The maths that made Voyager possible(bbc.co.uk)
bbc.co.uk
The maths that made Voyager possible
http://www.bbc.co.uk/news/science-environment-20033940
9 comments
Thanks for that link. Minovitch seems to still live in LA.
He also mentions his solution as addressing the three-body problem, so maybe that's where the writer of the linked article got misled on that point. Too bad the writer of TFA didn't check this out with an independent expert.
The group at JPL that Minovitch mentions is still intact (http://ssd.jpl.nasa.gov/). They provide the highest-quality ephemeris available anywhere (AFAIK) to all NASA missions.
He also mentions his solution as addressing the three-body problem, so maybe that's where the writer of the linked article got misled on that point. Too bad the writer of TFA didn't check this out with an independent expert.
The group at JPL that Minovitch mentions is still intact (http://ssd.jpl.nasa.gov/). They provide the highest-quality ephemeris available anywhere (AFAIK) to all NASA missions.
I had no idea before reading this article that it was hard to escape from the attraction of the sun! It makes me wonder if we now have the capabilities to build a rocket that can do it without the help of the attraction of the outer planets.
Does somebody here who's knowledgeable on the subject have some reference?
Does somebody here who's knowledgeable on the subject have some reference?
Thanks for all the links guys!
It's very common to use gravity assist, especially in outer planets missions. Fuel is very expensive and has diminishing returns (the more fuel you put on, the more fuel you need to lift the extra fuel you put on). After Voyager, Galileo, Cassini, and New Horizons (among others) have used gravity assist to get to Jupiter, Saturn, and Pluto respectively (NH is still en route).
Even Stereo, a two-satellite pair in earth-trailing and earth-following orbits looking at the Sun, used gravity assist (with the Moon).
Gravity assist is one way to provide "delta-v" (velocity change, the coin of the realm in propulsion). You can provide negative delta-v using aerobraking -- orbiting your destination, Mars say, and slowing down using atmospheric friction. This is used on the Mars orbiters.
As usual, see: http://en.wikipedia.org/wiki/Delta-v_budget
Even Stereo, a two-satellite pair in earth-trailing and earth-following orbits looking at the Sun, used gravity assist (with the Moon).
Gravity assist is one way to provide "delta-v" (velocity change, the coin of the realm in propulsion). You can provide negative delta-v using aerobraking -- orbiting your destination, Mars say, and slowing down using atmospheric friction. This is used on the Mars orbiters.
As usual, see: http://en.wikipedia.org/wiki/Delta-v_budget
I watched the Dawn spacecraft[1] launch, it uses an ion propulsion drive which Wikipedia says can perform a velocity change of over 10 km/s over the mission.
My understanding is that if they left the ion drive on long enough, the craft would continue to accelerate.
[1]http://en.wikipedia.org/wiki/Dawn_%28spacecraft%29#Propulsio...
My understanding is that if they left the ion drive on long enough, the craft would continue to accelerate.
[1]http://en.wikipedia.org/wiki/Dawn_%28spacecraft%29#Propulsio...
It can be much better than that. The ion thrusters in Dawn have a specific impulse of 3,100 seconds (30 km/s exhaust velocity). Later thrusters designed for the Jupiter Icy Moons Orbiter achieved 9,600 seconds in a lab (94 km/s e.v.) JIMO itself is designed for a delta-v of 40 km/s.
https://en.wikipedia.org/wiki/High_Power_Electric_Propulsion
https://www.lpi.usra.edu/meetings/jimo2003/hartman.pdf
delta-v is proportional to the specific impulse (or exhaust velocity), and logarithmic in the propellant ratio. For instance, with a propellant ratio of e = 2.7, you can get a delta-v equal to the exhaust velocity. For a delta-v twice that, you need a propellant ratio of e^2 = 7.4. Obviously it's not practical to go much faster the exhaust velocity; the propellant demand grows exponentially.
https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
https://en.wikipedia.org/wiki/High_Power_Electric_Propulsion
https://www.lpi.usra.edu/meetings/jimo2003/hartman.pdf
delta-v is proportional to the specific impulse (or exhaust velocity), and logarithmic in the propellant ratio. For instance, with a propellant ratio of e = 2.7, you can get a delta-v equal to the exhaust velocity. For a delta-v twice that, you need a propellant ratio of e^2 = 7.4. Obviously it's not practical to go much faster the exhaust velocity; the propellant demand grows exponentially.
https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
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If you are interested in gaining a more intuitive understanding of the forces in play (and have some time to kill), I recommend grabbing a copy of Kerbal Space Program. Its only in alpha right now, but its a heck of a lot of fun already and does a really good job of teaching you how to use orbital mechanics to land on other planets (or to shoot a probe out of the solar system, if you want to try to do that).
Their model is definitely simplified (no lagrange points, for example), but the major aspects are modeled well enough to give you an idea of how interplanetary space travel works.
http://kerbalspaceprogram.com/
Their model is definitely simplified (no lagrange points, for example), but the major aspects are modeled well enough to give you an idea of how interplanetary space travel works.
http://kerbalspaceprogram.com/
Yes, easily. Solar escape delta-v is about 21 km/s from earth orbit (not including earth's gravity). The Jupiter Icy Moons Orbiter is designed with a delta-v twice that, 40 km/s, using nuclear-powered ion thrusters. To be used to maneuver within Jupiter's gravity well, moving from one moon to another.
http://www.lpi.usra.edu/meetings/jimo2003/hartman.pdf
It's a completely doable project sidelined by budget priorities (NASA thinking space tourism more important than science).
http://www.lpi.usra.edu/meetings/jimo2003/hartman.pdf
It's a completely doable project sidelined by budget priorities (NASA thinking space tourism more important than science).
It's entirely possible to build a rocket that doesn't need help from gravity assists, but rocket fuel is very expensive to send to the outer planets. Better to roll downhill towards Jupiter rather than uphill away from the sun.
There are other fun things that we can do with gravity assists as well:
A rocket burn is significantly more effective when close to a large gravitational source.
http://en.wikipedia.org/wiki/Oberth_effect
If you are willing to wait long enough there is a way to get almost anywhere in the solar system for very little fuel.
http://en.wikipedia.org/wiki/Interplanetary_Transport_Networ...
There are other fun things that we can do with gravity assists as well:
A rocket burn is significantly more effective when close to a large gravitational source.
http://en.wikipedia.org/wiki/Oberth_effect
If you are willing to wait long enough there is a way to get almost anywhere in the solar system for very little fuel.
http://en.wikipedia.org/wiki/Interplanetary_Transport_Networ...
A quote: "Undeterred by the fact that some of the finest minds in history, including Isaac Newton hadn't solved the three-body problem, Minovitch became focused on cracking it."
This is misleading. The three-body problem is known to be insoluble in closed form, but anyone cam model it numerically. The person being describes was one of the first to do this, but the comparison with Newton is misleading.
Many kinds of problems are soluble through numerical modeling that aren't remotely soluble in closed form, and it is important to distinguish between the two kinds of solution.
On reading the article, it occurs to me that the author simply doesn't understand the math well enough to grasp the difference between an analytical and a numerical solution.
This is misleading. The three-body problem is known to be insoluble in closed form, but anyone cam model it numerically. The person being describes was one of the first to do this, but the comparison with Newton is misleading.
Many kinds of problems are soluble through numerical modeling that aren't remotely soluble in closed form, and it is important to distinguish between the two kinds of solution.
On reading the article, it occurs to me that the author simply doesn't understand the math well enough to grasp the difference between an analytical and a numerical solution.
Moreover, "three body problem" is generally meant to mean the three bodies with comparable mass, so they influence each others trajectory. But in this case, Mass_sun >> Mass_planet >> Mass_probe, which greatly simplifies the problem.
Nonetheless, kudos to the guy to understand that a gravitational slingshot is possible, and proving it.
Nonetheless, kudos to the guy to understand that a gravitational slingshot is possible, and proving it.
Theoretically, that doesn't simplify the problem at all. Practically, we can say that Mass_probe=0, in which case we have a 2-body problem. We need to do that even if we do find a closed form solution to the n-body problem (which might be provably impossible), becuase in reality there is an infinite number of bodys in the system.
And this is an important distinction to you, and it could be construed as misleading, but this is still a lovely article and I learned a little more about the voyagers.
Sorry, It's an important distinction in an absolute sense, and not a matter of personal taste. He did not 'solve' it in the sense that 'all the great mathematicians ever' were trying to solve it, as the article and the clip make out.
Similarly, I am not ringing up the Clay Institute to claim my $1M prize for 'solving' Navier-Stokes because I've just run a toy computational-fluid-dynamics problem in OpenFoam.
There is nothing good to be gained from obfuscation and sensationalisation in the public understanding of science.
Similarly, I am not ringing up the Clay Institute to claim my $1M prize for 'solving' Navier-Stokes because I've just run a toy computational-fluid-dynamics problem in OpenFoam.
There is nothing good to be gained from obfuscation and sensationalisation in the public understanding of science.
I don't know what you are complaining about. He solved a problem that helped launch voyager probes and made them a success. The problem was hard, not solved before and he did it. Its absolutely brilliant for that effort, and the kind of impact it has had on human history. Even if it was easy, by a common mathematicians measure, its still great. Because he took it head on and solved it.
Your point of argument is a metaphor which a non technical author would have used or even used in exaggeration by mistake.
Sorry but pedantic arguments make a persons case look bad. Its like complaining about Khan academy's Python course. Smart intelligent people feel guilty when solving a problem well within their reach, was taken by somebody else and solved by them. It makes them feel more bad, when the solution becomes famous and brings a lot of fame to the inventor. It seems that is what you are going through here.
Your point of argument is a metaphor which a non technical author would have used or even used in exaggeration by mistake.
Sorry but pedantic arguments make a persons case look bad. Its like complaining about Khan academy's Python course. Smart intelligent people feel guilty when solving a problem well within their reach, was taken by somebody else and solved by them. It makes them feel more bad, when the solution becomes famous and brings a lot of fame to the inventor. It seems that is what you are going through here.
> I don't know what you are complaining about.
The issue is quite orthogonal to him personally and his achievements, for which I have the utmost respect. I am fascinated by the early days of space exploration and am as impressed by this work as I was when I first read about it a few years ago.
The issue is with the journalism, written by the journalists, which attempts to sensationalise the achievements (which can stand on their own two feet without it) by making comparisons with famous mathematicians that are not valid comparisons, as Paul Lutus explains in his first post. It's just apples and oranges, and will at best be lost on the lay reader and at worst confuse the lay reader who looks into the three body problem further. Hence my point that it is unhelpful to the public understanding of science.
I, for one, see your point. How about this part:
"At the time, Nasa couldn't guarantee a spacecraft for more than a few months of operational life, and so the outer planets were considered out of reach.
"That was until a 25-year-old mathematics graduate called Michael Minovitch came along in 1961."
Which is followed by,
"To reach Neptune [Voyager 1 and 2] would have to last for over a decade in space, operating in the darkest reaches of the Solar System billions of km from the Sun."
Solving a limited three-body problem and inventing the gravitational slingshot is way cool. Throwing in a mess of red herrings and yellow journalism detracts from the point of the article.
Oh, and anyone know why the Bbc doesn't want to capitalize 'NASA'?
"At the time, Nasa couldn't guarantee a spacecraft for more than a few months of operational life, and so the outer planets were considered out of reach.
"That was until a 25-year-old mathematics graduate called Michael Minovitch came along in 1961."
Which is followed by,
"To reach Neptune [Voyager 1 and 2] would have to last for over a decade in space, operating in the darkest reaches of the Solar System billions of km from the Sun."
Solving a limited three-body problem and inventing the gravitational slingshot is way cool. Throwing in a mess of red herrings and yellow journalism detracts from the point of the article.
Oh, and anyone know why the Bbc doesn't want to capitalize 'NASA'?
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My biggest take away was that, and I can't believe I didn't know this already, the Voyager probes relied on once-in-a-couple-centuries planetary alignments. I wonder how long until propulsion technologies make that irrelevant.
Well, specifically only Voyager 2 did to reach Neptune. Voyager 1 slingshot only Jupiter-to-Saturn, which is available much more often in a much larger set of planetary positions. Pioneer 11 was essentially rerouted on the fly to do that, and Cassini also flew a planned Jupiter-Saturn trajectory.
There's also a bit of a multiple endpoints situation in singling out the 4-out-of-4 giant planets scenario. That is indeed infrequent, but say a 3-out-of-4 lineup with either Uranus or Neptune, or 4-out-of-5 with Uranus and Pluto as the final two [dwarf] planets, also would have made for a fine and successful mission.
OTOH, we could even argue that we were unlucky that the giant planet alignment occured for that 1977 launch window. If it occurred this decade instead, we could send a much better spacecraft with the capabilities of Cassini or Messenger or New Horizons.
There's also a bit of a multiple endpoints situation in singling out the 4-out-of-4 giant planets scenario. That is indeed infrequent, but say a 3-out-of-4 lineup with either Uranus or Neptune, or 4-out-of-5 with Uranus and Pluto as the final two [dwarf] planets, also would have made for a fine and successful mission.
OTOH, we could even argue that we were unlucky that the giant planet alignment occured for that 1977 launch window. If it occurred this decade instead, we could send a much better spacecraft with the capabilities of Cassini or Messenger or New Horizons.
unrelated to the article, sorry for hijacking but I'm very curios why people like SparrowOS post things like that?
What do they have to gain from it?
What do they have to gain from it?
You are asking about a top-level comment that many users will not see (because it is autokilled on submission, presumably because the author has been hellbanned for previous off-topic comments like that). Usually, I read HN with "showdead" turned off in my user profile. Once in a while, I turn showdead back on, only to be reminded why many comments and stories are killed on submission.
SparrowOS suffers from schizophrenia.
I was expecting something more like this: http://en.wikipedia.org/wiki/Binary_Golay_code
I always wondered why would you send a probe around a planet... It seemed dumb. But it seems that the probe would steal some energy from the planet's speed http://en.wikipedia.org/wiki/Gravity_assist
http://www.gravityassist.com/
He sounds rather bitter that his story has not made him more famous, and comes off as something of a crank at that ("How Did Minovitch Discover (Create) His New Theory Of Space Travel?"). I think Minovitch is basically an engineer at heart, and is resentful that all of the attention seems to go to the scientists, i.e. people who come up with the actual physical theories about mass and energy and so forth.
Our culture does value scientists more than engineers. You could argue that this is good because theories are universally applicable and represent fundamental understanding, or that this is bad because many theories have absolutely no applications and that it's the engineers who deliver value to society. You could also argue that the amount of prestige that we heap on scientists tends to go to their heads and they stop doing good work. But whatever. Stay sharp, do what you're best at, and don't pay attention to other people's benefits packages.