Thread by @markmccaughrean

A few hours from now, #JWST will make its Mid-Course Correction 2 (MCC-2) burn, injecting it into its operational orbit around the Sun-Earth L2 point, ~1.5 million kilometres away.

What, why, how, when?!

A thread.

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First, a reminder: #JWST was launched on #Ariane5 #VA256 from Europe's spaceport in French Guiana on 25 December 2021. The #Ariane5 put it on a near-perfect trajectory towards L2 & two subsequent JWST Mid-Course Corrections have tweaked that.

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But why such a long journey to a place that's about four times further away from Earth than the Moon?

By contrast, the Hubble Space Telescope is in a low Earth orbit ~535km above the surface, making it accessible to several servicing missions over the past 31 years.

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The problem with being close to Earth is that Earth is warm & thus heats Hubble. And because Hubble orbits Earth every ~97 minutes, it spends roughly half the time in the dark & half being heated by the Sun.

This is not what we need for #JWST.

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As #JWST operates in the infrared, we want the telescope & instruments to be very cold (i.e. at -233ºC / 40K or so) to avoid them emitting light at the same wavelengths we're trying to detect from our targets.

So we need to be far from Earth & block the Sun.

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At the same time, you don't want to be *too* far from Earth, because the greater the distance, the lower the data transmission rates.

And the amazing science instruments on #JWST can generate a lot of data very quickly, so being too far away would limit the science.

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So, the question is, can we find a place not too far away where both the Sun & Earth will always be on one side of a giant parasol, allowing the other side where the telescope & instruments are to get very, very cold?

The answer is "yes" & that's L2.

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So what is L2? And for that matter, what is L1 & are there any other Ln places?

The answers lie with Joseph-Louis Lagrange, an Italian-born, naturalised French astronomer & mathematician.

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Among many other important contributions, Lagrange studied planetary orbits, & found some interesting solutions to the so-called "three-body problem".

This aims to describe the motion of three objects moving around each other under gravity, a notoriously tricky problem.

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What Lagrange found was a family of of solutions for the situation where two of the objects (e.g. the Sun & Earth) are massive, but the third (e.g. #JWST) is much lighter.

That is, the gravity of the Sun & Earth influence the situation, but that of #JWST is negligible.

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In more detail, Lagrange found five points in such a system where the interplay between the gravity of the two large bodies & their centripetal forces as they orbit creates points of equilibrium where the third object can sit without much orbital correction needed.

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The not-to-scale diagram below shows where these points are relatively to the Sun & Earth.

L1, L2, & L3 are along a straight line joining the Sun & Earth; L4 & L5 are at the vertices of equilateral triangles with the Sun & Earth at the other two vertices.

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The arrows in the diagram above show how the potential at each L-point works. L4 & L5 can be thought of as large flat hilltops & combining gravity, centripetal force, & Coriolis force in a rotating system, these are stable: they're hard to fall off.

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physics.stackexchange.com/questions/3609…

[Thanks to @NMK_ZeroG for catching my schoolboy error there, where I previously described L4 & L5 as valleys – I'd completely forgotten about the Coriolis forces 😱

Apologies for deleting & reposting.]

@NMK_ZeroG Many asteroids have collected in the L4 & L5 points of the Sun-Jupiter system: those that lead Jupiter by 60º are called "Greeks"; those that trail, "Trojans".

Generically, such L4/L5 objects in any system are called trojans & a couple of Earth trojans are known.

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@NMK_ZeroG Looking back at the Lagrange point diagram in tweet 12 though, you'll see that L1, L2, & L3 are different.

Instead of flat hilltops with downward slopes in all directions, these are better thought of as "saddles".

Image: Wikipedia/BLW

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@NMK_ZeroG That is, at each of L1, L2, & L3, there are upward "hills" in the direction along the orbit, but downward "slopes" towards & away from Earth.

As a result, these are not stable equilibrium points like L4 & L5: it's possible to fall off them, like sliding off a saddle.

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@NMK_ZeroG Without going to deeply into the maths, it's possible to have an intuitive understanding of why this is so.

First, consider Earth, orbiting the Sun in a 365.25 Earth days, one Earth year.

Now think about the other planets & how long they take to orbit the Sun.

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Sorry: the full 42 tweet thread got broken here. Let’s see if I can glue it back together 🤞

https://twitter.com/markmccaughrean/status/1485659601672491010