Where do space telescopes orbit?

Like all satellites, the orbit depends on the purpose of the telescope.

The Hubble Space Telescope orbits in "low Earth orbit", a little higher than the International Space Station does but still within range of the Shuttle. This is because the Hubble was designed for easy maintenance and parts replacement by Shuttle astronauts. in fact, three Shuttle missions have been dedicated to performing maintenance and upgrades of the Hubble, including one just last year.

The Spitzer Space Telescope does not orbit the Earth at all; it is in orbit around the Sun, trailing a few million miles behind the Earth. Spitzer does not observe visible light, but infrared; it is a "heat" telescope. This selection of orbit keeps the Spitzer telescope well away from the hot Earth, allowing its temperature to decrease to about 40 degrees Kelvin, which reduces the load on the cryogenic mechanisms.
Like all satellites, the orbit depends on the purpose of the telescope.

The Hubble Space Telescope orbits in "low Earth orbit", a little higher than the International Space Station does but still within range of the Shuttle. This is because the Hubble was designed for easy maintenance and parts replacement by Shuttle astronauts. in fact, three Shuttle missions have been dedicated to performing maintenance and upgrades of the Hubble, including one just last year.

The Spitzer Space Telescope does not orbit the Earth at all; it is in orbit around the Sun, trailing a few million miles behind the Earth. Spitzer does not observe visible light, but infrared; it is a "heat" telescope. This selection of orbit keeps the Spitzer telescope well away from the hot Earth, allowing its temperature to decrease to about 40 degrees Kelvin, which reduces the load on the cryogenic mechanisms.