Launch Windows: the road to MarsName

NgoJulayi 2020, izithuthi ezintathu zashiya ihlabathi ziye eMars kwiintsuku ezilishumi elinambini: i-United Arab Emirates’ Hope orbiter, i-China’s Tianwen-1 kunye ne NASA’s Perseverance rover. Oku akuzange kube kukudibana. IMars ingafikelwa kuphela ngexabiso eliphantsi xa iiplanethi zibekwe ngokuchanekileyo, kwaye oku kwenzeka malunga nenyanga nganye ye-26.

Awunakubhekisa kwiplanethi. Ubeka injongo apho izakuba khona.

Bona

Ihlabathi neMars zombini zijikeleza ilanga, ihlabathi kwindlela yangaphakathi kwaye ngokukhawuleza. Inqwelomoya yesathelayithi eshiya ihlabathi ayihambi ngomgca othe tye: iyalandela umjikelo wayo wokwandisa ujikelezo lwelanga, i-ellipse ephakathi eqala kumjikelo wehlabathi kwaye iphele kwi-Mars.

• The trip takes about 259 days on the cheapest path.
• In that time Mars moves on too, so it must be about 44 degrees ahead of Earth at departure.
• Ihlabathi lidlula iMars kwaye uluhlu olufanayo luphindaphindwa kuphela ngazo zonke ii 780 zeentsuku, malunga neenyanga ezili-26.

Ulahle ifestile ngeeveki ezimbalwa kwaye uhambo luza kubiza kakhulu kwifuthe, okanye luya kuba nzima kwiroketi onayo. Lindela, kwaye ifestile elandelayo iya kuba yiminyaka emibini kude.

Ukuqonda

Ukuphatha zombini ii-orbit njengezijikelezi (Ihlabathi kwi 1 AU, iMars kwi 1.524 AU) kwaye usebenzisa ilanga le μ = 1.327 × 10¹¹ km³/s²:

• I-ellipse yokudlulisa ine-a = (1 + 1.524)/2 = 1.262 AU; isiqendu sayo siyi 259 iintsuku.
• Ukushiya ihlabathi, inqanawa yesathelayithi ifuna 2.94 km/s ngaphezulu kwehlabathi leyo 29.8 km/s ejikeleze ilanga.
• Ifika kwindlela yeMars 2.65 km/s ihamba phantsi kuneMars kwaye kufuneka ithathelwe (isifundo esilandelayo).
• I-engile yexesha: kwiintsuku ezingama-259 iMars igubungela 360° × 259/687 ≈ 136°, ngoko kufuneka iqale nge-180° - 136° ≈ 44° phambi.

Ii-orbit ezinyanzelekileyo zincinci kwaye zijikeleze, ngoko ke ifestile nganye ihlukile; abayili bemisiyo bakhangela amawaka omhla wokuqalisa nokufika ngexesha elinye nge “porkchop plots”. Ukufumana i Δv eninzi kakhulu kuthatha uhambo olufutshane: Ukuqhubeka kwathatha iintsuku ezili-203.

Umphathi

Ixesha le-synodic:

1/S = 1/P_Earth − 1/P_Mars  →  S = 1 / (1/365.25 − 1/686.98) ≈ 780 imihla

Ukusuka kwi-orbit yehlabathi ephantsi akuyiyo kuphela 2.94 km/s: oko kukhawuleziso olungaphezulu kwe-hyperbolic v∞ ihlabathi kufuneka lishiyeke nalo. Ukutshisa kwi-200 km ubude, isantya esifunekayo yi √(v∞² + 2μ_E/r), ngoko ukutshisa ukusuka kwi7.79 km/s indawo yokupaka ijikeleza malunga ne 3.6 km/s, kwaye uOberth ubangela ukuba kube lula kunokongeza ii-2.94 km/s kude kumhlaba. Izithuthi eziqalayo zichaza oku njenge C3 = v∞² ≈ 8.7 km²/s², incinci yokuyeka kweMars.