Lagrange zviratidzo: kusimba kwezuva

A spacecraft yakareba kubva kuSun kupfuura Earth inofanira circle it slower uye kugara pasi. Asi James Webb Space Telescope, 1.5 miriyoni km kunze kwenyika, inotevedzera nguva yedu gore rose. Inomira pa Lagrange point, imwe yemakumi mana enzvimbo uko kudhonza kwezviviri zvemasangano uye chirevo chekuenda round balance out.

Makumi maviri enzvimbo dzekugara munyika, uye chete mbiri dzavo dziri dzemahara.

Ona

Kufungidzira nzvimbo uko kukwira kunoreva “kusvika sei kune simba kuti ugare pano” kwechinhu chinotenderera pasi pezuva nenyika:

• Mabwe maviri akadzika akaoma pazuva uye panyika.
• L1 uye L2: maviri mapass (maseddles) emakomo panzvimbo imwe neimwe yenyika, anenge 1.5 million km kubva kwatiri. Yakaenzana, asi chete chete: kukanda chikepe chepasi uye chinosvibisa. Misheni idzi dzinoita zvidiki zvinogadziriswa mazuva ese.
• L3: imwe saddle pashure pezuva. Hapana chinhu chinokosha chinoenda kwatiri, nekuti Sun inotidzivirira kubva kwatiri.
• L4 uye L5: maviri akapfava matombo 60 degrees pamberi penyika uye mushure menyika. Unogona kutarisira zvinhu kuti zviite, asi Coriolis mhedzisiro yekutenderera inoshandura slide kuita loop. Vanogara vakachengeteka, uye hunhu hunozvipa: L4 neL5 yeJupiter inotora kupfuura makumi maviri emamiriyoni Trojan asteroids.

Chii chinogara pano: SOHO yakatarisana nezuva kubva kuL1 kubvira 1996; inoona mabhureki ezuva mushure mekunge asvika kwatiri. Webb anoshanda paL2, uko zuva, nyika nemwedzi zvese zvinogara pane rimwe divi, pasi pesunscreen, zvichichengeta telescope pa-230 °C.

_Zvinyorwa

Muframe iyo inotenderera nenyika, chinhu chidiki chinonzwa gravity yezuva, gravity yenyika uye centrifugal effect yekutenderera. Kana zvitatu izvi zvichivharwa, inogona kugara ichiramba iri muchikamu ichi, icho chinogona kutenderera pasi pezuva kwegore rimwe chete.

KuL1 neL2, mativi enzvimbo kubva pamuviri mudiki ndeaya anoenzana neHill radius:

r ≈ a · ∛(m / 3M)

For the Sun and Earth: 149.6 million km × ∛(3.04 × 10⁻⁶ / 3) ≈ 1.5 million km. Kugadzirisa توازن zvakajeka zvinopa 1.49 miriyoni km yeL1 uye 1.51 miriyoni km yeL2.

Munyori

Muzvidimbu zvakavharwa zvemabhodhoro matatu, nemamiriro ezvinhu muzvikamu zvekuparadzana uye μ = m / (M + m), iyo yakasimba simba ndeye

Ω(x, y) = −(1−μ)/r₁ − μ/r₂ − ½(x² + y²)

Mativi maviri anosangana panzvimbo imwecheteyo uye zvinozoita kuti ∂Ω/∂x = 0 pane x-axis (a quintic, anoshandiswa nesimba); L4 neL5 zvinoumba ma triangles akaenzana nezvinhu zviviri. Kuongorora kwelinear stability kunoratidza kuti L1-L3 hazvina kugadzikana, uye L4/L5 zvinoramba zviripo kana μ < μ_Routh = ½(1 − √(23/27)) ≈ 0.0385. Zvikepe zvepasi zvinofamba muL1 neL2 zvichienda muhalo kana Lissajous orbits pamusoro penzvimbo yekuti dzirege kugara padzo.