CDS (II) 2024 General Knowledge · Question 30 of 120

Correct — B, an equilateral triangle. The triangular Lagrange points L4 and L5 each sit at the third vertex of an equilateral triangle whose other two vertices are the two massive bodies.

• (a)an isosceles triangle — An isosceles triangle would only require two equal sides. The geometry here is stricter: all three sides are equal, since L4 is one full Sun-Earth distance from each body.
• (c)a straight line — L1, L2 and L3 are the collinear points, lying on the Sun-Earth line. L4 is not among them.
• (d)a scalene triangle — A scalene triangle has three unequal sides, which is the opposite of the actual configuration.

At L4 and L5 the combined gravitational pull of the two bodies provides exactly the centripetal force needed to orbit with the same period as the smaller body, and the geometry that satisfies this is an equilateral triangle.

L4 and L5 are the only Lagrange points that are dynamically stable for a large mass ratio, so material accumulates there — the Jupiter Trojan asteroids occupy the Sun-Jupiter L4 and L5. Anchored to the 2024 exam, NASA's Lucy mission was already en route to the Jupiter Trojans.

• L4 leads the smaller body by 60 degrees; L5 trails it by 60 degrees.
• Each side of the triangle equals the separation of the two bodies.
• L1, L2 and L3 are collinear and unstable; L4 and L5 are stable.
• Aditya-L1 sits at L1, a collinear point, not at L4.

• Answering isosceles because the triangle merely looks symmetrical.
• Placing L4 on the Sun-Earth line with L1 and L2.

Lagrange-point items test the geometry directly, so the equilateral fact is worth memorising with the 60-degree lead and lag.

No directly related past PYQ was found.

• practice — not a real PYQ

  The James Webb Space Telescope operates near which Lagrange point of the Sun-Earth system?

  • (a)L1
  • (b)L2
  • (c)L4
  • (d)L5

  Answer(b) L2 — beyond the Earth, letting its sunshield block the Sun, Earth and Moon together.