Those Lagrangian Points

Lagrangian Points of the Earth:Sun system, not to scale.

Hubble’s replacement, the gargantuan James Webb Space Telescope, which was supposed to be launched now, in the autumn of 2018, has been postponed yet again. Figure another two years. And when it’s finally launched, it will not orbit Earth. Instead, it will head for Lagrangian Point Number 2, which is four times farther away than the Moon. Not an easy place to reach for a repair mission.

Lagrangian points are very cool. So why haven’t we ever explored them on this page in the 44 years this column has run? Beats me. Let’s do it now.

Finding stable places in space started as solutions to the famous three-body problem. The renowned mathematician Leonhard Euler came up with three of the points, and a few years later Joseph LaGrange announced the final two. These five places are where a lightweight object like a spacecraft or a small asteroid can more or less remain in place, relative to a massive object orbiting around an even more massive one. Turns out, those stable places exist only if one of the two big objects is at least 25 times heavier than the other. If you want to be really precise, the required mass ratio is >24.96 to one.


The Earth:Moon system qualifies because the Earth is 88 times more massive than the Moon. The Earth:Sun System even more easily qualifies, because the Sun is 333,000 times more massive than the Earth. So we’re in business, and in both those systems there are five places where a spacecraft could more or less park and remain in place. But that’s a simplification. The spacecraft doesn’t just go to a Lagrangian Point and sit there. It slowly orbits around that spot, but can do so using very little propulsion fuel.

The next big question is whether any of these five places have value to us.

Lagrangian Points 1, 2 and 3 are all directly on the line between the Earth and the Sun. L1 is between us and the Sun – roughly one percent of the distance to the Sun, or about one million miles from here, which is where our gravities balance. Some very important Sun-observing spacecraft were sent there: Soho and Ace. When violent high-speed material from the Sun, from the giant explosions named coronal mass ejections, is on route to Earth, it sweeps past those spacecraft a few hours before arriving here, giving us a heads-up warning.

Lagrangian 2 lies in the opposite direction, meaning away from the Sun. It’s on that same line from Sun to Earth, but a million miles beyond our orbit: some four times farther than the Moon. The WMAP and Planck spacecraft, both measuring the cosmic microwave background, were parked there. It’s where the James Webb will go if it ever gets launched. It’s the perfect place for that infrared telescope, because a giant sunshade will block the heat from both the Sun and the Earth, with that telescope on the far side of the shade.

Those are the only useful Lagrangian points to date: L1 and L2.  Nobody has found a use for L3, which is also on a line connecting the Earth and the Sun – but way beyond the Sun, where the line meets Earth’s orbit on the far side. It’s the science-fiction location of the second Earth where each of us has an opposite analogue, always hidden from view behind the Sun.

The only truly stable Lagrangian points, which have ironically never been utilized by NASA, are L4 and L5: places right on Earth’s orbit, one-sixth of the way ahead of us around the Sun, and also one-sixth of the way backward behind us. These points form perfect equilateral triangles with both the Sun and the Earth. Anything that goes there stays there, so they’re each like Las Vegas. And you don’t need fuel to maintain your position there – meaning that natural objects might be found in those places.

And they have. Earth’s L4 and L5 locations have clouds of dust, and also a single asteroid discovered back in 2010. Jupiter’s L4 and L5 Lagrangian points are populated with asteroids called the Trojans, including three big ones.

So now you know, though you’ll probably not again hear about those fascinating places until Webb gets launched. We can probably stop holding our breath.

Want to know more? To read Bob’s previous columns, visit our Almanac Weekly website at Check out Bob‘s new podcast, Astounding Universe, co-hosted by Pulse of the Planet’s Jim Metzner.