Kukhazikitsa mawindo: njira ku Mars

Mu Julayi 2020, miyezo itatu idachoka kudziko lapansi kupita ku Mars m’masiku asanu ndi awiri: orbiter ya United Arab Emirates Hope, China’s Tianwen-1 ndi NASA’s Perseverance rover. Sikuti zinali zosayembekezereka. Mars can only be reached cheaply when the planets are lined up just right, and that happens about every 26 months.

Musagwiritse ntchito pa planetary. Mu aimitsidwa pa kumene idzakhala.

Onani

M’malo mwake, Mars ndi dziko lapansi zimayenda mozungulira dzuwa, ndipo nyengo ya mwezi imakhala yotentha kwambiri. M’madera ena, monga ku Africa, nyengo imayamba pa nthawi ya mwezi wa March ndipo imatha mpaka pa nthawi ya mwezi wa June.

• The trip takes about 259 masiku pa njira yosavuta.
• Pamenepo Mars imayendanso, choncho iyenera kukhala pafupifupi 44 degre kumbuyo kwa dziko lapansi panthawi yoyamba.
• Dziko limakhala ndi Mars ndipo limatilola kuti tichite izi nthawi iliyonse 780 masiku, za 26 miyezi.

Kulephera kwa m’mphepete mwa maola angapo ndi ulendo wotsika mtengo kwambiri, kapena kumakhala kovuta kwa rocket yomwe muli nayo. Timayembekezera, ndipo zenera lotsatira ndi zaka ziwiri zopitilira.

Kumvetsa

Kugwiritsa ntchito ma orbits awiriwa monga zigawo (dziko pa 1 AU, Mars pa 1.524 AU) ndi kugwiritsa ntchito m’mawa μ = 1.327 × 10¹¹ km³/s²:

• Kusinthanitsa kwa ellipse ndi = (1 + 1.524) / 2 = 1.262 AU; the half its period is 259 masiku.
• Kuchokera pa dziko lapansi, ndege ya kunyanja iyenera 2.94 km/s kuposa 29.8 km/s ya dziko lapansi yozungulira dzuwa.
• Ifika pa orbit ya Mars 2.65 km/s mofulumira kuposa Mars ndipo iyenera kutengedwa (kuphunzira kwachiwiri).
• M’zaka 259, Mars imazungulira dziko lapansili mozungulira 360° × 259/687 ≈ 136°, choncho iyenera kuyambira 180° − 136° ≈ 44° m’mbuyo.

Ma orbits anzeru ndi ozungulira ndipo amadula, choncho mawindo onse ndi osiyana; opanga ntchito amafuna kufunsa anthu ambirimbiri za tsiku loyamba ndi tsiku la kufika pamodzi ndi “porkchop plots”. Kulipira pang’ono Δv kumagula ulendo wofupi: Perseverance idatenga masiku 203.

Woyang’anira

Nthawi ya synodic:

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

Kuchokera pa orbit ya Earth yotsika, sikuti 2.94 km / s: kuti ndi hyperbolic excess speed v∞ Earth iyenera kuchoka ndi. Kutentha kwa 200 km, kufunikira kwa kuthamanga ndi √(v∞² + 2μ_E/r), kotero kutentha kuchokera pa 7.79 km / s parking orbit ndi pafupifupi 3.6 km / s, ndipo Oberth effect imapangitsa kuti ikhale yotsika mtengo kuposa kuwonjezera 2.94 km / s kumbuyo kwa dziko lapansi. Magalimoto oyendetsa ndege amagwiritsa ntchito C3 = v∞² ≈ 8.7 km²/s², zomwe ndi zosakwanira kuti Mars ipite kumwamba.