Celestial diagram

Real science

Maciej Boniuk on celestial mechanics
RE | Issue 14 | 2018


Lagrange points are positions in space where the gravitational forces of a system of two massive bodies—such as the Sun and Earth—allow a small object to maintain its position relative to them. Space agencies use Lagrange points as locations for scientific equipment.


Celestial mechanics

Three of the five Lagrange points (L1, L2 and L3) lie along the line connecting the two large masses; and two of them (L4 and L5) form the apex of two equilateral triangles which have the large masses at their vertices. Let’s apply this to a system in which the two large masses are the Sun (our sun) and Earth. 

Celestial crop

L1 lies between Earth and the Sun. L2 lies on the opposite side of Earth, away from the Sun. Both are about 1.5 million kilometres from Earth. L3 lies on the opposite side of the Sun (roughly the same distance from the Sun as Earth). L1, L2 and L3 are not fully stable and are not inhabited by natural objects. (Energy expenditure is required for an object to stay there.)

L4 lies at the corner of an equilateral triangle formed by the Sun–Earth–Lagrange point. As does L5. L4 leads and L5 trails Earth as our planet orbits the Sun. L4 and L5 are stable and often serve as parking spaces for small natural objects in two-body systems across our solar system.  These natural objects are called Trojans. Earth, Mars, Jupiter, Saturn, Uranus and Neptune each form a two-body system with the Sun and all have Trojans. Earth has only one (located at L4 with a diameter of about 300 metres); but Jupiter has, we think, about one million Trojans, each with a diameter of over one kilometre, at both L4 (‘the Greek camp’) and L5 (‘the Trojan camp’).

Saturn has two Trojan moon systems: Saturn and its moon Tethys constitute the two large masses, and two small moons—Telesto and Calypso—lie at L4 and L5. The Earth–Moon system is believed to have large collections of dust at its L4 and L5 points.

L1 in the Sun–Earth system is a convenient location for scientific missions studying the Sun—such as the Solar & Heliospheric Observatory, a joint project of the European Space Agency and NASA.

L2 in the Sun–Earth system is the current location of ESA’s Gaia mission and the planned location of NASA’s James Webb Space Telescope.

L2 in the Earth–Moon system is orbited by the Queqiao relay satellite; this will enable communication between Earth and China’s Chang’e-4 lunar exploration mission studying the far side of the Moon.

First published in RE issue 14 (2018). Maciej Boniuk is based in Warsaw.