The possibility of mining asteroids for valuable resources has long captured the imaginations of science fiction writers, entrepreneurs and rocket scientists. Indeed in 2012, Richard Branson, Larry Page and Eric Schmidt among others, announced that they had invested in a start up called Planetary Resources. The goal: to cost-effectively mine resources in space.

That raises an interesting question. How many asteroids are there that can be mined in a commercially viable way?

Today we get an answer thanks to the work of Martin Elvis at the Harvard-Smithsonian Center for Astrophysics in Cambridge. He has developed a “Drake-like” equation that estimates the number of commercially-viable asteroids in the Solar System that are worth mining for materials such as platinum and water. (The famous Drake equation takes a similar approach to estimate the number of advanced civilisations in the galaxy)

The answer is likely to disappoint all the Bransons, the Pages and the Schmidts out there. In a paper in press at the journal Planetary and Space Science, the “Elvis equation” predicts that there are probably about ten asteroids with commercially viable veins of platinum group metals.

The process of calculating the number of mineable asteroids is straightforward in principle. Simply start with the total number of asteroids and determine the fraction that meet the requirements for commercial mining.

That’s similar in principle to the approach Frank Drake took in the 1960s to determine the number of intelligent civilisations: start with the total number of stars in the galaxy and work out the fraction that meet the requirements for the presence of intelligent life. His eponymous equation has since become hugely famous.

Elvis’s approach is similar. He essentially works out the factors that determine whether an asteroid is commercially viable to mine and the proportion of space rocks that meet this requirement.

First of all, the asteroid has to be relatively easy to get to. That rules out all but the nearest objects that orbit the Sun close to Earth. The key parameter here is the change in velocity, or delta-v, needed to send mining equipment to such an asteroid and to return with a much larger mass of ore that has been extracted.

Elvis says that a delta-v of 4.5 kilometres per second is a reasonable goal for today’s rocket technology. This makes only 2.5 per cent of known Near Earth Objects accessible (although this figure rises to 25 per cent if the delta-v can be increased to 5.7 km/s).

Next, the asteroid has to contain the required ore. Platinum group metals—platinum, rhodium, osmium, iridium, palladium and rhenium— are rare in the Earth’s crust because they dissolve easily in molten iron and so are mainly concentrated in the our planet’s interior. So the most promising asteroids are probably those rich in iron and nickel and known as M-type. Elvis reckons these make up about 4 per cent of known space rocks.

These asteroids must also contain a high enough concentration of platinum group metals to make them worth mining. Meteorite studies suggest that perhaps 50 per cent of M-type asteroids will make the grade.

Finally, it is not worth mining small asteroids because the total amount of ore they can produce will not cover the mission costs, which Elvis estimates in the billion dollar range. So that rules out asteroids smaller than a certain threshold.

To determine this threshold, Elvis has to work out the value of the ore that a mining mission would produce. That raises the interesting question of how valuable this ore would be if it were returned to Earth.

Platinum currently sells for about $50,000/kg. Elvis says the annual production on Earth is about 200 metric tonnes per year, which is about ten times more than a decent mission might return. For that reason, he says: “I am assuming here that asteroid mining does not flood the market and depress platinum group metal prices, which is plausible for the first deliveries.”

However, he also points out with an element of understatement that markets do not always respond linearly to changes in supply.

Supposing that Elvis is right about the price, then a 100-metre asteroid satisfying all the above criteria would bring in about $1.2 billion. That makes the 100-metre size the minimum that is worth targeting.

It’s worth pointing out here that most of the estimates here have huge error bars. But taking these and plugging them into Elvis’s Drake-like equation gives a lower bound on the number of asteroids worth mining.

That number is likely to be about 10, he says.

The numbers are slightly better for water-bearing asteroids, which are also likely to be highly sought after since H2O can be broken down into hydrogen and oxygen for fuel or used to maintain bio-habitats. In this case, Elvis estimates that there are likely to be around 18 water-ore-bearing asteroids with a diameter greater than 100 metres.

Elvis is quick to point out that there are large uncertainties in his calculations, saying these are conservative estimates. Nevertheless they are unlikely to make comfortable reading for those hoping to make money out of raiding the Solar System’s resources. “The number is surely smaller than would-be asteroid miners may have expected,” he says.

That has important implications. With so few spacerocks worth mining, the discovery of just one is likely to be hugely valuable information. Expect the exploration and prospecting of asteroids in the next few years to become a highly secretive endeavour.

Ref: arxiv.org/abs/1312.4450: How Many Ore-Bearing Asteroids?