Sun-Earth Lagrange Points L2 and L3 Overview

Lagrange points (L1, L2, L3, L4, L5) represent locations in space where the gravitational forces of a two-body system (like the Sun and Earth) allow a smaller object to maintain a stable position relative to the larger bodies. Points L1, L2, and L3 are collinear, lying on the line connecting the centers of the Sun and Earth.

Relative Positions of L2 and L3

• The L2 point is located on the Sun-Earth line, beyond the Earth, further from the Sun.
• The L3 point is located on the Sun-Earth line, on the opposite side of the Sun relative to Earth.

Distance Calculation for L2-L3

The distance between L2 and L3 can be approximated by considering their positions relative to the Sun:

• The average distance between the Sun and Earth is approximately 1 Astronomical Unit (AU), which is about 15 crore kilometres.
• The L2 point is situated slightly beyond Earth's orbit, roughly 1.015 AU from the Sun. (1 AU + ~1.5 million km).
• The L3 point is located roughly 1 AU from the Sun but on the opposite side of Earth.

Therefore, the distance between L2 and L3 is approximately the sum of their distances from the Sun along the collinear axis:

Distance(L2 to L3) $\approx$ (Distance Sun to L2) + (Distance Sun to L3)

Distance(L2 to L3) $\approx 1.015$ AU + 1 AU $\approx 2.015$ AU

Converting this distance to kilometres using 1 AU $\approx 15$ crore km:

Distance(L2 to L3) $\approx 2.015 \times 15$ crore km

Distance(L2 to L3) $\approx 30.225$ crore km

Determining the Correct Option

The calculated distance is approximately 30.225 crore kilometres. Comparing this value to the given options:

• 15 lakh km = 0.15 crore km
• 30 lakh km = 0.3 crore km
• 16 crore km
• 32 crore km

The value 30.225 crore km is closest to 32 crore km.