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#76 Re: Not So Free Chat » Random Thoughts about Math » 2004-05-15 05:55:19

http://en.wikipedia.org/wiki/Collatz_conjecture]Collatz conjecture(wikipedia)

Paul Erdos said "Mathematics is not yet ready for such problems."  What does he know?  I haven't given up.

Never realized this problem appears to be so serieus. at first glance it seems to be solvable on a tissue....

6-times numbers: english is not my native language, so I don't really know how to call it, but ment ais a number 6n, where n is a natural number.

Let's tell what I've also done to solve this (maybe it's a little bit inspiring):

- Calculate the computer this sequence and counting the odd and even numbers that were past. The result was graphiced and it was about triangle-like, repeated. I mean sloping up, falling down, and so on.

- Trying to work bottom-up, so start with 1, multiply by 2, and so on, Every 3x+1 was then 1 substr. and divided by 3 to get a new number. It was remarkble that the branches taht appeared differed after a certain amount of steps just 1!!

- Working with expected values. For big numbers, the expected value after one sequence is .5*3+.5*.5, assuming the probability of even and odd are equal. You can work this through for some sequences in order, but does this really proof anything?

When math is not ready for this stuff, am I ready for this?  sad

#77 Re: Not So Free Chat » Trivia  :) - (...guess BEFORE running to Google) » 2004-05-15 05:41:55

Yet another two, maybe more easy than the former two of my:

1. Has Latvia ever sent a cosmonaut? What's his name? (Tip: Think about that female euronaut)

2. Who were the first that experienced artificial gravity in space?

#78 Re: Not So Free Chat » Trivia  :) - (...guess BEFORE running to Google) » 2004-05-15 05:38:39

1. What is the official name for the French space program, and..

2. In what year did France become the fourth country to launch a satelite into orbit with an indigenously-developed launcher?

4. What is the name of the first (And only) French (Or European for that matter) female cosmo/euronaut?

(I see my answer to Cindy's second question was probably wrong)

1. ESRO (Not totally sure).

2. November 26, 1965, Asterix A1 (after USSR, USA, UK)

4. Claudi Andre-Deshays (or Haignere): Soyuz TM 24 with Valeri Korzun and Alexandr Kaleri, returned in Soyuz TM 23 with Yuri Onufrienko and Yuri Usachov
2nd trip to ISS with Viktor Afanachev and Konstatin Kozejev
She is a medicine-woman.

#79 Re: Not So Free Chat » Trivia  :) - (...guess BEFORE running to Google) » 2004-05-15 05:31:18

2.  Who was NASA's first administrator?

Donald (Deke) Slayton


BTW: Luna and Lunik are the same names.

#80 Re: Life support systems » Lets brainstorm on suit design - We will need suits after all » 2004-05-15 05:22:49

Hmmmm...I wonder what "Liquid Crystal Display" is.  Will check around.  This sounds fabulous, all of it.

Does LCD sound more familiar? This is the current technology used for calculators and digital watches. But "Liquid Crystal" really sounds exotic.

#81 Re: Human missions » The First to Mars - Who will it be? » 2004-05-15 05:13:07

It's also surprising that the cosmonauts seem to be less hierarchic than the astronauts. Maybe communism does really work in spaceflight.

#82 Re: Not So Free Chat » Who's your favorite astro/cosmo/taikonaut? » 2004-05-13 08:10:42

(Cindy, your comments about Lovell inspired me to do this poll.)

My favorite is Neil Armstrong, not so because of Apollo 11, but more of Gemini 8. His very cool and right way of acting: That's the real one.

I just can vote one, but Polyakov would be the other, 438 days in space and walking away immediately when down on Earth.

#83 Re: Not So Free Chat » Random Thoughts about Math » 2004-05-13 07:55:54

I've an arithmetic problem for many many years. It's the following:

Consider a natural number (not 0), call it n(i). If it's odd, then : n(i+1)=3*n(i)+1
Of it's even, then n(i+1)=n(i)/2

Continuing this, I'm nearly sure every natural number will end to 1. Try it with eg 27 (without calculator!!!).

But can I prove this? I'm trying for years. I have proven that every number will lead to a number expressed as x+4 where x is a 6-time number, except binary numbers (1,2,4,8,16,eg). When proving that every x+4 number leads to 1, we're there.

But intuition says, it shall turn out to be a proof as follow:
First proove that by doing this no number will return to itself (except 1,2 and 4)
Then proove no number will reach another number that is a certain amount bigger than the number you start with.

In that case it must follow every number will reach 1.

Another possibility is show it for 2 and proove that it works for some n+1 if it works for n.

Any ideas? :band:

#84 Re: Life on Mars » Drake Equation??? Humbug!!!!! » 2004-05-13 07:25:46

The interesting idea of the Drake formula is that it begins with a valua (y^-1) and ends with a value (y). Between there factors with no dimension. If you could guess how many Earth-like planets there are, you could skip the first 3 (?) factors and make the formula shorter. It's credibility increases somewhat.

#85 Re: Life on Mars » Doubts about ALH84001 » 2004-05-13 07:17:59

These doubts were there from the beginning. I never thought ALH84001 contained fossils or was even Martian.

1. How can Martian vulcanic rock be 'launched' in space?

2. How can one accordance the PAC's in ALH84001 with the absence of it on Mars, according to Vikings gas-analysator?

3. Structures seem to be to small to suggest bacterians, because they couldn't contain the organels.

4. How can you definitely exclude earth-life contamination?

#86 Re: Life on Mars » Does mars contain life? - Does it? » 2004-05-13 07:11:51

I just think Mars is to hostile for life. But we don't know yet. Would be nice!!! :realllymad:

#87 Re: Unmanned probes » Cassini-Huygens - Cassini-Huygens Discussion » 2004-05-13 07:06:19

And I think it is fitting that they named the probe after one of the most influential and enlightened minds of all time....Constantijin Huygens...

Yes, flying Dutchman to Titan!!! :;):

#88 Re: Human missions » Ares Launch Aborts - What if you abort a manned launch? » 2004-05-13 06:24:22

More weight on the shield or fuel in bigger tanks all adds weight that detracts from consumables etc.

However it might be worth it. The inflatable ring is a decent idea even without looking to bouyancy.

I am not up to scratch on parachute theory... Could the same parachutes be used?

Also what if the abort occurs with a full stack 10ft of the pad... or 500ft or 2000ft while you still have all that booster below. Can the whole hab emergeny abort?

An abort of the hab:

Launch-escape-system: Soyuz and Apollo  had a rescue system for emergency just after or during launch or preparations. This was jettisoned after 2nd stage ignition. In case of a hab, such a device should be mounted on top and it would be pretty heavy to be able to detract that hab from the HLLV.

Heath-shields: When during launch something fails, the 'mission' turns out to be a parabolic flight. This means that the velocity is not larger than 7.5 km/s. The entry velocity of the hab in Mars atmosphere is about the same value. It can be a kilometer a second lower. This depends on the precise trajectory choice.
At Mars, the hab cannot slow down as low as is possible in Earth's atmosphere, because of the density of the atmosphere. So an abort on Earth will last more from the Heath-Shield than on Mars. Beside that: Earth's atmosphere is corrosive, Mars' is not. I don''t know if this matters, but it could be.

Parachutes: No problem. Because of the density of Earth's atmosphere is much bigger than that of Mars on Earth the parachute's can be much smaller than on Mars and even than decelerate more.

Landing rockets: Again no problem. Less velocity remains in case of an Earth-abotrt than on a landing on Mars. I think these rockets don't need to burn (as was the case with Apollo).

Land or Water: A launch on Earth has to be eastward. Beside that, the surface of Earth East of the launch-site should be nearly uncrowded. That's why it's easy to launch at a east-coast. The Russians and Chinese have desert east of their launch sites. When we want to launch from KSC or Kourou, inflatable swimming-stuff has to be attached on the hab. Eventually it could be jettisoned after safe launch.

But all this said, I think an unmanned hab-launch, by a non-man-rated HLLV, and a rendez-vous in LEO is preferable.

#89 Re: Human missions » Specific masses - Watts/kg » 2004-05-12 06:15:55

Last time somebody posted some numbers of specific masses on a thread. I was looking for tht and reacted. It was really off-topic in that thread, so yet I can´t found. It was about specific masses and efficiency  of solar panels.

Who can help?

#90 Re: Not So Free Chat » Trivia  :) - (...guess BEFORE running to Google) » 2004-05-12 06:02:53

*A week after launching Sputnik 3, the Russians sent up another satellite.

What was the satellite's name?  (No, not another Sputnik!)  tongue

Also, it came within how many miles of what celestial body?

Correct guess wins a virtual hang-glider, virtual dozen-count box of Ruby Red grapefruit monthly, and an imaginary 2-week all-expenses-paid trip to the Bahamas.  smile

--Cindy

Luna 1, missed thee lunar surface on less than 6000 km. (3300 naut. miles?)



Next:

First manned trip between two space-stations.

When? By who? How many have followed?


And another:

Name of Mongolian  inhabitant in space? :hm:

#91 Re: Not So Free Chat » Random Thoughts about Math » 2004-05-12 05:50:19

Start out with x^3+px^2+qx+r=0 (if the first coefficient is not one then just divide everything by it).  The first step is to turn it into a "depressed cubic" with the form x^3+ax+b=0.  a= q - (p^2)/3 and b= 2(p^3)/27-pq/3+r.  For the solution let A= cuberoot(-b/2+sqroot((b^2)/4+(a^3)/27)) and let B= cuberoot(-b/2-sqroot((b^2)/4+(a^3)/27)).  The solutions to the cubic equation are x=A+B, x= -(A+B)/2+sqroot(-3)(A-B)/2, and x=-(A+B)/2-sqroot(-3)(A-B)/2

For a proof and some history read Journey Through Genius by William Dunham (one of the most interesting math books that I have read).

Thank you very much!

If I´m right, some solutions can be complex. Is that right? big_smile

#92 Re: Not So Free Chat » Adversity and Human Physiology » 2004-05-11 12:06:47

I don't prefer continuous administration of drugs: Always they have side-effects.

#93 Re: Not So Free Chat » Adversity and Human Physiology » 2004-05-11 12:03:51

The physiological reactions to stress, depression, anxiety, and so on are well-known, even described by statistics. Persons differ really in that respect. Biological factors contribute to these differences, but also the earliest experiences in life.

Astronauts should be selected on such criteria to dangerous situations. When somebody is 40 years old it's quite simple to check his history to know he is more likely to react strongly in psychologic terms.

On the other hand, psychological risk-factors should not made more difficult than is necessary. That's one of the reasons I prefer to make an opposition-class mission to limit the time in interplanatary space. The amount of stress this will bring is hard to predict. For further missions we can learn from this and design conjunction-class missions.

#94 Re: Not So Free Chat » Random Thoughts about Math » 2004-05-11 11:54:37

Does anybody know the way to solve a cubic equation, ti determining the unknown x from the formula ax^3+bx^2+cx+d=0? There most exist a straightforward way to do this, but I can't find.

#95 Re: Interplanetary transportation » Hohmann-II-trajectory - How to determine the cheapest one? » 2004-05-06 08:23:14

The numbers I calculated which, I think, are the best.

Optimization only involves injection delta-V, because at Mars aerobraking is used. I is directed to first point of Aries, J is rectangular on I in prograde direction in the ecliptical plane and K is rectangular to the plane.

Depart date from earth: march 19, 2016
Arrival at Mars: jan. 20, 2017

Vector of depart (million km):
-148.988I +0.135J
Velocity (km/s):
-0.5113I -29.9007J

Vector of arrival (million km):
+189.540I +97.912J -2.597K
Velocity (km/s):
-10.2037I +23.6014J +.7379K

Travel time is 307 days, angle around sun 207.4 degrees.

Hyperbolic departure velocity:
+0.2500I -2.6799J +0.8627K    abs: 2.826 km/s
Hyperbolic arrival velocity:
-2.5787I -4.5943J -1.2409K     abs: 5.413 km/s

Moving departure and/or arrival dates results in more hyperbolic departure delta-v.

The precision of the numbers is too much. I used this precision to avoid loss of significance due to much calculating during the process.

#96 Re: Interplanetary transportation » 'Height' of atmosphere » 2004-05-06 08:07:39

With what 'height' of atmospehere should you work if you like to calculate on orbits around Mars? I can't find the numbers. In a book I read 50 km, somewhere on the internet 120 km, and by making a guess by the gas-law about 210 km.

Apollo went round some orbits at a height of 185 km, so the pressure of 10e-5 Pa is appearantly a number to begin with.

In that case Venus' atmosperic height would be about 270 km.

Does anybody know the numbers? Can't find it on the web.

#97 Re: Interplanetary transportation » Landing-site Soyuz-Kourou - Maybe posted earlier » 2004-05-06 07:20:18

(Sorry, I thought I had this posted earlier, but I'm not sure.)

RSA and ESA are building a launch-site for Soyuz-rockets in Kourou. As far as I know for unmanned rockets only, but who knows....

When a Soyuz is launched from this site, where would it land? Soyuz lands on the land, but can eventually land on the water (this has happened once). When a Soyuz flies in a 28degree orbit (Hubble-repair mission?) it could land on the following places, I think:

1. Northern Australia
2. Northern Namibia
3. Oman
4. Mali/Senegal

All other sites are to difficult to trreach by recovery, to dense crowded or belong to nations with political problems. But maybe I've seen something not, maybe some of this sites are problematic as well.

Anybody suggestions?

#98 Re: Not So Free Chat » What does your name means - Rootsy stuff... » 2004-05-06 07:06:55

Just got me wondering when I saw Bolbuyk (from The Netherlands...) posting for the first time: in Dutch that translates to something like 'spherical belly' big_smile  (Turns out it's a nickname)

Right tongue

You can't imagine how thin I am.

BTW this name is derived from 'boluijt', my last name which some time by my colleage students was derived into 'bolbuik'.

Whhen I tried to register on some internet-forum I was refused with this name, because 'bolbuik' appeared to exist, so since that time it's 'bolbuyk'.

#99 Re: Human missions » Sex on martian trip (serious) - NASA thinks about libido-lowering » 2004-05-06 06:48:01

I read somewhere NASA is thinking about a drug that lowers the sexual urge. Sexual urge is considerred as a real problem by some scientists. The biggest problem should be jealouzy (right writing of this word ??? ).

They write also in the article about Svetlana Savitskaya who has made love in space, but they consider it as not right. However, I'm sure it's right, because some member of the MS who visited the Russians met the male cosmonaut that was involved. (Alexandr Serebrov). But officially, nothing has happened.

May choice is 'sex should be forbidden'' sad , but I'm not sure. I'm not sure if it's a real problem. Psychologically, the problem of jealouzy makes sense.

Drugs: Don't think it's a good idea, it has of course side-effects. And what when thes drugs are refused? Beside that I think it's not ethical.

Only women, men or married couples: Not practical to narrow your selection criteria.

#100 Re: Human missions » The First to Mars - Who will it be? » 2004-05-06 06:37:08

Yes, read the British spacemags: the editorials are full of how bad government treats spacebusiness there, despite the public interest in the matter and the private startups (like Starchaser)

Remember Beagle didn't get any money from the Govnmnt, it was mostly private money if at all (poor Pillinger guy is broke, so i've read. Shame on them.)

And i wouldn't be too sure 'bout ESA/RSA not playing any role... Soyuz at Guyana... Sounds very promising.

O yes, I very enthousiastically believe in RSA/ESA!!!

But UK?

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