With the huge cost of space travel, how can is be economically feasible to mine astroids? What is so valuable on astroids?

The other answer mentions spectral type, and this is certainly one part of a two-pronged research approach. The other half involves doing elemental composition analysis of meteorites. Using nuclear methods, we can detect extremely tiny elemental concentrations using Earth-based lab techniques. Even a very tiny quantity can be measured.

Then, we have a more speculative step of connecting the type of meteorite to the asteroid spectral class, and after that, we have some work we can do connecting geological resources on Earth with prehistoric meteorites.

From all of this, we have basically concluded that the early Earth caused certain elements to migrate away from the surface. Being heavy, and having certain chemistry, they all concentrated toward the center of the planet. Because of that, for those rare elements, the only sources we can mine come from prehistoric (large) asteroid hits. While Earth was partially built by asteroid bombardment, this is small compared to the mass it accumulated in the proto-planet phase. So you could say that rare metals to us are really just locally rare due to the geologic history of Earth, and that asteroids will have the "normal" concentrations of them, which are deduced from the various methods I've mentioned.

There's the other fact that the most valuable rocks quoted by advocates tend to be the largest. Notably:

http://en.wikipedia.org/wiki/3554_Amun

This asteroid has a diameter of like 2.5 km. If you compared this to a mine on Earth, this is extremely large. Over all that volume, if you are able to process a small concentration of an element, you can get a lot of a valuable metal. So the crazy figures come from a combination of a) cherry picking spectral type and b) picking the largest ones. In truth, this asteroid isn't a near-term asset and the most useful ones will first be those that can produce rocket propellant.

/r/askscience Thread