne daban; mission masu zane-zane nema dubban da farawa da kuma zuwa ranakun a lokaci guda da “porkchop plots”. Kuma idan aka biya Δv kaɗan mafi yawa sai a saya tafiya mai gajewa: Perseverance ta dauki kwanaki 203.

Master

Dakata

1/S = 1/P_Duniya − 1/P_Mars  →  S = 1 / (1/365.25 − 1/686.98) ≈ kwanaki 780

Cikakken lokaci daga saukar da orbit na ƙasa ba kawai 2.94 km / s: wannan shine sauri hyperbolic na ƙarshe v∞ Earth dole ne a bar shi tare. A cikin 200 km, gudun da ake buƙata shine √(v∞² + 2μ_E/r), don haka gudun daga 7.79 km/s parking orbit yana da kusan 3.6 km/s, kuma tasirin Oberth ya sa shi mafi arha fiye da ƙarawa 2.94 km/s daga ƙasa. Jirgin farko ya ambaci wannan a matsayin C3 = v∞² ≈ 8.7 km²/s², mafi ƙarancin ga wani Mars tafiya.