Q:

How is it known that asteroid 2011 UW158 has so much platinum?

Today an asteroid, 2011 UW158, is passing within 2.4 million km of Earth. There are a lot of reports of this asteroid containing $5.4 trillion of platinum in its core. People seem to want to mine it, but how do they know there is so much platinum within it? They seem to have a fairly specific number.

A:

With all the hype in the news this was surprisingly hard to research for specifically 2011 UW158.  I never did find a source for the claim on the value, though the Slooh Community Observatory put the claim at "\$300 billion to as much as \$5.4 trillion dollars worth of precious metals and minerals".
The answer basically seems to come down to: we've analyzed the composition of meteorites, meteorites come from asteroids, we can make a guess at which asteroids would match the composition of meteorites we've analyzed based on spectroscopy and visible characteristics (such as 2011 UW158 is spinning fast enough that if it were rocks simply held together by gravity it would have flown apart, indicating it must be melted together).
Research results:
A more general search turned up Review of Asteroid Compositions.  To quote the summary at the top of the paper:

Most of our information on asteroid surface compositions comes from telescopic reflectance spectroscopy, and most of our information on asteroid bulk compositions has been determined from the study of meteorites.

With respect to platinum specifically I found this paper: The Role of Near-Earth Asteroids in Long-Term Platinum Supply
While a large part of that paper discusses the uses and sources of platinum on earth page 7 starts discussing planetary formation and asteroids.  To summarize, the gravity of large bodies pulled platinum-group metals (PGMs) (and iron and nickel) into the core of the planets (which is why platinum is rare in the Earth's crust) but asteroids weren't big enough for gravity to separate their composition before they cooled.

Meteorite samples are the primary source of detailed data for asteroid chemical composition, especially trace metals.  Platinum, rhodium, iridium, rhenium, osmium, ruthenium, palladium, germanium and gold are found in significant concentrations (ranging from 1.1-30.7 grams per ton for each 
  metal) across a variety of meteorite samples attributed to the LL Chondrites (see Table 3).

And lower down:

Strong statistical continuity exists for the Chondrites examined by the planetary science community, providing a basis for the expectation that certain large asteroids match the chemical abundance of the meteorite samples 
  (it is hypothesized that these asteroids are the source of the meteorites).  However, without a sample returned from an asteroid, the evidence remains circumstantial.  Detailed asteroid reconnaissance by spacecraft is has 
  dramatically improved geologic models, but has only been carried out recently for a handful of asteroids.  Spectral analysis of data from telescopic observation can sometimes be used to infer general geological characteristics such as bulk composition for newer asteroid discoveries.

Just for fun, here's a website that's dedicated to listing asteroids along with the estimated profit of mining them: asterank

A:

Sorry to spoil everyone’s excitement, but one claim, credited to Mining.com, that the kilometer-wide asteroid might contain “up to 90 million metric tons of platinum and other precious metals” is wrong and is orders of magnitude too high.  Assuming the asteroid to be roughly spherical and 3280 feet (1 kilometer) across and being the more uncommon “nickel-iron” type (having a specific gravity of about 7.5) as opposed to the more common “stony” type, it would have a total mass of about 3.9 billion metric tons.
Nickel-iron asteroids, based on similar compositions to recovered nickel-iron meteorites, are expected to have more than 95% of their weight in just the metals iron, nickel and cobalt.  One good reference (http://authors.library.caltech.edu/51511/1/jgr4710.pdf ) states that the precious metals Ru, Rh, Pd, Ir, Pt are individually present in such meteorites in 1-10 ppm concentrations.  For convenience let’s optimistically assume these five precious metals total 50 ppm, and then let’s double that to get 100 ppm to account for all the other trace elements that might be considered “precious metals”.
The above considerations result in a net “precious metals” estimate of only 390,000 metric tons for the asteroid, a factor of about 230 lower than claimed by Mining.com.
Of course, this assumes that nickel and cobalt are not viewed as precious metals, which I believe is true.

