Which orbital point lets telescopes like JWST hover with Earth?

L2, the second Lagrange point, about 1.5 million kilometres directly out from the Sun - four times further than the Moon. It is a place where the combined pull of Sun and Earth keeps an object orbiting at exactly the same rate as Earth does, so it stays lined up permanently instead of drifting ahead or behind.

That alignment is the whole point for an infrared telescope. Sun, Earth and Moon all sit in one direction, so a single sunshield blocks all three at once and the instruments can be kept below 50 kelvin - which is essential, because a warm telescope glows in exactly the wavelengths it is trying to observe. Webb's shield is five layers of coated plastic the size of a tennis court, and the temperature difference across it is around 300 degrees.

L2 is not a hole but a saddle: stable in some directions and unstable in others, so spacecraft do not sit at the point itself. They fly a wide loop around it and fire small correction burns every few weeks. The fuel for those burns is what sets the mission's lifetime, and it is a one-way trip - nothing has been serviced that far out, and Hubble's repair missions are not repeatable at L2. There are five Lagrange points in any two-body system; the Trojan asteroids sit at Jupiter's L4 and L5, which are genuinely stable.