Lagrange points: A lesson in gravity and a path to space exploration

Years ago, I parked my car and dashed into a neighborhood shop, only to find that that my car had rolled downhill. Fortunately the slope was not too steep, and the car was stopped by a steep curb about 40 feet away. Ignoring the gawking passersby, I jumped in and drove off, embarrassed to have shown such a poor command of gravity. 

As it turns out, an understanding of gravity is also critical to knowing where to park objects like telescopes, satellites and stations in space. The Earth-Sun system has five special locations called Lagrange points, named after the Italian-French mathematician Joseph-Louis Lagrange who investigated the complex relationship between three separate objects. At the Lagrange points, the gravitational attraction of the Earth and Sun is equal to the centripetal force that allows the Earth to rotate the Sun. Therefore, an object stationed at one of the Lagrange points tends to stay at this position as the Earth orbits the Sun.

Lagrange points L1, L2, and L3 are aligned with the Earth and Sun, while L4 and L5 each form an equilateral triangle with the Earth and Sun. Because gravity and centripetal force depend on mass, the Lagrange points at these triangle positions are especially stable when the ratio of the larger mass to the smaller mass exceeds 24.96. Fortunately, the Sun is about 333,000 times heavier than the Earth, so L4 and L5 are fixed in position, making them good candidates for future space station or asteroid mining locations. Currently, some space rocks and dust have accumulated at these steady points, like dust collecting in the corner of a room.

As the Earth circulates the Sun, the linear Lagrange points (L1, L2 and L3) experience about 23 days in which they can slowly float away from their position over time. This period of slight instability means space telescopes at these positions must use some propellant to remain aligned. One such telescope is the James Webb Space Telescope (JWST), which reached the L2 position about a million miles from Earth in January. At nearly 2,700 times farther from Earth than the Hubble Space Telescope, it will be unserviceable, even if we still had a working space shuttle. However, the team hopes its distant location will provide observations of deep space and the universe’s far-off past.

The Earth-Sun system isn’t the only place Lagrange points are found. In fact, five Lagrange points exist between any two massive bodies. For example, a slew of asteroids, bits of rock and ice, comets and dwarf planets have gathered at the L4 and L5 points between Jupiter and the Sun. Additionally, the L2 point in the Earth-Moon system has served as the location for communications satellites covering the far side of the moon, and L4 and L5 between the Earth and the Moon would be especially stable for permanent space stations.

Researchers have also suggested placing shields at the L1 position directly between the two planetary bodies for various applications. For example, NASA scientists have proposed placing a magnetic shield at the Mars-Sun L1 point to make Mars more amenable to human exploration and settlement. This technology could create an artificial magnetic field that might restore the red planet’s protective magnetic shield and protect those on Mars from destructive solar wind.

In addition to their role in space missions, Lagrange point shields have been explored for their potential to combat climate change. One idea is to place small shields at the Earth-Sun system’s L1 point to block some of the sunlight reaching Earth, thereby (theoretically) reducing global warming. A similar proposal is to place a special lens at L1 to scatter the Sun’s rays and decrease the amount of light reaching the Earth. These extreme measures would be expensive and difficult to optimize to ensure that Earth still gets enough sunlight, but climate change is a desperate problem.

These applications of Lagrange points might sound like science fiction, but many exciting advances start out that way. For now, we can sit back and enjoy the fascinating images from the JWST at Lagrange point L2—and remember the importance of gravity when parking our cars.