But, I'm just in awe and I keep thinking 'how does he do it?'.

He's running two intensely technical and risky companies. Yet he seems involved in and knowledgeable about every aspect of their operations and tech. And finds the time to write a post like this before what is an incredibly important and defining endeavor.

What can us, mere mortals learn from him? We can't change our baseline raw intelligence (which effects how quickly and deeply you can learn new things), but are there other patterns we can replicate in our lives?

We already have industrial robots that can move and grasp heavy weights relatively quickly over distances of several metres -- it doesn't take much imagination to conceive of a similar contraption being used to arrest the descent of the rocket over the final few tens of metres of its' descent - a sort of brobdingnagian robotic catcher's mitt.

Granted, this might be a bit on the expensive / elaborate / bizarrely over-engineered side -- but it would look utterly awesome.

It is important to note that the amount of energy needed to achieve a given velocity increases with the square, so going from 1000 km/h to 2000 km/h takes four times as much energy as going from 0 km/h to 1000 km/h, not twice as much.

Three times, not four--you already spent a quarter of the energy getting to 1000 km/h. Getting the rest of the way to 2000 km/h takes the remaining three quarters.

I'm guessing the sacrifice is roughly equal to the mass of unburnt fuel in the booster at the point of booster separation, but don't much trust my intuition on these things.

"The reason they are floating around is that they have no net acceleration. The outward acceleration of (apparent) circular motion, which wants to sling them out into deep space, exactly balances the inward acceleration of gravity that wants to pull them down to Earth."

There is no "outward acceleration". The weightlessness is because the craft they are in is accelerating towards Earth with exactly the same acceleration. The reason they don't hit the ground is that they have a suitably high tangential velocity.

Did you get that, Jeff?

The truth is, they have both achieved an astonishing amount.

I'd like to meet the person that is both uneducated enough to think that gravity suddenly stops and after that is "zero g", and also undestands what "proportionate to the square of the distance" means!

Edit: Just got to the end and saw this was prior to launch, so before Bezos' "welcome to the club" tweet. I guess in that context it's a bit more subtle at least, but still seems like he was making a point of the difference from Blue Origin.

"Now imagine placing a marble somewhere on that slippery sheet -- it is guaranteed to fall into one of the funnels. "

This holds for the case where there are two objects initially at rest, but I don't see it as obviously true if there are more than two objects in the universe.

edit: just saw this at the bottom and it made me smile; "Apologies for any typos in the above."

– Any flat chunk of cement is a landing spot. That means more places to land in case of contingencies. For yesterday's mission, SpaceX had one primary and four alternate landing zones.[1]

– I doubt industrial robots can withstand rocket exhaust. As helicopter footage shows, the landing pad got lit-up pretty good.[2] Remember, the first stage is over 40 meters tall. Those are some massive flames.

…and most importantly:

– Landing legs work on other planets.

1. Map: http://www.americaspace.com/wp-content/uploads/2015/12/LZ1.j... (from http://www.americaspace.com/?p=89910)

2. https://www.youtube.com/watch?v=ZCBE8ocOkAQ

Parachutes, "catching" devices, etc. etc.

It all comes down to one thing, and one thing only.

Whatever the solution, it has to work on other planets with no infrastructure on that planet, and it has to leave the booster in a state that it's ready to go again with only a fuel fill up.

(No flight deck required -- just cables suspended between two towers and an arrester hook at the top of the rocket -- which just has to be lighter than folding legs at the bottom).

Also the empty rocket might be too weak to be grabbed by anything. They compare the thickness to a tin can.

   > how much payload is sacrificed by the need to keep fuel
   > in reserve for the return to base?

A more detailed answer is that building a system which can be reused is an economic proposition. So that the Falcon 9 can lift X Metric tons to orbit for $Y. The way in which they keep the value $Y low is by re-using the first stage. Every satellite project knows the throw weight of all the common launch vehicles and their cost per kilo. And that is how you plan you satellite design.

Now at the moment SpaceX gets 9 merlin engines and the first stage booster back for "free" (which is to say that the cost paid assumed it would be consumed in the launch) but as they learn what they can do they will use that cost savings to offer cheaper launch services (more business) until they have a full launch schedule and then keep any excess value for re-investment.

But an interesting question is this, given that they have a "used" first stage, who would be willing to launch on it? It has no track record and no reliability statistics other than it worked at least once before. To develop that information you need to re-launch them. And I'm hoping that SpaceX will make available some higher risk but lower cost "seats" on those test flights.

[1] http://www.spacex.com/falcon9

It's actually going to be much, much less than that due to the nature of the rocket equation. https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

Since the frame where the center of the rocket is stationary is a non-inertial frame, Newton's law doesn't apply [1]. However a modification of Newton's law that includes a so-called "ficticious force" applies [2] (I don't think this modification has a name). This is why the article says there's an outward acceleration, because in the frame where the center of the rocket is stationary, the outward acceleration is caused by the ficticious force.

[1]: https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion begins the laws with "when viewed in an inertial reference frame"

[2]: https://en.wikipedia.org/wiki/Non-inertial_reference_frame quotes, "One might say that F = ma holds in any coordinate system provided the term 'force' is redefined to include the so-called 'reversed effective forces' or 'inertia forces'."

The whole point of that comment was to apply only to at-rest things (he goes on to contrast it with objects with velocity), though I think maybe you got that.

If you have a marble and two other objects, the other objects make two funnels, and there is a saddle (itself curved) where the two objects's funnels are equipotent. That's the three-body case. If it were possible to balance perfectly on this line of equipotence, you'd just slide to the lowest point on that line, and stay there, out of the funnels. This, IIUC, is one of the Lagrange points... L1, I think. In theory it's possibly-stable, but its stability exhibits negative feedback, so in practice it's impossible (although with station-keeping rockets, it's cheaper to hover there than most places).

As you add more funnels, you just get more of these saddle lines intersecting. There are many infinitely-fussy places in the universe where you could in-theory-but-not-in-practice hover without falling into a funnel (if it weren't for brownian motion and maybe some other quantum effects that disturb your infinitely-difficult equilibrium).

Of course, this whole analogy doesn't account for the fact that all of the bodies are acting on each other, not just the funnels acting on the marble.