Where the Webb space telescope is going, Lagrange point 2, and why

Ms. Pickles, the teacher: It's science time again class. Ladies, put your Springfield XDs in your purses and your cell phones in your backpacks. 

This one is Springfield model XD-S Mod.2, which is a very slim and lightweight single stack firearm that makes a great handgun for easy conceal carry, and, better yet, they are conveniently available for 9mm, .40sw, or .45 acp ammunition; The ladies just love this reliable handgun, with plenty of knockdown power in the 9mm or .45 acp models, although the .40sw stings and that will draw the attention of any lucky recipient 

Gentlemen, put your Ruger GP100s and cell phones in your backpacks. 

The popular GP100 is a line of full-sized revolvers available with six, seven, eight, and ten shot capacities and a multitude of calibers including .22LR, and, when you need some serious firepower, the always popular .357 magnum and 10mm auto; These fine handguns reminisce of the Dirty Harry look with modern flare, reliability and knockdown power, making the GP100 line an epic firearm that resonates as one of the best selling revolvers to sixth graders on the market today! 😍

Ms. Pickles: Thank you so much for not blowing me away, class. My, my, you're such a wonderful, polite sixth-grade class. You make me and our beloved home, Texas, proud of you all. Now, take out your notebooks and pencils.

Lagrange point 2

Ms. Pickles starts the lesson: The James Webb space telescope (JWST) is going to park at a place in space called Lagrange point 2. For any two large objects in space, in this case the Sun and Earth, there are five Lagrange points, called L1, L2, L3, L4 and L5.

Interruption from Bowser, one of the boys in class: Ms. Pickles, is the Earth flat like my dad and our preacher say?

Pickles: Now, now Bowser, that topic will not come up until the 12th grade when we do advanced Christian science classes. So, for now, we'll just say it is flat and Scientology is not nearly as crackpot as some nice people say it is.

Pickles continuing: Lagrange points are areas of space where gravity and centrifugal orbital forces are in balance between two large objects. Smaller objects in these areas of space tend to stay put unless something sufficiently gravitational moves them out of the Lagrange area it is in. Here are some pictures of the Lagrange points for the Earth and Sun and the route the JWST is taking on its way to L2.

Smaller objects are pulled into L4 and L5, which keep some hold on them, preventing trapped objects from moving out of the L4 and L5 areas. By contrast, L1, L2 and L3 are metastable, meaning that there is almost no force keeping a smaller object in those three areas. Almost any little gravitational tug on an object that has settled in L1, L2 or L3 will nudge it out of the area. That is why the JWST carries fuel and has thrusters to keep it in the L2 area. The fuel that the JWST carries was intended to be able to keep it in L2 for 10 years, but that has been extended to 15-20 years because less fuel was used than anticipated to get the space craft on course to L2.  

This drawing shows the locations of the Lagrange points relative to the curvature of space that the Sun and Earth causes in our four-dimensional space-time universe. They are just at the edge of the gravity wells.

Sun and Earth gravity wells (space-time curvatures) 

relative to the five Lagrange points

Trojan asteroids at L4 and L5 

for the Sun and Jupiter

As you can see, the Lagrange areas are just at the edge of the gravity wells or space curvature that the mass of the Sun and the Earth create in space-time. A number of other space craft are already parked in the L2 area, and the JWST will be the next arrival from Earth to be parked there.

Class, as you might guess, the L1-L2 Lagrange points are unstable because they need to follow radial velocity of the two parent bodies as they orbit each other, in our case the Earth in a heliocentric orbit around the Sun, but none of them are really at the orbital altitude matching their radial velocity (too slow in L1 and too fast in L2). Since the Earth's orbit isn't exactly circular (orbital eccentricity of ~ 0.017), their altitude will also slightly change during one orbital period. This is less of a case with L4-L5, and arguably also L3, depending on orbital eccentricity of parent bodies, and is where we might find Trojan and Hilda family of asteroids, respectively. All these Lagrange points can also be perturbed by gravitational influence of other celestials in the system, for example Jupiter's and even Moon's orbit in case of L1-L2 Sun-Earth points. And this is of course about instabilities in the velocity vector along the M1 parent body. Orthogonal to it and towards the M1 and M2 bodies, it's just the tipping point in direction towards M1 or M2.

Can anyone think of any questions or maybe any uses for these areas of space relative to the Sun and Earth?

Yes, Bronywyn?

Bronywyn, one of the brighter bulbs in the drawer: Could aliens use L3 to hide an orbiting space station from Earth before launching an attack? It looks like L1, L2 and L3 are aligned in a straight line. L3 seems to be always hidden from Earth by being behind the Sun. 

Pickles: Yes, Bronywyn! Good for you. Here's 10 rounds of ammo for your gun. That's right. The three Lagrange areas do line up and L3 is directly behind the Sun relative to Earth. We cannot see it, so aliens could hide there as the prepare to disinfect Earth. Anyone else? . . . . Yes, Lumpy.

Lumpy: Could people build a huge space colony or something else at L4 or L5 and not worry much about the thing floating away? Since those two Lagrange points pull things in and keep 'em there, maybe that would be useful to keep something useful in those places.

Pickles: Correct Lumpy. Here's ammo for you. That has been proposed. Although there is a cloud of rocks and lumps stably situated at both L4 and L5, there is still plenty of room to build huge structures that would remain in the same place over time.  

Excellent job class. I think you've got it. A quiz on this will be tomorrow. Please familiarize yourselves with the Trojan and Hilda families of asteroids. And, be familiar with spatial instability associated with radial velocity concerns.

By Germaine: The science guy