My favorite way to describe orbits is 'constantly throwing yourself at the ground but moving so fast that you just keep missing', hence the constant free-fall/zero-g.
How fast do you have to go? Easy. Look out at the horizon far enough that you can see it drop (for example a mountain etc). You have to go so fast that in the time it takes you to reach that point, you only drop by the amount the horizon falls.
Could you make a cruise missile that didn't need any wings or other surfaces for lift - only forward propulsion - that just went so fast that it was effectively in orbit, but nor far above the ground?
You can't stay in orbit with plane wings because of air resistance, and with so little air you need rocket propulsion (for now, at least). But that's not to say there aren't some interesting games to be played with wings on the way up.
> This leads us to the central problem of getting into orbit: Reaching orbital speed takes much more fuel than reaching orbital height. Getting a ship up to 8 km/s takes a lot of booster rockets. Reaching orbital speed is hard enough; reaching to orbital speed while carrying enough fuel to slow back down would be completely impractical.[5]
Did SpaceX just solve this problem and rendered this paragraph obsolete? Or is that Falcon 9 reached space and turned around without achieving orbital velocity?
That paragraph was in reference to zeroing out your velocity before re-entry. The Falcon 9, iiuc, uses a combination of thrust and aerodynamic forces to slow itself down / put itself on the correct trajectory.
It's also worth noting that they only land the first stage, there's an entire next stage which isn't reusable which adds further speed to achieve full orbital velocity.
Clearly this man's intellect is through the roof. Reading this post and him explaining these concepts in such first-principle terms (despite not being a physicist/rocket engineer) indicates his in-depth understanding (nothing new there). I know he has a Bachelors in Physics but bear with me.
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?
In most companies the "Posts from the CEO" are a group effort (at my last company I wrote multiple statements that were supposedly from our CEO). What you're attributing to a single person is actually the work of many.
This leads to your question:
> But, I'm just in awe and I keep thinking 'how does he do it?'. 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?
Simply put, be willing to work hard enough to inspire people who are smarter than you to join your team.
>In most companies the "Posts from the CEO" are a group effort (at my last company I wrote multiple statements that were supposedly from our CEO). What you're attributing to a single person is actually the work of many.
If it's a group effort he was being pretty deceptive by ending with "apologies for typos in the above," making it sound like he just dashed it off himself.
Don't underestimate a good copywriter :) Christian Rudder's 'Dataclysm' has a funny example of someone who copy-pasted the same message to dozens of people on OK Cupid complete with an apology for spelling.
This hero worship is utterly stupid. It's also a disservice to children. We're teaching them that there are heroes, and then everyone else.
Bull. Work as hard as Elon did, and you'd make the same progress. It also required luck. No PayPal, no Elon. And there could only be one PayPal, at precisely that time in history.
A better question is, why did Carmack fail where Elon succeeded? Armadillo Aerospace was supposed to be SpaceX.
Carmack invested about $2 million into Armadillo in its first 6 years. Elon invested $100 million in that time frame (actually, the first 4 years of SpaceX).
Armadillo did OK actually, they just were on a completely different trajectory. It was very much a hobby project for Carmack.
Not only that, but wasn't Armadillo one of the "straight-up-to-100KM-and-return" (suborbital) designs? If so, then there is no money to be made in that (except for wealthy people that want a 20 minute thrill ride). It is the "lateral velocity of Mach 25" type of rocket that gets you satellite launch contracts.
Tim Urban, who co-hosted the live coverage, has written four in-depth articles on Musk and SpaceX. In the last article he attempts to describe the reason behind his success. TL;DR: Thinks from first-principles instead of analogy, treats human brains like computers.
There is one school of thought that goes that SpaceX's mission to "Get people to Mars" requires so much more than simply putting things in orbit that people set their expectations that this is only the beginning. If you set your expectations that you just wanted to get to space and straight back down again, you don't invest in things which would be helpful to a Mars mission.
So while building a resuable booster for rockets might be the entire goal of some company, for SpaceX it was only the first step in a lot of bigger goals in order to make it feasible to go to Mars. And in so doing, and creating a capability that they can sell today to fund future development.
He's commented on this type of thing before and it seems like he thinks it isn't any great trick. The main thing is that if you're going to reason well from first principles, you have to learn from first principles. If you build your "tree of knowledge" efficiently, then adding on to it isn't so difficult because you have a good core. Contrast this with the hobbyist that tries to learn rocket science when they don't have a good handle on first-year physics.
The article's description of newtonian mechanics of orbits and energy is freshman physics stuff, and every engineer should know it.
Nevertheless, Musk is an astonishing man and I suspect he'll go down in history as one of the greatest engineers. I wish I could buy a few shares of SpaceX and own a tiny morsel of the dream :-)
It's a response to Bezos's Blue Origins tweet. Getting to orbit takes far more energy than just getting to orbital altitude, which is the main point Musk is making.
Blue Origin isn't a serious competitor, though. United Launch Alliance (Lockheed-Martin and Boeing) is the real competitor. It's amazing that they're still using Atlas/Centaur, which, although there have been major redesigns and upgrades, first flew started in the 1950s. (Yes, the current Atlas is really a new design, using Russian engines. The Centaur upper stage hasn't changed as much; it still has the 1950s Rocketdyne engines.)
Space-X still wants the capability of landing on the barge, so they don't have to expend so much fuel to kill the horizontal vector and get back near the launch point. They may end up going with expendable boosters when lifting to geosync orbit. But they may be able to reuse ones recovered from previous low orbit missions.
It's well written and I'm glad he takes the time to write things like this. But I think you might be a bit biased by hero worship. Don't you think the rocket engineers explained it to him in about the same way? And there's probably not a lot else for the boss to do while waiting for liftoff.
In his interviews with Tim Urban from Wait But Why, there's a bit of detail about what he read leading up to his founding of SpaceX. They're all hard science texts – Rocket Propulsion Elements (Sutton), Aerothermodynamics of Gas Turbine and Rocket Propulsion (Oates), Fundamentals of Astrodynamics (Bate). From everything I've heard, he's well-versed in the material in a way that not many CEOs are.
The main difference between Elon Musk and 'the rest of us' is that he set himself a bunch of ambitious goals and applies each and every bit of his funds and intellect towards achieving those goals and inspires a large number of very smart people around him to share his dreams. It's a tough act to follow, but if you really wanted to you probably could. Whether or not you're prepared to pay the price is another matter.
“My proceeds from the PayPal acquisition were $180 million. I put $100 million in SpaceX, $70m in Tesla, and $10m in Solar City. I had to borrow money for rent.”
He works stupendously hard. Growing up my dad was always working, and it factored heavily into my decision to not pursue a career of long hours, it's a trade-off I wasn't willing to make. As a consequence, I won't have the financial resources he has. The amount of dedication that it takes to run businesses like tesla and spacex well is intimidating. To quote princess bride, it leaves no room for dilly-dallying.
Another take-away I get from musk's achievements is that the best software businesses are about applied software. Paypal is software applied to finance, tesla is software applied to cars, spacex is software applied to rockets. Combine great software with great hardware, and you get companies like apple, tesla, spacex, companies that change the world.
Indeed, I'd wager that raw intelligence is highly overrated. Hard work trumps intelligence. Hard work and intelligence are an unbeatable combination.
>> 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?
Intelligence undermines hard work all too often. I wasted years of my life coasting, as coming top of the class in everything was easy, and only actually started applying myself after university, when it rapidly became clear that intelligence alone doesn't cut it.
You've gotta be smart, you've gotta be prepared to work insane and thankless hours, you've gotta be tough as nails to hear but ignore the naysayers, you've gotta be willing to lose everything, and above all, you've gotta believe in yourself.
Only when you put all of those together (with krazy glue, of course), only when you are leading yourself, can you hope to lead others.
Try explaining to someone an easy to understand version of your life's work, it probably comes out pretty easy. Same thing here. The impressive part is Elons explanation about the science is not typical CEO material
Are you sure he writes these? I don't know enough about what he actually does. I'm pretty sure some C-level people have someone else write something about what they wanted to say (like an assistant or someone on the marketing team). Then maybe they review it and sign off. Just a thought.
Hmm. I used to believe this until a book recommendation by Bill Gates no less opened my mind a little to the thought that intelligence isn't a fixed or capped (to any level most of us hit anyways) attribute.
I would strongly recommend at least a read of Gates' book review and at best purchasing a copy of the book and applying it. Certainly one of the best books I've read of late.
Elon's whole gravity explanation is essentially a textual version of this excellent video/demonstration: https://www.youtube.com/watch?v=MTY1Kje0yLg (19 million views). Highly recommended, very memorable.
Yep, came here to post this. The funny thing is that there was a post about that video a while back, and the HN crowd criticized it pretty heavily for being a bad way to explain gravity. But... whatever. :)
If we can land the rocket accurately enough to put it down on a tiny barge only slightly larger than the rocket itself, then why do we need to tolerate the weight of the landing legs?
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.
There are several reasons why landing legs make more sense:
– 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.
Every time these discussions come up, people immediately come up with "other" suggestions for landing.
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.
I was under the assumption the primary reason is reusability on earth only. This would drastically reduce the cost for building new rockets and would decrease turn around time for new launches. Having it work on other planets is a nice plus but there's no demand for that and likely wont be for decades.
... or (as a less mechanically complex solution ...) use the same concept as the arrester cables on an aircraft carrier flight deck -- but upended to catch a vertically descending vehicle.
(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).
Nice article, but I couldn't pass up a chance to correct Elon Musk's math:
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 believe you've misunderstood his English. If it takes 1 Joule to accelerate the mass from 0-1000km/h, it will take 4 Joules to accelerate the same mass from 0-2000km/h.
Elon is calling that four times as much as because he's considering the total energy required to accelerate from 0 in both numbers. I think you're just accounting for it differently by saying it takes 3 times as much as the original energy input to go from 1000km/h to 2000km/h.
I'm a complete physics novice, I'm open to being schooled on this if I'm completely missing both yours and Elon's concepts here.
I think panic is correct. "from 1000 km/h to 2000 km/h" means from 1000 km/h to 2000 km/h, not 0-2000 kph. Though presumably Elon was thinking of the latter.
I don't think he worded it quite right but the inclusion of "not twice as much" makes it clearer that he was referring to "0 to 1,000" vs "0 to 2,000" (not 0 to 1,000 vs 1,000 to 2,000). So I believe the error was in the writing, not the math or understanding. Which he even pre-apologized for presumably in an attempt to assuage the nit-pickers.
One thing I've not seen mentioned in the coverage so far: how much payload is sacrificed by the need to keep fuel in reserve for the return to base?
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.
> how much payload is sacrificed by the need to keep fuel
> in reserve for the return to base?
Simple answer: None.
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.
SES already said that they're willing to be the first customer for a used booster[1].
Before they get that far, it'd be interesting to see if SpaceX flies a used engine, since they've got "one engine out" capability. Which has already been tested twice.
That article raises an interesting point I really hadn't considered, who owns the first stage? If you pay "full price" for a launch and SpaceX recovers the first stage to re-use, did the person who paid to launch it own it or does SpaceX? It was presumed lost of course. No doubt there is language in the contracts about that. Would be interesting to see a launch contract.
Just for reference, I got an inside look at what it took to get OSCAR16[1] launched and it isn't like flying :-). Now I don't doubt things are more streamlined now but every launch starts with a basic contract and that contract has to cover everything from contingencies to insurance to liability to disposal.
Trying to search for a boilerplate launch contract I found an article[1] where it discusses that Spaceflight Industries bought a Falcon 9 launcher [emphasis mine] which suggests that one buys the entire rocket. That would imply that if they land it, you still own it does it not? Can you then go over to the landing zone pick up your rocket and resell it for parts to offset your original purchase price? :-)
I am really confident that ownership of the first stage is covered in the launch contract if it is returned to the landing field. And the math there would no doubt be really interesting to an insurance company since you have the possibility that the launch is a success and the first stage lands, the launch is a success and the first stage crashes, the launch effectively fails (second stage failure) but the first stage successfully returns, and both stages are lost. That is a number of different outcomes to insure.
Frankly my mind is boggling at the potential legal complexity here.
[2] "SpaceIL has purchased launch services from Spaceflight Industries; an American space company who recently purchased a SpaceX Falcon 9 launcher and will manifest SpaceIL’s spacecraft as a co-lead spot, " -- http://lunar.xprize.org/press-release/israeli-google-lunar-x...
I think the real answer is that there will be a complex contractual relationship that "ownership" is too simple to describe, in either direction. E.g. I say I "own" my flat, but actually I am a shareholder in a company that owns the building and have a lease contract with that company (this is the standard (only?) way of "owning" a flat in the UK, because multiple flats stand on the same piece of land - you can't truly "own" something you don't have the right to destroy, but obviously you don't have the right to destroy a flat with someone else's above it).
> And the math there would no doubt be really interesting to an insurance company since you have the possibility that the launch is a success and the first stage lands, the launch is a success and the first stage crashes, the launch effectively fails (second stage failure) but the first stage successfully returns, and both stages are lost. That is a number of different outcomes to insure.
The insurance industry already deals with far more complex scenarios. A ship on an ocean voyage will often have the hull and cargo insured separately, different loss layers insured separately (e.g. first 10% of losses, 10-20%, 20-100% all separate), with multiple underwriters on each layer (and sometimes the same underwriter on multiple stamps).
I think you might be getting hung up on sloppy wording or a one-off situation. Clearly SpaceX owns its rockets and customers pay for the delivery of payloads.
I see what you mean and a literal reading of those words implies ownership but what if the intended meaning was that they were the sole occupant/tenant on that flight? My gut feeling is that the rocket company owns the rocket.
The jet engines on the Me-262 jet fighter were only good for 10 hours. (The airframe didn't last much longer, and so the Germans didn't bother with things like corrosion protection.)
Even so, a lot of expensive parts on the rocket likely have much longer service lives.
About 30% returning to landing site, 15% returning to a barge downrange. Note that the rocket's still perfectly capable of running an expendable mission if the payload requires it. The mass figure on their website[1] is for reusable.
You can run the first stage longer without any extra second stage fuel. Adding performance to either one (within limits) increases the performance of the system. Using the landing fuel for a launch would allow for a heavier payload without changing the second stage. The first stage would do more of the total work.
Ah yes, good point - I was implicitly assuming the liftoff weight was maxed out, by thinking that any upper stage weight increase would have to come from the 1st stage fuel load.
Except that the longer you run the first stage, the longer you have to carry the weight of the first stage. It eventually becomes much more efficient to jettison the first stage and use a slightly less powerful but much lighter weight second stage, because you no longer need as much power to get through the atmosphere. Which is the whole point behind staging (https://en.wikipedia.org/wiki/Multistage_rocket#Optimal_stag...).
On the second stage every 1 lb of reuse you lose 1 lb of payload, which is one of the big reasons why second stage reuse isn't really feasible on the F9.
That makes no sense. It's never advantageous to ditch the first stage while it's still producing thrust. At some point when designing a rocket, it's better to add performance to the second stage rather than the first. But when presented with an existing rocket, you'll achieve maximum payload capacity by burning all fuel in the first stage before staging. Every second it burns is more delta-v imparted to the payload. The only reason you'd stage early is if you want to save fuel for e.g. a landing attempt, if the first stage is too powerful and the acceleration or speed would become too great, or if you simply don't need the extra performance to get the payload to where it's supposed to go.
"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.
Both you and the article are right - you are analyzing it in the frame of reference where the center of the earth is stationary, while the article analyzes in the frame of motion where the center of the rocket is stationary.
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.
[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'."
Right, of course I understand that - but two points.
1) The whole original post appears to be worded for the layman to try and dispel myths around what orbit is. I don't think the layman is going to think about inertial frames of reference, rather I genuinely think the common misconception that there's really something 'pulling' the astronauts up will continue, much like many people think a car is throwing them out of a bend in the road, rather than the vehicle pushing them away from a straight line.
2) In any case, even if Musk implies the frame of reference, there's a reason a 'centrifugal force' is also referred to as a 'fictitious force' [1]
It's describing the dynamics in the (non-inertial) reference frame of the satellite (the reference frame in which the astronauts can be described as "floating around"). In this reference frame, the centrifugal force balances the gravitational force, leading to zero net acceleration.
I'm not sure if that's a question or a statement.Firstly, velocity and acceleration are different things. Velocity is change of distance with time (km/s), acceleration is change of velocity with time (km/s per second or km/s^2).
Secondly, an acceleration on a mass requires a force. Supposing there were an 'outward acceleration', where do you propose the 'outward force' is?
... We are talking a tangent on a circle that is changing every second.
So that is a change of velocity, which is acceleration. Outwards is clearly "out" of the circle. The tangent (on the curve) would be a snapshot of that "outward" velocity.
As a said: Tangential velocity is the same as saying outward acceleration. Unless you were referring to just that single "snapshot" in a frozen time scenario.
That "outward" force usually comes from a massive rocket... It is then maintained by the inward force of gravity.
If that were the case then you could get into orbit by simply going straight up. Why do they go laterally up to 8km/s then? (if not to generate an 'outward' force?).
There are two vectors being added here. One is gravity. The other is a tangental/outward vector. When added together, they form an orbit. Ignore one, and you leave orbit, either by going into space, or smashing into earth. But there are clearly two forces/vectors. And one of them, is having it's direction changed by the other, and thus is acceleration... I don't know what other words I can use to describe it. But I fail to see where I'm wrong :\
The only force, and therefore the only acceleration, when you're in orbit is the force of gravity. And therefore, the only acceleration is towards the center of Earth.
The thing in orbit is already moving with a high enough velocity that it isn't able to get closer to the Earth.
I guess maybe what you're saying, is if you take the velocity vector and apply the acceleration vector over time, that changes the velocity at the same rate as the curve of the Earth.
Either way, there is exactly one force vector (which causes exactly one acceleration vector), not two.
They get to that vast 8km/s veloctiy you mention with huge rocket engines. Then they turn them off.
At that point the astronauts and their craft are in freefall.
You mention an outward 'vector'? You can only talk about forces and their effects on masses really. There's an intertia that resists the downward acceleration, but that's not a force.
Blue Origin is cool but it's certainly not astonishing to me that a billionaire is able to send a rocket on a suborbital trajectory and recover it. It's certainly more than I've ever done by a long shot, but it's not a very interesting achievement unless you're interested in five-minute space tourism. I don't think BO's achievement here has many implications for space travel.
I wonder its implications for terrestrial travel, though? We are in a post-Concord era, after all, but suborbital flight could get you to any point on the planet pretty quickly if the price is right.
Comparing apples (going up then down) to oranges (getting into orbit). Pretty awesome to see these guys putting their cash towards this! Hope a rivalry heats up and I can goto Mars for $3.50.
That said, I'm not too sure I understand the line "the kinetic energy transfer at a 100 km reference altitude is what matters"...
What is the "kinetic energy transfer at 100km" ? Why not say that what matters is the "kinetic energy transfer", period? It doesn't make any sense to me to put it the former way.
Not trying to nit-pick, just trying to confirm my own understanding. But actually, accelerating a mass from 1000km/hr to 2000km/hr should take three times as much energy as from 0km/hr to 1000km/hr, right? I assume the quantity of "four times as much" was just used to get across the notion of energy being proportional to the square of velocity.
> Getting back to everyday reality, the impression that most people have is that gravity stops once you reach a certain altitude above Earth, at which point you start floating around in "zero g", but, as we just talked about, this is obviously not true. The force of gravity drops proportionate to the square of the distance between the centers of two objects.
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!
The article mentions that the water landing requires less fuel to return the rocket because it doesn't have to spend fuel overcoming its initial ballistic trajectory. In the water landing scenario, how far away from the launchpad is the landing barge? I'm wondering about the economics of launching from a site where your first stage trajectory is entirely overland, to avoid the complications of landing on a barge that's being tossed in the sea. Though it might be hard to find such a site in U.S. territory that's both near the equator and sparsely populated.
I found a reference that the barge was 320 km downrange in the earlier tests. The Bahamas look to be an appropriate distance from Florida, although to the southeast of Cape Canaveral. From SpaceX's planned Texas spaceport, there's nothing at that range but gulf.
Hypothetically, I imagine they could anchor a stable ocean platform out there if they find it's easier than the barge. No idea if it actually would be easier than the barge though.
It's important that the trajectory be fail-safe in terms of avoiding land - if the falcon were to explode early on it could sprinkle debris over a large area around the intended landing zone. So it'd have to be a small unpopulated island - a barge is probably easier. If they need more area or stability I'd think it's relatively easy to expand the barge or add more mass/sea anchors underneath.
I was wondering about that too. It would be cool if they could launch from somewhere south of San Antonio, TX on the water, and land in Florida so it doesn't fly over land mass for safety reasons.
Launch abort locations for Shuttle launches from Canaveral included Shannon in Ireland and the Azores off Spain. Both would seem ideal for recovery of eastbound first stages.
It's a good summary, but I'm not sure the repeated digs at Bezos are really necessary. I think anyone who would bother to read this already gets the differences. Not sure that he really needs to point out, twice, that height doesn't matter at that stage of testing.
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.
I'm having some trouble with the opening salvo here:
"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.
I see two aspects to your question/comment: at-rest, and two-objects.
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.
Right, the fact that all the bodies are acting on the other is what makes me feel the analogy is not kosher. The funnels are going to start moving around based on their mutual attraction, and I could see the marble being ejected to infinity, for example. It's less clear to me (but possible) that it could enter a stable orbit.
This was lovely writing, and successfully enlightened me on a few points, but my mind immediately saw the marble deform the sheet. I'd suggest a ping-pong ball and a frictionless sheet for a less perplexing thought experiment.
Yes. He's simplifying the description (though technically, he might still be correct; if only you and your pet existed in space and had no relative motion, it's entirely possible that dark energy would not exist, since we don't yet understand its origins or nature).
Great and easy to understand article, thanks for posting it.
Does anyone know it the spacex team uses the imperial or the metric system for development? Elon switches between both systems and it's messing with my head.
Fwiw, on their public webcast, they had on-screen telemetry showing km/h for speed and km for altitude (and no downrange distance). Not necessarily what they use internally, though.
Aerospace engineers traditionally uses knots, thousands of feet and nautical miles. SI units typically have km/s (not /h).
