## What Are Lagrange Points?

Article Updated: 7 Mar , 2016

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Think of the Earth and Sun, and imagine they are the only things in our solar system. Now add a satellite. Where would the gravitational pull of the Earth and Sun balance out the centripetal acceleration of the satellite, so that it would keep its relative location? As it turns out, there are five places where this occur, and they are called Lagrange points.

Name in honor of Josef Lagrange who discovered their existence, these points are useful for space-based observatories. What’s more, they are useful for helping to discern the behavior of objects in our Solar System. For example, the Earth Trojans – a series of asteroid that orbit the Sun in the vicinity of Earth – are located at Earth–Sun Lagrangian points L4 and L5, thus leading and following Earth by 60°.

But of course, the solar system is comprised of more than the Sun and Earth, so the Lagrange points are only approximations. In the end, any two masses will do, in terms of Lagrange points, so there are five Earth-Moon Lagrange points too, and five Sun-Jupiter points. And much like Earth, the hundreds of asteroids that make up the Jovian Trojan are found near (actually orbit around) the Sun-Jupiter L4 and L5 points.

## Description:

Like gravitational parking spaces, Lagrange points provide locations where spacecraft can be positioned to conduct valuable scientific observations of the Universe and perhaps someday even offer foundations for more permanent human outposts. Although there’s no actual physical mass at each of these locations, objects can be placed into orbit around them. In fact, the solar system has been doing just that for billions of years!

Named after Italian-French mathematician  Joseph-Louis Lagrange, who first proposed their existence in a 1772 paper, there are 5 such points within the Earth-Sun (as well as the Earth-Moon) orbital relationship, named L1 through L5.

## The Five Lagrange Points:

There are five Lagrangian points in the Sun-Earth system and such points also exist in the Earth-Moon system. Kepler’s Laws of Planetary Motion require that the closer a planet is to the Sun, the faster it will move. Any spacecraft going around the Sun in an orbit smaller than Earth’s will also soon overtake and move away, and will not keep a fixed station relative to Earth. However, there is a loophole..

If the spacecraft is placed between Sun and Earth, Earth’s gravity pulls it in the opposite direction and cancels some of the pull of the Sun. With a weaker pull towards the Sun, the spacecraft then needs less speed to maintain its orbit. If the distance is just right – about a hundredth of the distance to the Sun – the spacecraft, too, will keep its position between the Sun and the Earth and will need just one year to go around the Sun. This is L1.

Joseph-Louis Lagrange, engraving by Robert Hart. Credit: britannica.com

L1 is a very good position for monitoring the Sun. The solar wind reaches it about one hour before reaching Earth. In 1978, the International Sun-Earth Explorer-3 (ISEE-3) was launched towards L1, where it conducted such observations for several years. Now the ESA/NASA SOHO solar watchdog is positioned there.

Such spacecraft must have their own rocket engines because the position is unstable: if a spacecraft slips off L1, it will slowly drift away, and some correcting action is needed. In fact, the preferred position is actually some distance to the side of L1, because if the spacecraft is right on the Sun-Earth line, the antennas which track it from Earth are also aimed at the Sun, a source of interfering radio waves. Corrections are needed regularly.

An effect similar to that which causes the L1 point occurs on the “night side” of Earth (further away from the Sun but about the same distance from Earth). A spacecraft placed there is more distant from the Sun and therefore should orbit it more slowly than the Earth; but the extra pull of the Earth adds up to the Sun’s pull, and this allows the spacecraft to move faster and keep up with Earth.

At a certain point, the spacecraft?s orbital period equals that of Earth’s. This is L2. It is located 1.5 million kilometers directly ‘behind’ the Earth as viewed from the Sun. It is about four times further away from the Earth than the Moon. L2 is a great place from which to observe the larger Universe. A spacecraft would not have to make constant orbits of Earth, which result in it passing in and out of Earth’s shadow and causing it to heat up and cool down, distorting its view.

Diagram of the five Lagrange points associated with the sun-Earth system, showing DSCOVR orbiting the L-1 point. Image is not to scale. Credit: NASA/WMAP Science Team

Free from this restriction and far away from the heat radiated by Earth, L2 provides a much more stable viewpoint. ESA has a number of missions that will make use of this spot in the coming years. L2 will become home to ESA missions such as Herschel, Planck, Gaia and the James Webb Space Telescope.

L3 lies on a line defined by the Sun and Earth, but beyond the position of the Sun. On the opposite side of the Sun, just outside the orbit of Earth, the combination of the Sun?s and Earth?s gravity would cause a spaceraft’s orbital period to equal that of Earth. Since the position of this Lagrange point lies behind the Sun, any objects which may be orbiting there cannot be seen from Earth.

The L4 and L5 points lie at 60 degrees ahead of and behind Earth in its orbit as seen from the Sun. Unlike the other Lagrange points, L4 and L5 are resistant to gravitational perturbations. Because of this stability, objects tend to accumulate in these points, such as dust and some asteroid-type objects.

A spacecraft at L1, L2, or L3 is “meta-stable”, like a ball sitting on top of a hill. A little push or bump and it starts moving away. A spacecraft at one of these points has to use frequent rocket firings or other means to remain in the same place. Orbits around these points are called ‘halo orbits’.

The L2 (Lagrange 2) point in space. Image Credit: NASA

But at L4 or L5, a spacecraft is truly stable, like a ball in a bowl: when gently pushed away, it orbits the Lagrange point without drifting farther and farther, and without the need of frequent rocket firings. The Sun’s pull causes any object in the L4 and L5 locations to ?orbit? the Lagrange point in an 89-day cycle. These positions have been studied as possible sites for artificial space stations in the distant future.

We have written many interesting articles on Lagrange Points here at Universe Today. These include Sounds Painful: Are Deadly Asteroids Stuck in Earth’s Lagrangian Points?, NASA Scientists Calculate Space Highway, and Three Trojans Found in Neptune’s Orbit.

Astronomy Cast also has episodes on the subject, like Episode 76: Lagrange Points and Questions Show: Different Fields of Astronomy, Our Sibling Stars, and Hidden Lagrange Points. Be sure to check them out!

For a better idea of how Lagrange points work, Sixty Symbols has released a video featuring Professor Mike Merrifield, professor of astronomy at the University of Nottingham.

For more information, be sure to check out NASA’s Home on Lagrange, the ESA’s What are Lagrange Points? (ESA), and Princeton University’s Gravity Simulations.

Member
Charlie0061
June 11, 2013 5:29 PM

Very informative video. Thank you.