7 ms·

The maths that made Voyager possible

96 points by nekojima 14y ago

SparrowOS 14y ago
God says... 3:13 He that hath an ear, let him hear what the Spirit saith unto the churches. 3:14 And unto the angel of the church of the Laodiceans write; These things saith the Amen, the faithful and true witness, the beginning of the creation of God; 3:15 I know thy works, that thou art neither cold nor hot: I would thou wert cold or hot. 3:16 So then because thou art lukewarm, and neither cold nor hot, I will spue thee out of my mouth. 3:17 Because thou sayest, I am rich, and increased with goods, and have need of nothing; and knowest not that thou art wretched, and miserable, and poor, and blind, and naked: 3:18 I counsel thee to buy of me gold tried in the fire, that thou mayest be rich; and white raiment, that thou mayest be clothed, and that the shame of thy nakedness do not appear; and anoint thine eyes with eyesalve, that thou mayest see. ---- God says... addition shifted choleric perfecting same bye kindred go_ahead_make_my_day vex wavy table --- I wuv You, God. Praise You for penguines. Delightful critters. God says... 21:16 For thus hath the LORD said unto me, Within a year, according to the years of an hireling, and all the glory of Kedar shall fail: 21:17 And the residue of the number of archers, the mighty men of the children of Kedar, shall be diminished: for the LORD God of Israel hath spoken it. 22:1 The burden of the valley of vision. What aileth thee now, that thou art wholly gone up to the housetops? 22:2 Thou that art full of stirs, a tumultuous city, joyous city: thy slain men are not slain with the sword, nor dead in battle. 22:3 All thy rulers are fled together, they are bound by the archers: all that are found in thee are bound together, which have fled from far. 22:4 Therefore said I, Look away from me; I will weep bitterly, labour not to comfort me, because of the spoiling of the daughter of my people. ---- Eh? God says... compass Godhead arrogant hereafter contents Presently gratings dejectedness incense badge toss separateth still abidest allow createdst spectator length glory whirling Georgia moment presidentship emerge fragment frequently resend esteem gleams subtilty consist fifteen ---- Guy commenting on closed form vs numeric: Routh Horowitz can be used for stability if you don't like Akerman. I fergot most of that stuff. Actually, looking back it seems simpler that I thought at the time -- it's like I had mental blocks. Anyway, God, what's good to explore? (Christ is laughing) God said they should have put a microphone on the Mars rover. He said "Surf" was the reason a moon's atmosphere was unexpected. God says... 5:4 The sons of Joel; Shemaiah his son, Gog his son, Shimei his son, 5:5 Micah his son, Reaia his son, Baal his son, 5:6 Beerah his son, whom Tilgathpilneser king of Assyria carried away captive: he was prince of the Reubenites. 5:7 And his brethren by their families, when the genealogy of their generations was reckoned, were the chief, Jeiel, and Zechariah, 5:8 And Bela the son of Azaz, the son of Shema, the son of Joel, who dwelt in Aroer, even unto Nebo and Baalmeon: 5:9 And eastward he inhabited unto the entering in of the wilderness from the river Euphrates: because their cattle were multiplied in the land of Gilead. 5:10 And in the days of Saul they made war with the Hagarites, who fell by their hand: and they dwelt in their tents throughout all the east land of Gilead. 5:11 And the children of Gad dwelt over against them, in the land of Bashan unto Salcah: 5:12 Joel the chief, and Shapham the next, and Jaanai, and Shaphat in Bashan. ---- None of those names jump-out. Dud. Earlier one was about star gazing and Canadian word for "Stirs". God says... limbs gladiators Never asterisk rash Guardian silence partners Name's owe unlearned host Weight astrophysics well-being praises ideas unforgotten asks treble slumbers I'll_think_about_it silently awesome filths shelter mark-up Honor groat nests partaketh high blood theatre prose strings establish drawn understanding duties biting formlessness fighting dog weakened Like remainder unhappy praised lewd instant hereof wildness estimation calculations Moreover likedst bold-faced derided bowing secrecies notwithstanding Moses' ensues pearl engages contemplate blameworthy cares overboldness congregations break_some_woopass_on_you answering litigation find Holy government sounds second snare gifts Seven Incarnation Royalties distracting Cyprus EXPRESS fools freshness foul Cicero nostrils merciful vouchsafest Prophets riches envying offspring contemplate honest burst Eternal conceptions attested accursed modify day-break arise I'm_on_a_roll our held paper fig-tree primitive vices unhappily chewing what_would_Jesus_do calamity lottery surpassest forging I_could_swear ere point life-giving rest contemplating whazza_matter_for_you sublimities harmed winning sons thankful gains monster strengtheneth built condemning science fore-perceiving wealth MEDIUM commandments willed unrulily equably Psalter acts licence bepraised nurse vomited felicity larger miserable lest renew'd genuinely ---- You wanna be a teacher, God? Would You like that profession, or what profession would You like best? carpentry? God says... 20:19 He that goeth about as a talebearer revealeth secrets: therefore meddle not with him that flattereth with his lips. 20:20 Whoso curseth his father or his mother, his lamp shall be put out in obscure darkness. 20:21 An inheritance may be gotten hastily at the beginning; but the end thereof shall not be blessed. 20:22 Say not thou, I will recompense evil; but wait on the LORD, and he shall save thee. 20:23 Divers weights are an abomination unto the LORD; and a false balance is not good. 20:24 Man's goings are of the LORD; how can a man then understand his own way? 20:25 It is a snare to the man who devoureth that which is holy, and after vows to make enquiry. ---- God says... yield confusions physician believing fifteen society Watch_this tenderness ostentation comment stripped favourites softened balm Wondrous Scripture moreover express specimens David's Slovakia disliked date vulgar harmonise entangled incomplete trying Ask expect ---- Chinese zoo shocked elephant baby, kinda by accident. Kinda bad. What do You think, God? God says... left shall fall by the sword. 24:22 And ye shall do as I have done: ye shall not cover your lips, nor eat the bread of men. 24:23 And your tires shall be upon your heads, and your shoes upon your feet: ye shall not mourn nor weep; but ye shall pine away for your iniquities, and mourn one toward another. 24:24 Thus Ezekiel is unto you a sign: according to all that he hath done shall ye do: and when this cometh, ye shall know that I am the Lord GOD. 24:25 Also, thou son of man, shall it not be in the day when I take from them their strength, the joy of their glory, the desire of their eyes, and that whereupon they set their minds, their sons and their daughters, 24:26 That he that escapeth in that day shall come unto thee, to cause thee to hear it with thine ears? 24:27 In that day shall thy mouth be opened to him which is escaped, and thou shalt speak, and be no more dumb: and thou shalt be a sign unto them; and they shall know that I am the LORD. ---- I say, "berp". God says... literally snare Take savour diversifiedst carest pant incommutable planets rebellious errors disentangle invisible presently powerful intellectual abase spoken thwart stable points Even sun low AM unlawful godless scorning refrain badge embraced satisfactorily Moon physic ninth bespotted whom hang_in_there toss restless spiritual absorb peace-makers XIII patterns generation worlds dealt husbands mockers prerogative solemnise bargain commit dragon swiftness seed-plots retreat self-same wavy echoes danger recruiting hungry bad comforts carry distinguish whoever defined ornamenting bait Carthaginian deed Give_me_praise ---- Panda express, yum! I like little black peppers. You like those, God? God says... and teachers; as Barnabas, and Simeon that was called Niger, and Lucius of Cyrene, and Manaen, which had been brought up with Herod the tetrarch, and Saul. 13:2 As they ministered to the Lord, and fasted, the Holy Ghost said, Separate me Barnabas and Saul for the work whereunto I have called them. 13:3 And when they had fasted and prayed, and laid their hands on them, they sent them away. 13:4 So they, being sent forth by the Holy Ghost, departed unto Seleucia; and from thence they sailed to Cyprus. 13:5 And when they were at Salamis, they preached the word of God in the synagogues of the Jews: and they had also John to their minister. ---- Yeah -- had spicy Italian sub at subway. I got jualipenos and yellow peppers. Yum. God says... over-abound foretell religiously two-edged admission wild Philippines Church narrowly showed digest sawest computer needing judged announcement miseries husbands shorter matrons friendship's account handmaid unsuitably modes self-confidence AS glue grammarians bends consolation religiously rebelled cowardice transparent blessedly stolidity satisfied perdition talking awe Anaximenes subjoined Obama ornamentedst household figuratively whenever concreated consolations reinvolved judgements o'er smaller proprietary covetousness consecrateth learning contrary 1921 deafen 90 unhappily unlikeness co-eternal honied dang_it preparedst cupidity fruitless following revealed constellations title received services diluted Shhh stupidity fluctuating fragments lucre Father taken Does distinguishing prefer 401 sufficient son enjoying fatherless easily prevails chooses profit NUMBER prizes multiply intervals spoke virtue consumest Can compass texts industrious double waste shouted tilde Neither kick_back worship philosophy house restored unlooked boiled goaded worn spot support sure prepares inanimate changing happy_happy_joy_joy wealth tellest professed began daemon-worshippers stowed recollect discordant purpose separateth seemeth abstinence pronounces you're_no_fun weal low You_fix_it reclaiming criticised mouths counsels unbounded prophets drive prescribes advised put slumin
anotherbadlogin 14y ago
And this is why math is not supposed to be patentable. Too bad the USPTO "forgot" that.
lutusp 14y ago
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.
- kzahel 14y ago
  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.
  - ballooney 14y ago
    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.
    - kamaal 14y ago
      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.
yanowitz 14y ago
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.
- T-hawk 14y ago
  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.
tdrgabi 14y ago
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?
- tokenadult 14y ago
  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.
- Patient0 14y ago
  SparrowOS suffers from schizophrenia.
pmiller2 14y ago
I was expecting something more like this: http://en.wikipedia.org/wiki/Binary_Golay_code http://en.wikipedia.org/wiki/Binary_Golay_code
nodrama 14y ago
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://en.wikipedia.org/wiki/Gravity_assist
S4M 14y ago
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?
- mturmon 14y ago
  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 http://en.wikipedia.org/wiki/Delta-v_budget
- grecy 14y ago
  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#Propulsion_system http://en.wikipedia.org/wiki/Dawn_%28spacecraft%29#Propulsio...
  - uvdiv 14y ago
    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://en.wikipedia.org/wiki/High_Power_Electric_Propulsion https://www.lpi.usra.edu/meetings/jimo2003/hartman.pdf 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/Tsiolkovsky_rocket_equation
EvanMiller 14y ago
There is more information on Michael Minovitch's website: http://www.gravityassist.com/ 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.
- mturmon 14y ago
  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/ http://ssd.jpl.nasa.gov/). They provide the highest-quality ephemeris available anywhere (AFAIK) to all NASA missions.

96 points by nekojima 14y ago

God says... 3:13 He that hath an ear, let him hear what the Spirit saith unto the churches. 3:14 And unto the angel of the church of the Laodiceans write; These things saith the Amen, the faithful and true witness, the beginning of the creation of God; 3:15 I know thy works, that thou art neither cold nor hot: I would thou wert cold or hot. 3:16 So then because thou art lukewarm, and neither cold nor hot, I will spue thee out of my mouth. 3:17 Because thou sayest, I am rich, and increased with goods, and have need of nothing; and knowest not that thou art wretched, and miserable, and poor, and blind, and naked: 3:18 I counsel thee to buy of me gold tried in the fire, that thou mayest be rich; and white raiment, that thou mayest be clothed, and that the shame of thy nakedness do not appear; and anoint thine eyes with eyesalve, that thou mayest see. ---- God says... addition shifted choleric perfecting same bye kindred go_ahead_make_my_day vex wavy table --- I wuv You, God. Praise You for penguines. Delightful critters. God says... 21:16 For thus hath the LORD said unto me, Within a year, according to the years of an hireling, and all the glory of Kedar shall fail: 21:17 And the residue of the number of archers, the mighty men of the children of Kedar, shall be diminished: for the LORD God of Israel hath spoken it. 22:1 The burden of the valley of vision. What aileth thee now, that thou art wholly gone up to the housetops? 22:2 Thou that art full of stirs, a tumultuous city, joyous city: thy slain men are not slain with the sword, nor dead in battle. 22:3 All thy rulers are fled together, they are bound by the archers: all that are found in thee are bound together, which have fled from far. 22:4 Therefore said I, Look away from me; I will weep bitterly, labour not to comfort me, because of the spoiling of the daughter of my people. ---- Eh? God says... compass Godhead arrogant hereafter contents Presently gratings dejectedness incense badge toss separateth still abidest allow createdst spectator length glory whirling Georgia moment presidentship emerge fragment frequently resend esteem gleams subtilty consist fifteen ---- Guy commenting on closed form vs numeric: Routh Horowitz can be used for stability if you don't like Akerman. I fergot most of that stuff. Actually, looking back it seems simpler that I thought at the time -- it's like I had mental blocks. Anyway, God, what's good to explore? (Christ is laughing) God said they should have put a microphone on the Mars rover. He said "Surf" was the reason a moon's atmosphere was unexpected. God says... 5:4 The sons of Joel; Shemaiah his son, Gog his son, Shimei his son, 5:5 Micah his son, Reaia his son, Baal his son, 5:6 Beerah his son, whom Tilgathpilneser king of Assyria carried away captive: he was prince of the Reubenites. 5:7 And his brethren by their families, when the genealogy of their generations was reckoned, were the chief, Jeiel, and Zechariah, 5:8 And Bela the son of Azaz, the son of Shema, the son of Joel, who dwelt in Aroer, even unto Nebo and Baalmeon: 5:9 And eastward he inhabited unto the entering in of the wilderness from the river Euphrates: because their cattle were multiplied in the land of Gilead. 5:10 And in the days of Saul they made war with the Hagarites, who fell by their hand: and they dwelt in their tents throughout all the east land of Gilead. 5:11 And the children of Gad dwelt over against them, in the land of Bashan unto Salcah: 5:12 Joel the chief, and Shapham the next, and Jaanai, and Shaphat in Bashan. ---- None of those names jump-out. Dud. Earlier one was about star gazing and Canadian word for "Stirs". God says... limbs gladiators Never asterisk rash Guardian silence partners Name's owe unlearned host Weight astrophysics well-being praises ideas unforgotten asks treble slumbers I'll_think_about_it silently awesome filths shelter mark-up Honor groat nests partaketh high blood theatre prose strings establish drawn understanding duties biting formlessness fighting dog weakened Like remainder unhappy praised lewd instant hereof wildness estimation calculations Moreover likedst bold-faced derided bowing secrecies notwithstanding Moses' ensues pearl engages contemplate blameworthy cares overboldness congregations break_some_woopass_on_you answering litigation find Holy government sounds second snare gifts Seven Incarnation Royalties distracting Cyprus EXPRESS fools freshness foul Cicero nostrils merciful vouchsafest Prophets riches envying offspring contemplate honest burst Eternal conceptions attested accursed modify day-break arise I'm_on_a_roll our held paper fig-tree primitive vices unhappily chewing what_would_Jesus_do calamity lottery surpassest forging I_could_swear ere point life-giving rest contemplating whazza_matter_for_you sublimities harmed winning sons thankful gains monster strengtheneth built condemning science fore-perceiving wealth MEDIUM commandments willed unrulily equably Psalter acts licence bepraised nurse vomited felicity larger miserable lest renew'd genuinely ---- You wanna be a teacher, God? Would You like that profession, or what profession would You like best? carpentry? God says... 20:19 He that goeth about as a talebearer revealeth secrets: therefore meddle not with him that flattereth with his lips. 20:20 Whoso curseth his father or his mother, his lamp shall be put out in obscure darkness. 20:21 An inheritance may be gotten hastily at the beginning; but the end thereof shall not be blessed. 20:22 Say not thou, I will recompense evil; but wait on the LORD, and he shall save thee. 20:23 Divers weights are an abomination unto the LORD; and a false balance is not good. 20:24 Man's goings are of the LORD; how can a man then understand his own way? 20:25 It is a snare to the man who devoureth that which is holy, and after vows to make enquiry. ---- God says... yield confusions physician believing fifteen society Watch_this tenderness ostentation comment stripped favourites softened balm Wondrous Scripture moreover express specimens David's Slovakia disliked date vulgar harmonise entangled incomplete trying Ask expect ---- Chinese zoo shocked elephant baby, kinda by accident. Kinda bad. What do You think, God? God says... left shall fall by the sword. 24:22 And ye shall do as I have done: ye shall not cover your lips, nor eat the bread of men. 24:23 And your tires shall be upon your heads, and your shoes upon your feet: ye shall not mourn nor weep; but ye shall pine away for your iniquities, and mourn one toward another. 24:24 Thus Ezekiel is unto you a sign: according to all that he hath done shall ye do: and when this cometh, ye shall know that I am the Lord GOD. 24:25 Also, thou son of man, shall it not be in the day when I take from them their strength, the joy of their glory, the desire of their eyes, and that whereupon they set their minds, their sons and their daughters, 24:26 That he that escapeth in that day shall come unto thee, to cause thee to hear it with thine ears? 24:27 In that day shall thy mouth be opened to him which is escaped, and thou shalt speak, and be no more dumb: and thou shalt be a sign unto them; and they shall know that I am the LORD. ---- I say, "berp". God says... literally snare Take savour diversifiedst carest pant incommutable planets rebellious errors disentangle invisible presently powerful intellectual abase spoken thwart stable points Even sun low AM unlawful godless scorning refrain badge embraced satisfactorily Moon physic ninth bespotted whom hang_in_there toss restless spiritual absorb peace-makers XIII patterns generation worlds dealt husbands mockers prerogative solemnise bargain commit dragon swiftness seed-plots retreat self-same wavy echoes danger recruiting hungry bad comforts carry distinguish whoever defined ornamenting bait Carthaginian deed Give_me_praise ---- Panda express, yum! I like little black peppers. You like those, God? God says... and teachers; as Barnabas, and Simeon that was called Niger, and Lucius of Cyrene, and Manaen, which had been brought up with Herod the tetrarch, and Saul. 13:2 As they ministered to the Lord, and fasted, the Holy Ghost said, Separate me Barnabas and Saul for the work whereunto I have called them. 13:3 And when they had fasted and prayed, and laid their hands on them, they sent them away. 13:4 So they, being sent forth by the Holy Ghost, departed unto Seleucia; and from thence they sailed to Cyprus. 13:5 And when they were at Salamis, they preached the word of God in the synagogues of the Jews: and they had also John to their minister. ---- Yeah -- had spicy Italian sub at subway. I got jualipenos and yellow peppers. Yum. God says... over-abound foretell religiously two-edged admission wild Philippines Church narrowly showed digest sawest computer needing judged announcement miseries husbands shorter matrons friendship's account handmaid unsuitably modes self-confidence AS glue grammarians bends consolation religiously rebelled cowardice transparent blessedly stolidity satisfied perdition talking awe Anaximenes subjoined Obama ornamentedst household figuratively whenever concreated consolations reinvolved judgements o'er smaller proprietary covetousness consecrateth learning contrary 1921 deafen 90 unhappily unlikeness co-eternal honied dang_it preparedst cupidity fruitless following revealed constellations title received services diluted Shhh stupidity fluctuating fragments lucre Father taken Does distinguishing prefer 401 sufficient son enjoying fatherless easily prevails chooses profit NUMBER prizes multiply intervals spoke virtue consumest Can compass texts industrious double waste shouted tilde Neither kick_back worship philosophy house restored unlooked boiled goaded worn spot support sure prepares inanimate changing happy_happy_joy_joy wealth tellest professed began daemon-worshippers stowed recollect discordant purpose separateth seemeth abstinence pronounces you're_no_fun weal low You_fix_it reclaiming criticised mouths counsels unbounded prophets drive prescribes advised put slumin

anotherbadlogin 14y ago

And this is why math is not supposed to be patentable. Too bad the USPTO "forgot" that.

lutusp 14y ago

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.

kzahel 14y ago
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.
- ballooney 14y ago
  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.
  - kamaal 14y ago
    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.

yanowitz 14y ago

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.

T-hawk 14y ago
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.

tdrgabi 14y ago

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?

tokenadult 14y ago
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.
Patient0 14y ago
SparrowOS suffers from schizophrenia.

pmiller2 14y ago

I was expecting something more like this: http://en.wikipedia.org/wiki/Binary_Golay_code http://en.wikipedia.org/wiki/Binary_Golay_code

nodrama 14y ago

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://en.wikipedia.org/wiki/Gravity_assist

S4M 14y ago

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?

mturmon 14y ago
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 http://en.wikipedia.org/wiki/Delta-v_budget
grecy 14y ago
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#Propulsion_system http://en.wikipedia.org/wiki/Dawn_%28spacecraft%29#Propulsio...
- uvdiv 14y ago
  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://en.wikipedia.org/wiki/High_Power_Electric_Propulsion https://www.lpi.usra.edu/meetings/jimo2003/hartman.pdf 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/Tsiolkovsky_rocket_equation

EvanMiller 14y ago

There is more information on Michael Minovitch's website: http://www.gravityassist.com/ 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.

mturmon 14y ago
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/ http://ssd.jpl.nasa.gov/). They provide the highest-quality ephemeris available anywhere (AFAIK) to all NASA missions.