Lagrange Point Decoded

Lagrange point L2 is the place where NASA recently sent the James Webb space telescope (JWST) to study deep space.

What exactly is the concept behind L2? This is a startling discovery of science where Physics and Mathematics intersect. The genius behind this concept was Italian French Mathematician Josephy Louis Lagrange whose name is the Lagrange point. This is a natural concept, we only discovered it and then scientists found that many asteroids are also stationed at Lagrange point, something which I will discuss later.

Lagrange point is kind of a parking spot in the space which is a position where the objects tend to stay put. At the Lagrange point, the gravitational pull of two large masses precisely equals the centripetal force required for a small object and move with them. These points in space can be used by the spacecraft sent for research, it reduces fuel consumption needed to remain in position, and hence it enhances the research duration. It took a lot of research and mathematical calculations to find it. This mathematical problem known as the “General Three-Body Problem” was considered by Lagrange in his prize-winning paper (Essai sur le Probleme Des Trois Corps, 1772)

Concerning Sun, Earth, and Moon we have five special points called Lagrange points where a small mass can orbit in a constant pattern with two large masses. They are L1, L2, L3, L4, and L5. L3 is of no use as it is on the other side of the Sun and it remains hidden behind the Sun all the time. The idea of a hidden planet has been a popular topic in science fiction writing.

L1 and L2 are closer to Earth and hence can be used to send satellites for observation. For space research L2 is best suited and ideal for astronomy because a spacecraft is close enough to communicate with earth, can keep Sun, Earth, and Moon behind the spacecraft for Solar power, and (with shielding) provides a clear view of deep space for our telescopes.

L1 is in a better position and gives an uninterrupted view of the Sun and is home to the Solar and Heliospheric Observatory Satellite SOHO, where some spacecraft are already deployed to study the Sun. JWST is deployed on L2 where Sun Earth and Moon are aligned wherein JWST on one side is exposed to the Sun and on the other side which is the cooler one, is receiving the faint Infra-Red signals coming from Space.

The L1 and L2 points are unstable on a time scale of approximately 23 days, which requires regular course and altitude corrections.

The L4 and L5 points are home to stable orbits so long as the mass ratio between the two large masses exceeds 24.96. This condition is satisfied for both the Earth-Sun and Earth-Moon systems, and many other pairs of bodies in the Solar System.

Some asteroids found orbiting at the L4 and L5 points are called Trojans (after the three large asteroids Agamemnon, Achilles, and Hector that orbit in the L4 and L5 points of the Jupiter-Sun system). There are hundreds of Trojan Asteroids in the solar system. Most are with Jupiter, but others orbit with Mars. In addition, several of Saturn’s moons have Trojan companions.

Coming back to the James Webb space telescope, the Sun, Earth (and Moon) are always on one side. At L2, Webb’s sun shield can always face all of these heat and light sources to protect Webb’s optics and instruments, which have to stay super cold to detect faint heat signals in the universe.

Why doesn’t Webb just sit at L2?

NASA has answered that it’s simpler and more efficient for Webb to orbit L2

Power – This orbit also ensures that Webb will never have the Sun eclipsed by Earth which is necessary for Webb’s thermal stability and power generation.

Communication – L2 is convenient for always maintaining contact with Mission Operations Center through the Deep Space Network. Webb isn’t the first spacecraft to orbit L2 either! Other observatories like WMAP and Herschel also orbit L2 for these reasons.??