X-ray

There are four: Hubble Space Telescope, Compton Gamma Ray Observatory, Chandra X-ray Observatory, and the Spitzer Space Telescope.

Because X-Rays do not penetrate the earth's surface. The Chandra X-Ray Observatory would be completely useless on the ground because it detects X-Rays. Therefore, it must be in space to detect the rays.

Unmanded mission:)

I would have to say the Moon, but there are many famous satellites that orbit Earth (Hubble, the International Space Station, Chandra X-ray Observatory, etc.)