Orbital insertion: getting captured

Pa 10 March 2006, mushure memwedzi misere muspace, NASA’s Mars Reconnaissance Orbiter yakavhara yayo gumi nemaviri ekutanga masimba emashini ayo kwe27 maminitsi. Panguva iyoyo yaiva pasi peMars, pasina munhu aigona kusangana nayo neradio: hapana munhu panyika ainge achiziva kana yakanga yakashanda. Kana kuora kwakakundikana, spacecraft yaizofamba pasi peMars uye muorbit isina kupera pamusoro pezuva.

Kusvika hakuvi ku足。 Unofanira kusungwa.

Ona

A spacecraft haisi “kuvhara” paplaneti. Inowira kunzvimbo yake, Kukurumidza sezvayo inosvika, panzvimbo yakavhurika kurongeka rinonzi a hyperbola. Kudzokera kunyika, akatanga kutamba nechisimba uye akazvipira kuita zvese zvaaigona kuti awane mari.

Kuti igare, inofanira kushaya simba panguva yakakodzera, iyo inodarika nzira:

1. Kutora burn. Mamwe masimba anouraya kusvikira kutendeuka. A modest burn inoshandura yakavhurika kurwisa kuita yakareba, yakavharwa ellipse.
2. Aerobraking. Sezvo mhepo iri kupisa, mabhatiri anowedzera simba rekudziya uye zvinokonzera kuti zvive nyore kuisa zvinhu muorbit. Nese kutevedzera, a little air drag inoderedza spacecraft uye high point zvipfuwo.
3. Science orbit. mushure memakore makumi maviri nemana, MRO yakasvika panzvimbo yepasi pezuva ine 250 km kusvika ku316 km pamusoro penyika, uye yakatanga kuita mapikicha eMars.

_Zvinyorwa

Kubva panyika pane Hohmann-se nzira, spacecraft inosvika Mars pamusoro 2.65 km/s zvishoma kupfuura Mars. Kubva panzvimbo yekuona yeMars iyo ndiyo “speed at infinity”, v∞. Kukwira kusvika 426 km pamusoro pevhu, inowedzera kusvika

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

Pa ellipse kubva 426 km kusvika 44,500 km, mwero wenguva yepasi pezuva unofanira kunge uri 4.56 km/s (vis-viva). Iyo yakakwana, instantaneous capture burn ndeyekuti 0.87 km/s. A 27-minute burn isiri yakakwana nekuti inoparadzwa pasi pekurongeka; MRO’s yakaderera spacecraft ne1 km/s.

Kutora zvizere mu low circular orbit ichadhura pamusoro 2 km / s (ona Try it). Aerobraking inochengeta zhinji yeiyo kukosha, uye iyo yakachengetedzwa fuel inowanzoshandiswa musainzi nendege.

Munyori

Hyperbola ine semi-makuru axis a = −μ/v∞² uye eccentricity e = 1 + r_p v∞²/μ. Kufamba kwezuva kubva kumabvazuva kusvika kumadokero kunoitwa neKepler’s equation M = e sinh F − F.

The kuunganidza Δv pa periapsis r_p mu ellipse ne apoapsis r_a is

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

iyo iri yakakura kwazvo kune yakaoma ellipse (r_a → large): chikepe chepasi hachina kuonekwa. Izvi ndizvo zvinokonzera kuti vafambi vaende muorbit, uye nei vachiita aerobraking kana kuuraya zvinhu zvidiki. For manned Mars missions, aerocapture (imwe yakadzika pasi kuburikidza neatmosphere pamberi pemhepo shiri) inogona kuchinja kuchengetedza burn zvakananga.