Throwback to an ancient thread on Reddit by AdmiralPelleon

It takes 6 BFR launches to put a fully fueled BFS in orbit, going for $7 million/launch. I'll be generous, and pretend that the BFS making the trip to the asteroid doesn't lose value along the way (hint: it does).

So let's plug in the Rocket Equation for a fully-fueled BFS in orbit, let's see how much fuel we must expend to get the BFS to the asteroid to pick up it's cargo:

Delta-v to Ryugu (a near-earth asteroid) has $95 billion of minerals on it = Raptor Engine ISP * ln( (start fuel mass + empty mass)/ (start fuel mass - fuel used + empty mass) )

OR: 4666 = 3759.81ln((1100+85)/(1100-fuel used + 85))

fuel used = 851.67

So just getting the BFS to the closest near earth object takes up 851,000 kg of fuel! This is before we've loaded any minerals on board. To calculate how much payload we can bring back do earth, it's the same equation except:

Delta-v to Earth = Raptor Engine ISP * ln( (start fuel mass + payload + empty mass)/ (payload + empty mass) )

OR: 4666 = 3759.81ln((1100-852+p+85)/(p + 85))

payload = 28.893 metric tons

So that sucks! We go all that way, launch 6 rockets, spend probably years in outer space, and all we get are 29 metric tons of cobalt!?! At current prices, that's worth ~$899,000. Compare that to the "best case" cost of 6 BFR launches or $42 million.

BUT WAIT!

It's commonly agreed that some sort of ISRU (creating fuel out of the asteroid itself) will be required for space mining. The asteroid Ryugu probably has water, and while I don't think it has carbon, amateur scientists like us need not be constrained by such petty laws of chemistry! Let's assume that, once the ship arrives, it is fully refueled at zero cost. Now our return-payload looks like:

Delta-v to Earth = Raptor Engine ISP * ln( (start fuel mass + payload + empty mass)/ (payload + empty mass) )

OR: 4666 = 3759.81ln((1100+p+85)/(p+ 85))

payload = 345.5 metric tons

The good news is we've increased our revenues by an order of magnitude (~$ 10,710,500)! The bad news is we are now at just over 25% of our fixed, "best case" costs. (I'm actually not sure if the BFS could land with that much payload, but at this point it doesn't really matter does it?)

These numbers can be made to work for elements like Helium 3 and Platinum, due to their super-high cost-per-kg (345.5 metric tons of Platinum is technically worth over $10 billion). However, the world's yearly supply of platinum is roughly just 243 metric tons, and increasing this significantly would serve to quickly crater the price.

All this is to say that no, asteroid mining is not, and may never be, feasible>