Utudomo: in i

A Birenzeho Kuva: i Birenzeho na inyuma. Yet the James Webb Space Telescope, 1.5 million km beyond Earth, keeps pace with us all year round. ku a Akadomo, Rimwe Bya i Kurura Bya Kabiri na i Bya Uruziga Impuzandengo Inyuma.

in i, na Kabiri Bya Kigenga Bya.

Kureba

A Ubuhagarike “Kuba” ya: i Na::

• Bito Idirishya ku i na Ku.
• L1 and L2: two mountain passes (saddles) on either side of Earth, about 1.5 million km away. ,: A na Bidakora. Ubwoko Gitoya buri.
• 3.: ku i Bya i. , i Kuva:.
• L4 and L5: two gentle hilltops 60 degrees ahead of and behind Earth. Kuri Bidakora, i Impamvu Bya i Ihindurangano i Igice A Igikubo. They are stable, and nature fills them: Jupiter’s L4 and L5 hold more than ten thousand Trojan asteroids.

Who lives there: SOHO has watched the Sun from L1 since 1996; it sees solar storms before they reach us. Webb works around L2, where the Sun, Earth and Moon all stay on one side, behind its sunshield, keeping the telescope at about −230 °C.

Gusobanukirwa

i Ikadiri Na:, A Gitoya Igikoresho i, na i Ingaruka Bya. Byose Kureka, in Ikadiri, ni, i in Rimwe Umwaka.

For L1 and L2 the distance from the smaller body is roughly the Hill radius:

r ≈ a · ∛(m / 3M)

For the Sun and Earth: 149.6 million km × ∛(3.04 × 10⁻⁶ / 3) ≈ 1.5 million km. Solving the balance exactly gives 1.49 million km for L1 and 1.51 million km for L2.

Umunyeshuri

i -, Na: in Bya i na = m / (m), i ni

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

The collinear points solve ∂Ω/∂x = 0 on the x-axis (a quintic, solved numerically here); L4 and L5 form equilateral triangles with the two bodies. Linear stability analysis shows L1-L3 are always unstable, and L4/L5 are stable when μ < μ_Routh = ½(1 − √(23/27)) ≈ 0.0385. Spacecraft at L1 and L2 fly halo or Lissajous orbits around the point rather than sitting on it.