In Sun-Earth system, the distance between Lagrange points L2 and L3 is about

Correct — D, 32 crore kilometre. L2 and L3 lie on opposite sides of the Sun. L2 is on the Sun-Earth line about 15 lakh kilometres beyond the Earth, so it is about 1 astronomical unit plus 15 lakh kilometres from the Sun. L3 sits on the same line but on the far side of the Sun, close to 1 astronomical unit out. Adding the two gives roughly 2 astronomical units, and since 1 astronomical unit is about 15 crore kilometres the separation works out at about 30 crore kilometres. Only one option is anywhere near that figure: 32 crore kilometre. The other three are out by a factor of two hundred, a hundred, or two.

• (a)15 lakh kilometre — 15 lakh kilometre is the Earth-to-L2 distance, not the L2-to-L3 distance. It is the number quoted for the James Webb Space Telescope's station and for Aditya-L1's halo orbit about L1, which is why it is the most tempting wrong answer here.
• (b)30 lakh kilometre — 30 lakh kilometre would be the L1-to-L2 span, since those two points sit about 15 lakh kilometres either side of the Earth. It is a hundred times too small for a separation that has to cross the whole diameter of the Earth's orbit.
• (c)16 crore kilometre — 16 crore kilometre is close to a single astronomical unit, that is the Sun-to-Earth or Sun-to-L3 distance. The question asks for a gap that spans the Sun, so one astronomical unit is only half of what is needed.

In a two-body system such as Sun and Earth there are five points where a small object can hold a fixed position relative to both. L1, L2 and L3 lie on the line joining the two bodies — L1 between them, L2 beyond the smaller one, L3 beyond the larger one. L4 and L5 sit at the two points that form equilateral triangles with the Sun and the Earth. The collinear three are unstable and need station-keeping fuel; L4 and L5 are stable.

The whole item is a scale check dressed as astronomy. Once you place L2 just outside the Earth's orbit and L3 just outside it on the opposite side, the separation has to be a little more than the diameter of the Earth's orbit, which is about 30 crore kilometres. The examiner's printed value of 32 crore is a round overstatement of that figure rather than an exact one, but the arithmetic still rules out every other option by at least a factor of two, so the item resolves cleanly. Anchoring one number is enough — 1 astronomical unit is about 15 crore kilometres, and the 15 lakh kilometre figure that Indian candidates know from Aditya-L1 is a hundred times smaller.

• A Sun-Earth system has five Lagrange points; L1, L2 and L3 are collinear with the two bodies, L4 and L5 form equilateral triangles.
• L1 and L2 each lie about 15 lakh kilometres from the Earth, on the sunward and anti-sunward sides.
• L3 lies beyond the Sun, close to 1 astronomical unit from it, permanently hidden from Earth by the Sun.
• 1 astronomical unit is about 15 crore kilometres, so L2 to L3 spans a little over 2 astronomical units.
• India's Aditya-L1, launched in September 2023, orbits the Sun-Earth L1 point; the James Webb Space Telescope orbits L2.

• Answering 15 lakh kilometre from memory of the Aditya-L1 headlines without reading which two points are named.
• Forgetting that L3 is on the opposite side of the Sun, and so halving the answer.
• Mixing lakh with crore when converting, which shifts the answer by a factor of a hundred.

An order-of-magnitude item. The examiner supplies one familiar number as bait and expects you to notice that the question asks for a different span altogether.

• practice — not a real PYQ

  The Aditya-L1 spacecraft was placed in a halo orbit around which Lagrange point of the Sun-Earth system?

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

  Answer(a) L1 — the point between the Sun and the Earth, which allows an uninterrupted view of the Sun.

• practice — not a real PYQ

  Which of the Lagrange points of a two-body system are stable?

  • (a)L1 and L2
  • (b)L2 and L3
  • (c)L4 and L5
  • (d)L1 and L3

  Answer(c) L4 and L5 — the two triangular points, which is why Trojan asteroids collect there.