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.
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.
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.
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.
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.
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.
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.
... 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 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.
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.
"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'."
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.
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.
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.
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.
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.
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).
nathanielc|10 years ago
yellowbeard|10 years ago
"The reason it's hard to get to orbit isn't that space is high up. It's hard to get to orbit because you have to go so fast."
Swizec|10 years ago
JabavuAdams|10 years ago
blizkreeg|10 years ago
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?
tedivm|10 years ago
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.
sillysaurus3|10 years ago
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.
tunesmith|10 years ago
WalterBright|10 years ago
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 :-)
Animats|10 years ago
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.
skybrian|10 years ago
JabavuAdams|10 years ago
Also, he does have an undergrad degree in physics, and was accepted to a physics PhD program at Stanford.
The guy's incredibly impressive, but there are many almost-Elons. It's not like he's an alien or a superhuman.
jacquesm|10 years ago
Joeri|10 years ago
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.
the_economist|10 years ago
pinkrooftop|10 years ago
jupiter90000|10 years ago
Retric|10 years ago
Sure, he does not have a MS or PHD but he was trained in physics.
leonroy|10 years ago
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.
http://www.gatesnotes.com/Books/Mindset-The-New-Psychology-o...
manigandham|10 years ago
We're all humans here. Productivity is a complicated output of intelligence, ambition, application, luck and financial fortune.
serge2k|10 years ago
dcgoss|10 years ago
enraged_camel|10 years ago
alerkay|10 years ago
w_t_payne|10 years ago
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.
ggreer|10 years ago
– 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
grecy|10 years ago
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.
w_t_payne|10 years ago
(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).
mrfusion|10 years ago
Also the empty rocket might be too weak to be grabbed by anything. They compare the thickness to a tin can.
panic|10 years ago
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.
notdonspaulding|10 years ago
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.
pbreit|10 years ago
caio1982|10 years ago
agumonkey|10 years ago
johnm1019|10 years ago
mrec|10 years ago
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.
ChuckMcM|10 years ago
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.
rory096|10 years ago
[1] http://www.spacex.com/falcon9
johntb86|10 years ago
msandford|10 years ago
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
mannykannot|10 years ago
marcosscriven|10 years ago
"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.
zodiac|10 years ago
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'."
timbre|10 years ago
1stop|10 years ago
mannykannot|10 years ago
Did you get that, Jeff?
The truth is, they have both achieved an astonishing amount.
mikeash|10 years ago
andys627|10 years ago
alerkay|10 years ago
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.
sixQuarks|10 years ago
dcgoss|10 years ago
veritas3241|10 years ago
marcus_holmes|10 years ago
sopooneo|10 years ago
rimantas|10 years ago
IshKebab|10 years ago
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!
kibwen|10 years ago
timdierks|10 years ago
lmm|10 years ago
grecy|10 years ago
dingaling|10 years ago
pbreit|10 years ago
tempestn|10 years ago
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.
idlewords|10 years ago
"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.
jholman|10 years ago
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.
lips|10 years ago
mrfusion|10 years ago
4ad|10 years ago
v4n4d1s|10 years ago
exDM69|10 years ago
Aerospace engineers traditionally uses knots, thousands of feet and nautical miles. SI units typically have km/s (not /h).
soperj|10 years ago
edit: just saw this at the bottom and it made me smile; "Apologies for any typos in the above."
aparent|10 years ago
https://en.m.wikipedia.org/wiki/Attitude_control
zrail|10 years ago