Qala amafasitela: indlela eya eMars

In July 2020 three missions left Earth for Mars within twelve days: the United Arab Emirates’ Hope orbiter, China’s Tianwen-1 and NASA’s Perseverance rover. Akukho sizathu. IMars ingafinyelelwa kuphela ngentengo ephansi lapho amaplanethi abekwe ngokuvumelana, futhi lokhu kwenziwa cishe nganyanga ngayinye engu-26.

Awukho umbono weplanethi. Uzobeka inhloso lapho izobe khona.

Bona

Izwe neMars zombili zijikeleza ilanga, izwe lihamba ngaphakathi futhi lihamba ngokushesha. I-satellite eshiya iplanethi ayihambanga ngomgwaqo oqondile: ilandela umgwaqo wayo wokwehlisa ilanga, i-ellipse engxenyeni eqala ku-orbit yeplanethi futhi iphele ku-Mars.

• Indiza ithatha cishe izinsuku ezingama-259 ngendlela ebiza kakhulu.
• Ngosikhathi esifanayo iMars ihamba futhi, ngakho kufanele kube yilokho Amadigri angama-44 phambili iplanethi lapho iphuma khona.
• Izwe lidlula iMars futhi le ngxenye efana nayo iphinda njalo izinsuku ezingama-780, cishe amasonto angama-26.

Uma ushiya ifasitela ngeviki elilodwa noma ezimbili, uhambo luzobiza kakhulu ngephethiloli, noma ngeke lube lula nge-rocket yakho. Lindela, futhi ifasitela elilandelayo lineminyaka emibini kude.

Ukuqonda

Ukuphatha ama-orbit amabili njengezijikelezo (Iplanethi ku-1 AU, iMars ku-1.524 AU) futhi usebenzisa uMhlaba we-μ = 1.327 × 10¹¹ km³/s²:

• I-ellipse yokudlulisa ine a = (1 + 1.524)/2 = 1.262 AU; inhlamvu yesikhathi sayo yi 259 izinsuku.
• Ukushiya iplanethi, isindiza somhlaba sidinga 2.94 km/s ngaphezulu kweplanethi yezwe 29.8 km/s ejikeleza ilanga.
• Ifika e-orbit yeMars 2.65 km/s ihamba kancane kuna-Mars futhi kufanele ithathwe (isifundo esilandelayo).
• I-phase angle: ngezinsuku ezingama-259 iMars ihlanganisa ama-360° × 259/687 ≈ 136°, ngakho kufanele iqale ngama-180° − 136° ≈ 44° phambili.

Ama-orbit angempela ancane futhi ahamba ngokujikeleza, ngakho ifasitela ngalinye lihlukile; abazokhangisi bemisiyo bafuna amawaka ezinsuku zokuqashwa nokufika kanye nge “porkchop plots”. Ukukhokha Δv encane kakhulu kwenza ukuthi uhambe kancane: Ukwethembeka kwathatha izinsuku ezingama-203.

Umphathi

Isikhathi se-synodic:

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

Ukusuka e-orbit yeplanethi eseduze akuyona nje 2.94 km/s: lokhu kuyizinga elingaphezulu le-hyperbolic v∞ Earth kumele lishiyeke. Ukudlidliza ku-200 km ubude, isivinini esidingekayo yi √(v∞² + 2μ_E/r), ngakho ukudlidliza kusuka e-7.79 km/s parking orbit kuyinto engu 3.6 km/s, futhi i-Oberth effect iyenza ibe ngcono kunalokho okufaka ama-2.94 km/s kude neplanethi. Izimoto zokuqapha zichaza lokhu njenge C3 = v∞² ≈ 8.7 km²/s², okuncane kakhulu kokuphuma kweMars.