The James Webb space telescope has arrived at L2 (opens in new tab)

Picture rolling a ball up a hill. If you don't roll it fast enough it will roll back down before reaching the top. If you roll it too fast it will go over the top and roll down the other side. Just right, and it will stop at the top of the hill. But being at the top of the hill, it's an unstable orbit, and any small drift will end up with the ball eventually rolling back down the hill. That's why occasional course corrections are required, and why the lifetime of the satellite is determined by the amount of fuel it has.

It's like bowls, or curling (the sports). It's a million mile curl. At the end of the curl, the telescope has close to zero radial velocity with respect to Earth (that is, its orbit around the Sun is parallel to Earth's and has the same period). At that point there will be an orbit injection burn to put it into a small elliptical orbit around the Lagrange point.

The telescope slows down over time due to Earth’s gravitational pull. IIRC the trip to L2 was all driven by momentum after the rocket released it. The rocket boosted it in the right direction/speed so that gravity would slow it to a stop at the right place.

"...Webb will orbit around L2, not sit stationary precisely at L2..."

https://webb.nasa.gov/content/about/orbit.html

JWST is solar powered. Sun-Earth L2 is in permanent eclipse and may have unstable lighting or heating conditions. A halo orbit about L2 is extraordinarily boring and always in full sunlight.

Maintaining L2 or an L2 halo requires propellant.

L2 is unstable so sitting there is not a win. By orbiting (and orbiting at quite a long distance from the actual L2 point) the JWST can ensure its solar panels get maximum sunlight.

If anyone wants to build a fun intuition of how Lagrange orbits work, I recommend trying Kerbal Space Program with the Principia mod (n-body gravity and selectable reference frames).

No. I thought so too, but it's orbit around L2 is bigger than the Moon's orbit around the Earth. It's never in Earth's shadow, but it's position allows it to block both the Sun and the Earth consistently with one shield without moving it. At least that's my current understanding...

But things should be cooling down fast. There's a lot of different bits that all have different temperatures; here's a 2019 projected timeline of where we expect each bit to be. (We should be around day 30 today)

https://www.reddit.com/r/jameswebb/comments/s4yfs8/jwst_temp...