What are Lagrange points?

Published: 11th February, 2022 at 07:00
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You’ll have heard about L2 in the news, as it’s recently become home to the James Webb Space Telescope. Meanwhile, there’s a new Earth Trojan asteroid lurking at L4. But what does all this actually mean?

What are Lagrange points?

When two massive bodies orbit each other, there are five locations around these bodies where the gravitational forces balance. And it’s at these gravitational sweet spots, called Lagrange points, where a smaller object can stay in equilibrium. So, for the Earth-Sun system, a spacecraft or natural object can orbit the Sun, while keeping a position relative to the Sun and the Earth, as they ‘hover’ at these Lagrange points.

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When we talk about the Earth-Sun system or the Jupiter-Sun system, this refers to how the two bodies interact (i.e., one orbits the other), and their associated Lagrange points.

Of these five Lagrange points, L1 to L5, two - L4 and L5 - are stable. This means that if a small object at L4 or L5 is nudged, there would be an effective restoring force and it will come back to this spot. Nudge a small object at one of the three unstable Lagrange points, L1, L2 or L3, and it will break orbit and drift off into interplanetary space.

Lagrange points were first theorised in 1772, by French mathematician and astronomer Joseph-Louis Lagrange. Then 134 years later, in 1906, the first Trojan asteroids were discovered at these points in the Jupiter-Sun system.

How many Lagrange points are there in the Solar System?

The five Lagrange points exist in the same relative positions around all major bodies in our Solar System, where one body orbits a more massive body. So, there are Lagrange points in the Earth-Sun system, the Mars-Sun system, the Jupiter-Sun system, and so on. They also exist for planets and their moons: Earth-Moon, Mars-Phobos, Jupiter-Io, Saturn-Titan etc. However, they do not exist for sibling planets, Earth-Mars, for example, as they both orbit the Sun and neither Earth nor Mars orbit the other.

Discover more about space:

Where are the five Lagrange points?

What are Lagrange points © NASA:Wikinson Microwave Anistropy Probe
An illustration showing the position of the five Lagrange points around the Earth-Sun system © NASA/Wilkinson Microwave Anisotropy Probe

Lagrange point L1, unstable

L1 is located between the Earth and the Sun. It’s approximately 1.5 million km (1 million miles) from the Earth and offers uninterrupted views of the Sun.

Lagrange point L2, unstable

L2 is also 1.5 million km from the Earth, but on the opposite side to L1 so it’s the ideal location to study deep space.

Lagrange point L3, unstable

L3 lies beyond the Sun and is the furthest of the Lagrange points from Earth.

Lagrange point L4, stable

L4 is 60° ahead of the Earth, i.e., Earth-leading. L4 is where Earth will be in two months’ time.

Lagrange point L5, stable

L5 is 60° behind Earth, i.e., Earth-trailing. L5 is where Earth was two months ago.

Why is the James Webb Space Telescope at L2?

The James Webb Space Telescope (JWST) arrived at its new home, Lagrange point L2, on 24 January 2022, after its launch on Christmas Day, 2021. Here, it will stay, orbiting around this gravitationally special position 1.5 million km away for the next 10 or 20 (or more) years, as L2 itself orbits the Sun, keeping Earth behind it.

As L2 is on the opposite side of the Earth from the Sun, JWST will have a clear view of deep space. With its sunshield deployed and facing away from the Sun, Earth and Moon, the JWST can keep its optics and instruments shaded, and the view is not blocked by the Earth. And as the temperature at L2 is cold, and doesn’t experience huge temperature swings, the onboard equipment will be kept stable.

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What are Lagrange points?
James Webb Space Telescope is orbiting Lagrange point L2, facing away from the Earth © Getty

As L2 is gravitationally unstable, the JWST will need to make small adjustments every three-ish weeks, burning its thrusters to help keep it in position. It’s expected that the JWST will remain at L2 until it runs out of fuel to continue making these adjustments.

But this isn’t the first time we’ve utilised Lagrange points to our advantage. Among others, L2 was also previously home to NASA’s Wilkinson Microwave Anisotropy Probe (WMAP) and ESA’s subsequent Planck spacecraft until 2010 and 2013, when they were both deactivated and sent into a heliocentric graveyard orbit (an orbit that lies away from operational orbits).

The Solar and Heliospheric Observatory (SOHO), which launched in 1995, is in a halo orbit around L1 in the Earth-Sun system. It orbits L1 every six months, and is still in operation, having discovered over 4,000 comets.

Is there anything at L3 Lagrange point?

In the Earth-Sun system, when viewed from the Earth, L3 is always hidden behind the Sun. There are currently no known objects at L3. If you’re familiar with early science fiction stories, you might remember tales of invading forces of creatures from Planet X, a mysterious Earth-sized 'twin' planet hidden behind the Sun.

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However, as the orbit of L3 is exponentially unstable, this just isn’t possible (sorry). Although, a document created by Neil J. Cornish for WMAP Education and Outreach notes that L3 would be a good place to park your invasion force for a while…

Authors

Holly SpannerStaff Writer, BBC Science Focus

Holly is the staff writer at BBC Science Focus. Before joining the team she was a geoenvironmental consultant and holds an MSc in Geoscience from UCL.

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