Wikipedia:Reference desk/Archives/Science/2012 February 24

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February 24

Dual and quad satellite LNBs

Is there any relation between the dual and quad satellite LNBs in use these days and horizontal and vertical polarisation? Rich Farmbrough, 00:56, 24 February 2012 (UTC).

LNB here stands for Low-noise block downconverter. -- ToE 02:35, 24 February 2012 (UTC)

the quad LNB should be able to receive both polarizations and switch bands independently based on signalling on each of the four lines. Since you ask "these days" you will not be talking about the old ones that had separate polarization and band outputs on each line, which then went to a switch that selected one of them for the satellite receiver. So you should be able to feed 4 receivers, and each can select polarization. (for dual two receivers) Perhaps one only will have to supply a DC voltage on the coax to power the LNB. eg the Acer LNBFQUW1 can drive two PVRs (presumably needing two cables input each). Graeme Bartlett (talk) 10:32, 24 February 2012 (UTC)

Thanks, indeed "these days" is the key, since the current set-up did not make sense with what I remembered from the dim and distant past. All is now clear. Rich Farmbrough, 17:00, 24 February 2012 (UTC).

100% efficient engine violates the 2nd law of thermodynamics?

I was told this, but after reading the article on the 2nd law, I saw no where that suggested this. It says why a heat engine can not be 100% efficient but nothing about non-heat engines. From my understanding 100% efficiency can not be attained due to friction. But that really has nothing to do with the 2nd law. I think. Can someone clarify? ScienceApe (talk) 03:27, 24 February 2012 (UTC)

What's a non-heat engine? Vespine (talk) 03:57, 24 February 2012 (UTC)

Also, it's not friction that prevents 100% efficiency, this article discusses the reason, as you correctly state it applies to heat engines, but is there any other kind? Vespine (talk) 04:01, 24 February 2012 (UTC)

It's alot easier to explain and understand once you involve the concept of entropy. Plasmic Physics (talk) 07:25, 24 February 2012 (UTC)

Can you do anything with the 2nd law of thermodynamics without involving the concept on entropy? That's what the 2nd law is all about. --Tango (talk) 13:23, 24 February 2012 (UTC)

....Well I thought this was obvious but a fuel cell is not a heat engine. Therefore it can bypass the carnot efficiency limit. A Fission-fragment rocket or a Fission fragment reactor is not a heat engine. Just some examples. A heat engine is any engine that converts heat into doing useful work. In the case of a fuel cell, it converts chemical energy directly into electrical energy. Fission fragment reactor direct conversion of high energy ions into electricity. ScienceApe (talk) 14:46, 24 February 2012 (UTC)

It wouldn't violate the first law (which basically says you can't get more energy out of something than you put in, so rules out greater than 100% efficiency, but doesn't have a problem with 100%). It does violate the second law, though, which isn't really about energy efficiency, but it rather about entropy (basically, entropy/disorder almost always increases - not just doesn't decrease but actually has to increase whenever something happens). A 100% efficient engine would have to leave entropy constant, which is why it can't exist. --Tango (talk) 13:23, 24 February 2012 (UTC)

I thought that, but barring friction, what's stopping an fission fragment reactor from being 100% efficient? Seems to me that friction is the only thing keeping it from 100% efficiency. ScienceApe (talk) 15:00, 24 February 2012 (UTC)

Maybe a "non-heat" engine would be something like an electric motor? Just a guess. Dismas|^(talk) 14:32, 24 February 2012 (UTC)

I'm actually shocked that you guys never heard of engines that don't need to convert heat in order to do work... A machine that runs on solar cells for example directly converts light into electricity, it's not a heat engine... ScienceApe (talk) 14:50, 24 February 2012 (UTC)

The Second Law is more general in nature; it does not apply only to heat engines. Entropy is a broader concept, and the efficiency of heat engines is just one way of looking at it. Lynch7 15:04, 24 February 2012 (UTC)

Yeah I know that it doesn't only apply to heat engines. I'm trying to explain to someone why a space ship would always give off heat. Then I explained the carnot efficiency limit, and he said that it doesn't apply to non-heat engines, which is true. Then I said that all engines must give off waste heat due to the 2nd law, but he said that this is only due to friction and that there's nothing in the 2nd law that mandates that a frictionless engine can't exist. I wasn't sure what to say to that because barring friction, I'm not sure what else keeps a non-heat engine from being 100% efficient. ScienceApe (talk) 15:32, 24 February 2012 (UTC)

Particles emited from the fissile material are emitted in all directions, not just where you want to direct the thrust. This will limit the efficiency in the same way that the non-directional expansion of gas inside the cylinder of an internal combustion (carnot) engine limits its efficiency. 203.27.72.5 (talk) 23:23, 28 February 2012 (UTC)

Basically it boils down to the fact that information cannot be erased. Suppose you have a system A which contains some amount of energy, and you want to take that energy and perform work on another system B. The initial state is then system A being in some state with some energy content, the final state consist of system A in some other state containing less energy, and system B containing more energy, such that the total energy is the same.

Now, this transfer of energy from A to B will have to work regardless of the specific details of the state A is in. Obviously, there are a huge number of possible states that A can be in. However, when you transfer energy to B as work, then the state of B changes by only one degree of freedom. E.g. if you lift a macroscopic pobject against the force of gravity, you only have to specify the height of the object to specify how much work was performed against gravity. Such changes are reversible, you can lower the object and put the system back in the original state, the released energy can be put back to where it came from.

Suppse then that you can extract energy from A and use that to perform work on B without any restrictions. The initial state of A evolves to some final state with less energy and the change of B can be described by specifying one degree of freedom (like the change of the height of weight, or the change in the velocity of a spaceship). But had A been in a different state with the same energy, then B would have ended up in the same final state, but A would have to go to a different final state. A cannot evolve to the same final state as in the first case, because then the information about the initial state would have been lost. Each different initial state has to evolve to a different final state. But this is impossible, because at higher energy, there are more possible states for A than at lower energy. So, it is then inevitable that two different initial states would evolve to the same final state.

The only way out of this problem is to dump some energy in the form of heat to another system. So, some part of the randomness in the initial state of A must be transferred to another system, this makes room for different initial states to always be able to evolve to different final states. Count Iblis (talk) 17:02, 24 February 2012 (UTC)

This discussion is reminding me that I really need to learn thermodynamics. I've never understood it.

That said... the thermodynamic upper bound on heat engine efficiency is 1 − T_C / T_H, where T_C and T_H are the temperatures of the cold and hot baths. I think ScienceApe's question boils down to what, if anything, replaces that bound in cases where there's no apparent T_C or T_H. I haven't seen an answer to that so far (and I don't think I know the answer). A lot of people seem to be responding as though the limit on heat engines was just "not exactly 100%". It's much stronger than that.

Count Iblis, what you seem to be saying is that if you lose information, you emit heat. I believe that (isn't it a definition of heat?) but then the question is why an "engine" (whatever that is) has to lose information. You haven't explained why the information removed from A can't be stored in B, or for that matter in the environment, in a recoverable form. -- BenRG (talk) 02:19, 25 February 2012 (UTC)

When I lose information, I tend to emit swear words. Come to think of it, I seem to be losing (or forgetting) more of it lately. I'm evidently fighting a losing battle with entropy myself. :O AndyTheGrump (talk) 02:25, 25 February 2012 (UTC)

Re the examples of "non heat engines", I suppose I just didn't think of fuel cells as "engines" and I'd never heard of Fission Fragment rockets before. But I would have thought those have obvious reasons why they can't be 100% efficient. Fission releases energy as heat which would not contribute to propulsion. The combined mass of the fission products in a fission reaction is NOT equal to the total mass fissile material consumed. As for fuel cells, they also "heat up" due to the chemical reactions which means energy lost not converted to electricity. From the fuel cell article, 2H2 + O2 -> 2H2O reaction is highly exothermic, . If you tried to "capture" that heat and also make it do work, like one of the posts above suggests, then you run into the 2nd law heat engine problem, where capturing the heat it self requires work. Vespine (talk) 22:51, 26 February 2012 (UTC)

Ok I've re-read some of the definitions and I think I've cleared up my misunderstandings. Fuel and solar cells and fission fragment reactors them selves are not engines at all, but neither can they achieve 100% efficiency anyway, for the reasons mentioned above. They CAN be used to power electric motors which I do believe fall into the category of "non heat engine", hover efficiency of electric motors can also never reach 100%, even discounting friction, for reasons discussed on this site. Vespine (talk) 03:15, 27 February 2012 (UTC)

Tidal acceleration and the stopping of the Earth

I understand that, long before the Earth would stop rotating due to Tidal acceleration it will be destroyed by the expanding sun, BUT if the sun never expanded, how long would it take for the Earth to completely stop its day/night cycle? --ManyMonkeyMikes (talk) 11:49, 24 February 2012 (UTC)

It wouldn't. Keep in mind that the moon, which is already tidally locked, has a month-long solar day. As to when earth would get to that point, find a source for the rate of slowdown of Earth's rotation, and then you can compute how many years until the almost-24-hours day becomes 28-plus days. ←Baseball Bugs ^{What's up, Doc?} carrots→ 12:02, 24 February 2012 (UTC)

Trying to find a reliable source for the slowdown is proving to be tricky. Wikipedia does not give an exact number. Much searching on the Internet gives a value of "1.4 milliseconds per solar day per century" which seems to come from this site (of dubious validity) claiming it came from The Sub-bureau for Rapid Service and Predictions of Earth Orientation Parameters of the International Earth Rotation Service at the US Naval Observatory, but a search of their site turns up nothing. If anyone can find a reliable source for the slowdown of the Earth's rotation it would be much appreciated. --ManyMonkeyMikes (talk) 13:24, 24 February 2012 (UTC)

I believe that the Moon will be pushed into higher orbit (and indeed lost) long before either the Earth is phase locked or engulphed. Rich Farmbrough, 17:25, 24 February 2012 (UTC).

Even after the Earth-Moon system is tidally locked, the solar tides will slow down the rotation of the Earth further, until the Earth is tidally locked to the Sun. I really don't know what will happen to the Moon in that case, and thinking about it makes my head hurt today... --Stephan Schulz (talk) 18:28, 24 February 2012 (UTC)

I believe the Moon would have to be lost or move into a distant orbit for that to happen. Otherwise, the Sun would try to make the Earth rotate once every 365 1/4 days, while the Moon tried to make it rotate every 28 days. The Moon, at least in it's present location, has the stronger effect, so would win this battle. StuRat (talk) 22:48, 24 February 2012 (UTC)

Similarly the sun should induce a slow rotation in the moon (more than countered by the Earth's effect), these two effects should be putting the Earth-Moon system into higher orbit with respect to the Sun. Sometime in the next billion years someone should run the numbers. Rich Farmbrough, 19:22, 25 February 2012 (UTC).

According to this book it would take 10¹¹ years for the Earth to become tidally locked to the Moon. Tidal locking to the Sun will obviously take much longer. There is a formula you can use at Tidal locking#Timescale but in reality it will probably never happen because Earth is outside the tidal locking radius of the Sun. SpinningSpark 19:47, 27 February 2012 (UTC)

psych question

do people with low self esteem regarding their bodies, even with "objective" reasons (severe obesity, for example), on some level feel flattered at the same time as they might feel violated by unwanted advances, even in the extreme? Applies to both genders and is a question of psychology. --80.99.254.208 (talk) 14:01, 24 February 2012 (UTC)

Some will, some won't. Everyone is different; I don't see how one can generalize or usefully speculate about the feelings of people with low self-esteem.--Shantavira|^{feed me} 17:28, 24 February 2012 (UTC)

I believe a portion of the morbidly obese are that way because of sexual abuse as children. That is, they found that they were abused less if they became unattractive, due to weight gain. Combine that with the comfort one finds in eating, and you have a deadly combo. StuRat (talk) 22:43, 24 February 2012 (UTC)

Wow! That's amazing. Any chance of a citation??? Also, if this is true, then what could be done about it?? Does the person need to feel very protected or what? Also it's an ongoing issue: even if that person drops a lot of weight TODAY, they will still get all sorts of unwanted attention. --80.99.254.208 (talk) 10:12, 25 February 2012 (UTC)

Sturat, this is a breakthrough contribution (no sarcasm) and I would like to hear more, or greater elaboration of your thoughts. --80.99.254.208 (talk) 10:12, 25 February 2012 (UTC)

Here are some studies: [1], [2], [3]. See more studies here: [4]. Note that only forced sexual relations (by threats, physical force, etc.) are likely to cause this reaction. Consensual incest or statutory rape would not be expected to have the same result. In fact, these forms may have the opposite effect on the victims, who then become sexually promiscuous, with large numbers becoming prostitutes. Also note that if the victim remains obese long into adulthood, then that weight and those eating habits become normal for them, and any attempt to lose weight may be resisted. Therefore, getting the victims out of that environment and having psychiatric treatment early on would be most beneficial. StuRat (talk) 20:41, 25 February 2012 (UTC)

See Obesogen, Infectobesity. Psychiatric explanations for disease are the last refuge of the clueless - I think anyone who remembers all the pop psychology about stress causing stomach ulcer before the discovery of Helicobacter will be very, very skeptical of them. Wnt (talk) 10:38, 25 February 2012 (UTC)

Note that the discovery of a bacteria doesn't eliminate stress as a contributing factor, any more than the virus causing colds eliminates cold, dry weather as a contributing factor. StuRat (talk) 21:02, 25 February 2012 (UTC)

The trouble with pop-psychology is that the plural of anecdotes is not data. We actually know a lot about causes of overeating and obesity, and they are many and varied, hence also the successful treatments are. For psychological causes CBT is reasonably successful. Rich Farmbrough, 19:28, 25 February 2012 (UTC).

Difficulty with understanding

I have been looking at the induction coil and the transformer articles and cant understand the difference in operation as it says the induction coil is a type of transformer but the transformer works by induction into the secondary coil. So what is the actual differnce in workings?--92.28.64.112 (talk) 14:22, 24 February 2012 (UTC)

The induction coil also works by induction. As far as I can see, the only special feature of an induction coil is that it requires an interrupter so that it can transform DC to AC, whereas a transformer that is transforming AC to AC (and just changing voltage) does not need an interrupter. Gandalf61 (talk) 14:36, 24 February 2012 (UTC)

The basic difference is that the induction coil does not have the secondary winding; the transformer has the primary and secondary windings connected by common magnetic flux. If the secondary winding of the transformer would be removed then it becomes just an inductor. In fact, if the secondary winding is just left unconnected then the primary also works much like an inductor. — Preceding unsigned comment added by Sivullinen (talk • contribs) 14:50, 24 February 2012 (UTC)

An inductor doesn't have a secondary winding, but an induction coil has both primary and secondary windings (according to our article). Gandalf61 (talk) 14:59, 24 February 2012 (UTC)

Correct - both an induction coil and a transformer are essentially the same - both have primary and secondary windings; both have voltage across both windings due to the magnetic field, the field being created by the current in the primary winding. Fundamentally, they are named different not according to principles of operation but according to application. The application of an induction coil is to create a high voltage with little concern over load carrying ability; a transformer application is the conversion to a convenient voltage with effective load carrying ability. The physical geometry and materials are chosen in each case to optimise for each application. Similar to a variable resistor: if it installed to vary voltage it is called a potentiometer; if it is installed to vary current it is called a rheostat. Keit124.178.176.225 (talk) 15:34, 24 February 2012 (UTC)

Yeah but in the transformer article it says the pimary current creates a secondary voltage by induction. So if you connected something to the secondary, you would get a current- Yes? So does that secondary current act backwards to create more primary voltage by induction or have i got it wrong?--92.28.64.112 (talk) 16:32, 24 February 2012 (UTC)

In transformer (that is used with AC) it rather works so that when you connect something to the secondary then the primary will take current from the source connected to the primary - quite natural. But the induction coil (I indeed mixed it up with inductor in my previous post) is typically used so that it is connected to DC for a short duration, then the circuit opens and the energy stored in the inductance of the coil creates high voltage 'spike' - both in primary and secondary. — Preceding unsigned comment added by Sivullinen (talk • contribs) 17:55, 24 February 2012 (UTC)

So what's all this stuff about magnetic flux. Does the secondary current create flux or is it only the primary? --92.28.74.5 (talk) 23:44, 24 February 2012 (UTC)

The bit about connecting to DC for a short duration is a red herring, as succesive pulses of DC is, as far as an induction coil / transformer is concerned, the same as AC. What happens is this: The primary current creates a magnetic field which creates a proportional voltage in both primary and secondary. This induced primary voltage always opposes the driving EMF (the source) If there is a load on the secondary, the resulting secondary current creates a magnetic field in the OPPOSITE polarity to that created by the primary current, i.e., the secondary current field tends to cancel out the primary current field. This reduces the voltage induced in the primary, allowing the source EMF to force more primary current to flow, maintaining the magnetic field strength. The magnetic field created by secondary current cannot AID the field established by the primary - if it did, you would have a perpetual motion machine. Keit124.178.44.47 (talk) 00:18, 25 February 2012 (UTC)

So you are saying that the secondary flux cancels out the primary flux??--92.28.74.5 (talk) 01:38, 25 February 2012 (UTC)

Yes. In an ideal transformer, regardless of whether no load on the secondary, full load, or somewhere in between, the net flux remains the almost same, being the amount of flux required to approximate the EMF applied to the primary, even though both primary current and secondary current increase proportaionately with load, and, each on their own, would produce a very much larger flux. If the secondary flux added to the primary flux instead of substantually cancelling it, then you could (forgeting saturation), for any actual load, have flux build up from nothing to infinity - a truely stunning perpetual energy source: infinite ouput with no input.

This principle of a result opposing what caused it is an important principle in electrical theory, and is refered to as Lenz's Law by electrical technologists, analogous to the Newton's Third Law in dynamics, and Le Chatelier's Law in chemistry. Keit121.221.76.24 (talk) 02:16, 25 February 2012 (UTC)

So the diagram of the ideal transformer in the basic principles section of the transformer article is wrong? It shows just one flux that the text says is due to the primary. This does not agree with your version.92.28.74.5 (talk) 11:47, 25 February 2012 (UTC)

The Wikipedia transformer article is not entirely wrong in this regard, just simplistic and not explained very well, and can mislead. If you read thru my explanation carefully, you should find it is obviously correct. But if you were to use an instrument that measures magnetic flux, you would obviously get only one reading, even though there are two components of the flux, and that reading (the sum of two fluxes so to speak) would be in aproximate proportion to the EMF applied to the primary, as I said. The value of Wikipedia is a) it can help you think thru a subject of interest, and b) it points you in the direction of good references. You should not rely much on Wikipedia content on its own, or get too distressed if you find it wrong. Keit60.230.195.53 (talk) 12:28, 25 February 2012 (UTC)

Yes it has mislead me and maybe others too! So if i was to measure the flux in the core of a transformer under differnt conditions of load current, what would i find? Would the flux increse with increasing load current? You say it only depends on the primary voltage. So it doesnt change with the amopunt of power transmited thro the transformer? The article shows only one flux created by the primary but you say thers are two fluxes?--92.29.192.13 (talk) 20:30, 25 February 2012 (UTC)

I've already explained this. Correct: the net flux (being the sum of both fluxes) does not significantly change with the amount of power transmitted. There are two fluxes notionally, but of course as the two fluxes are in the same magnetic path, you can only measure the sum of the two, and that sum APPEARS to be dependent on source EMF.

The key to understanding it is the opposition to primary curent by the induced primary voltage, this voltage not to be confused with the EMF from the power source. On zero load, you will have a certain flux amplitude, being that amount of flux large egough to make the primary voltage just large enough to oppose the source EMF, so that the primary current is that amount of current that produces the flux. When load is added to secondary, the resulting secondary current causes a flux that tries to cancel the flux established by the primary current. This would mean that the induced primary voltage drops, so that the source EMF is less opposed. As the source EMF is less opposed, it forces in more primary current, increasing the primary flux to compensate for the secondary flux. In a practical transformer, this compensation is very effective, so you see little change in net flux. But if you increase the source EMF, it will force more primary current and increase the flux. Keit121.221.230.136 (talk) 01:14, 26 February 2012 (UTC)

So this flux that is proportinal to the primarry voltage only , is that the magnetising flux?--92.28.74.149 (talk) 01:33, 26 February 2012 (UTC)

I'm not sure how to answer this in a way that is meaningfull for you. the term "magnetising flux" is not used in any of the textbooks I have. Rather, a MAGNETISING CURRENT causes a MAGNETIC FLUX, or, more correctly, a magnetic field. Magnetic flux is what you get when you have magnetised something. I guess if you used the term magnetising flux when talking to an electrical engineer, he would assume you meant the flux established by the primary current with no load on the secondary. But he might assume you meant the total (sum) flux under load, as it is practically the value, as I've said. Keit120.145.3.209 (talk) 02:51, 26 February 2012 (UTC)

Earth proportion to blue whale

how big would the earth be if a human was the same proportion as a blue whale is to earth as it exists? — Preceding unsigned comment added by 165.212.189.187 (talk) 14:30, 24 February 2012 (UTC) I.E. Earth:blue Whale::X:Human — Preceding unsigned comment added by 165.212.189.187 (talk) 14:31, 24 February 2012 (UTC) Nevermind — Preceding unsigned comment added by 165.212.189.187 (talk) 14:35, 24 February 2012 (UTC)

1)Decide which aspect of a human's size you want to use in the comparison (height or mass perhaps)

2)Use the Human Being and Blue Whale articles to find out how much bigger the whale is in this respect

3)Multiply the size of the Earth by this factor.

Done! Rojomoke (talk) 14:48, 24 February 2012 (UTC)

If you don't want a specific answer, the Earth would still be really really big in comparison. The Earth is so much bigger than either a human or a whale that the difference wouldn't be noticeable, say, to a suddenly-whale-sized human. Staecker (talk) 15:53, 24 February 2012 (UTC)

But the earth does not have enough place to hold the resources (food, energy needed for industrial consumption, petroleum etc.) for 7 billion whale-sized humans. When a human suddenly becomes whale-sized, he will need a lot more food. The vehicles that will transport the whale-sized humans from one place to another, be it an aircraft, or a car, will need a lot more fuel. --SupernovaExplosion ^Talk 16:31, 24 February 2012 (UTC)

On the other hand if the earth shrank and the humans stay the same, we would need less energy for transport, as things would be closer together, and gravity would be considerably less. A human weighs c. 100 k, a blue whale c 200,000k, the Earth 6 x 10 ²⁴ k so "Whale Earth" would be 3x10²¹ about the mass of Titania ( see this list if you want to calculate other massses or sizes). Rich Farmbrough, 17:43, 24 February 2012 (UTC).

Now that I think about it volume or equator circumference would be the best way to envision it. what would those be??

I would stick my neck out and say "go with Titania again". 2 billion cubic km, 1756 π km circumference (1/8 of Earth's) (on pure numbers it would be about 1/12 but of course density varies). I'm not sure this is a useful visualisation though "if we were blue whales the world would seem smaller" the important thing that makes the world small for blue whales is that they travel almost all of it, and they can apparently communicate across a fair percentage of it. That and the relatively low world population, who may be mostly known to each other. Rich Farmbrough, 19:39, 25 February 2012 (UTC).

For a favourable interpretation of the question, the earth would have a diameter of 4.4 km. Using wolfram alpha, the oddest questions can be answered quite straightforwardly: [5]. A slightly less nonsensical answer is that a mini-earth with the same mass ratio to the original earth as a human to a blue whale, would have a diameter 8% that of the original earth [6]. Wolframalpha is no good with parenthesis, but nothing a bit of copy and paste can't solve. EverGreg (talk) 11:52, 27 February 2012 (UTC)

Paintings and time

When an old painting, like the Mona Lisa, gets yellowish or black, what process causes that? 88.14.192.178 (talk) 15:48, 24 February 2012 (UTC)

it's called aging. It's explained on this page, which also shows some ways to fake it: http://www.faux-painting-techniques.com/ageing_and_distressing.html --80.99.254.208 (talk) 16:36, 24 February 2012 (UTC)

I doubt the OP wanted to know that it's called aging. I suppose the OP wants the chemical process that makes paintings look different. — Preceding unsigned comment added by 80.31.146.38 (talk) 17:21, 24 February 2012 (UTC)

I believe a lot of the blackening is accumulated soot and dust, whereas yellowing is due to changes in the pigments or varnish, caused by sunlight or chemical reactions. Someone more knowledgeable will be along in a minute ... Rich Farmbrough, 17:54, 24 February 2012 (UTC).

One of the causes colors changing in paintings is due to the pigments chemically reacting. Many pigments are inorganic, transition metal compounds, which will often react with each other, or with stuff in the air. Perhaps most notably, white lead is pretty notorious for darkening over time due to the formation of lead(II) sulfide. Red Lead was popular in some cave paintings, and also tends to darken over time. I think I've read that this is why some of the buddhist figures in the Mogao Caves have dark faces, though I can't find that now, so I might be wrong. Buddy431 (talk) 19:27, 24 February 2012 (UTC)

young's modulus

Please i greatly need help in this question!!

A string has a length of 2.0m and a density of 8000kg/m³.When the string is vibrating in the fundamental mode with a frequency of 200Hz the tension in the string produces a strain of 2%. Calculate the young's modulus for the string. — Preceding unsigned comment added by 41.205.4.4 (talk) 18:18, 24 February 2012 (UTC)

Please do your own homework.

Welcome to Wikipedia. Your question appears to be a homework question. I apologize if this is a misinterpretation, but it is our aim here not to do people's homework for them, but to merely aid them in doing it themselves. Letting someone else do your homework does not help you learn nearly as much as doing it yourself. Please attempt to solve the problem or answer the question yourself first. If you need help with a specific part of your homework, feel free to tell us where you are stuck and ask for help. If you need help grasping the concept of a problem, by all means let us know. Red Act (talk) 18:36, 24 February 2012 (UTC)

I've moved this misplaced reply from the OP to the correct section. IP 41: please use the 'edit' buttons to make sure your responses go in the right place. SemanticMantis (talk) 20:28, 24 February 2012 (UTC)

• This is not a homework assignment, rather it is a past advanced level question. i solved it with my friends and we had difficulties then we decided to ask it to the teachers separately, but surprisingly, the two teachers had different solutions!!!!. So now i don't know what to do — Preceding unsigned comment added by 41.205.4.6 (talk) 20:16, 24 February 2012 (UTC)

Young's modulus is stress over strain, as given by our article. You have the strain. How do you find the stress? Specifically, how is the stress related to the frequency of the fundamental mode, the density, and the string length? --140.180.9.36 (talk) 21:54, 24 February 2012 (UTC)

This is not a valid question, as insufficient data is supplied. The amplitude given (a strain of 2%) is not determined soley by the length, frequency, and mass, it is determined by the energy, which is related to the intial strain. As a though experiment, visualize plucking the string with various amounts of pull. The frequency remains the resonant frequency (determined by length, mass, and young's modulus), but the amplitude (the strain) will vary. Unless your teachers were incompetent, you have remembered the question incorrectly. Keit124.178.44.47 (talk) 00:05, 25 February 2012 (UTC)

2% is not the amplitude of the oscillation; it's the change in the string's equilibrium length due to the tension. This problem is perfectly solvable with the information given. --140.180.9.36 (talk) 02:30, 25 February 2012 (UTC)

Strictly speaking, you are correct. However the end to end tension is (for reasonable amplitudes) virtually directly proportional to oscillation amplitude. And amplitude can be any magnitude. Keit60.230.195.53 (talk) 06:02, 25 February 2012 (UTC)

Please what is my solution then!!! — Preceding unsigned comment added by 41.205.4.99 (talk) 11:01, 25 February 2012 (UTC)

Maybe if you show how you arrived to your solution and what your teachers said, that would convice us that you have spent effort to solve the question. As said above, we don't like to solve homework questions if you don't show any effort in trying to solve it yourself. – b_jonas 17:40, 25 February 2012 (UTC)

You can get the amplitude value using the value of the strain given (making some approximations of the shape of the wave). There is no information about the forces acting, and I don't really know how to use the frequency. With the given data, and as far as my knowledge goes, the best thing that can be done is to use the bending and deflection equation (Its a second order differential equation). Since we know the amount of deflection (the amplitude that is), and making some reasonable assumption of the shape of the cross section of the wire (in order to calculate the second moment of area), we can arrive at the value of the Young's modulus. But I don't know where to plug in the frequency. Lynch7 18:07, 25 February 2012 (UTC)

I've realised my initial response was wrong. You get that! Amplitude can be deduced from the strain, using trig. We now have amplitude and frequency, so we can nd get acceleration. With acceleration and the mass (given), we can use Newton to calculate peak force and relate it back to strain. So we now have both stress and strain and calculate Young's Modulus. Sorry teachers. Keit121.221.230.136 (talk) 01:01, 26 February 2012 (UTC)

Extra moons and tides

A bit of a silly question:

I'm starting up a new DnD campaign where a rogue intelligent planet invades the solar system and gets close enough for atmospheres to touch so that dragons can fly orks over to invade the realm. It has the power to not destroy orbits so things won't crash into the sun or fly out into space unless it wants to, but I was wondering how bodies of water would act in a situation like this? If another earth parked in the sky so that the atmospheres were kissing, would all of the oceans slowly shift to one side of the planet? Would it be enough to trigger plate tectonic shifting and cataclysmic earthquakes? Thanks for any insight 142.244.35.91 (talk) 18:22, 24 February 2012 (UTC)

If the new planet still has gravity, then the occeans would shift, but not slowly, and not just the occeans. The planets would violently crash into each other and pretty much be destroyed. If this is somehow magically being prevented, then you have to consider: what things on the old planet are affected by the gravity of the new planet and what things aren't? Anything on the old planet that is subject to the new planet's gravity will be violently stripped off, including occeans, atmosphere, tectonic plates, people, dragons, etc. If the old planet is not affected by the gravity of the new planet, well then of course nothing will happen. Rckrone (talk) 18:42, 24 February 2012 (UTC)

(ec) For two planets to be in such close contact, either their relative orbital speeds will have to be immense, or they will collide. (In other words, the angular momentum has to be huge in order to avoid falling into each other). This is part of the reason, conceptually, why the three body problem tends to be unstable. Furthermore, since you've described atmospheric contact, gas drag is going to be a pretty huge factor as well - so even if the orbit began stably, it will quickly decay, and the planets will collide. Since you're already using a lot of imagination, it's probably worth closing this one as "magical physics," and ignore the consequences. Nimur (talk) 18:46, 24 February 2012 (UTC)

This sounds very all or nothing, but I did get a cool idea of having daring navies riding a massive waterspout to the other planet. Awesome.142.244.35.91 (talk) 19:14, 24 February 2012 (UTC)

The Science Fiction writer Bob Shaw's Land and Overland trilogy was set on a double planet with a common atmosphere, enabling flight from one to the other: you might want to read it to see how he avoided mentioning the problems that would, in reality, ensue. He used to claim that it was set in an alternative universe where the value of π was different, allowing the setup to exist, but when asked what that value was, said (as I recall) "Whatever it takes to make my planets work."

For inter-planetary waterspouts, you might also want to check out Robert Forward's Rocheworld and sequels, where two planets mutually orbit so close as to periodically exchange seawater. Forward being a researcher in gravitation, his underlying maths are probably more rigorous than BoSh's. {The poster formerly known as 87.81.230.195} 90.197.66.60 (talk) 21:06, 24 February 2012 (UTC)

How about if instead of making it a new planet, you make it something smaller, like a comet, which was frozen in the outer reaches of the solar system for thousands or millions of years, but occasionally comes close to the star, causing it to temporarily melt and develop an atmosphere, which would be lost to space in time, but it has the near miss before it gets the chance. The much lower mass of the comet would mean it's effect on the planet would be far less. You could also make it skip off the planet's atmosphere, by striking at a shallow angle. StuRat (talk) 22:37, 24 February 2012 (UTC)

Are you sure you understand how close this is? Here's a picture of Earth's atmosphere to scale. Note that while 100 km is the nominal "thickness of the atmosphere", it's not breathable (to humans) above about 3 km. -- BenRG (talk) 23:17, 24 February 2012 (UTC)

? 3km is only 9842 feet, 6 and 15 ⁄ 64th of an inch. List of highest towns by country in feet.--Aspro (talk) 23:52, 24 February 2012 (UTC)

Since you do have the means to bring in an alien planet and other wonderful things, for its atmosphere to touch ours and prevent atmospheric drag, you will want to maintain these planets in a very precise and mutual geostationary orbit. Currently, this orbit is at about an 22,000 miles altitude. A much larger, but far less dense planet of equal mass might work at this distance (with a radius five and a half times ours, its surface gravity is thirty times less so its upper atmosphere would need to be considerably thicker to obtain an atmospheric pressure), but for adding another Earth-like planet, the geostationary orbiting distance could be reduced by doubling the Earth's rotational velocity.

Given a stable configuration (by means of magic or not, for the orbit is similar in configuration to the proposed space elevator), there will be less gravity experienced on Earth near the other planet, as well as an 11% increase or less in gravity on the opposite sides (each of the more distant planet's center is at least three times more distant and gravity drops off by the inverse square law). On Earth, the directions of the gravitational field will still point in the general direction towards the ground (some will notice a small eastward or westward shift in direction). Between the planets where their gravities become more or less equal, each will oppose one another so our pond water and atmosphere there will weigh considerably less. Less weight means less pressure, thus the atmospheres will expand outward to build pressure (which in turns means that the planets' orbit altitude can also be considerably higher).

In the exact middle between these planets (in the shared portion of their upper atmosphere should the other planet have a similar radius), your dragons' and the DnD characters will be completely weightless, so make sure they have some fun with that scenario.

Our ocean at the center will still have a small weight due to it being on Earth's surface, but weighing substantially less it will bulge or increase to a large height that will depend on the exact altitude chosen. Thus you may want to park the new planet over the vast Pacific Ocean after first evacuating the islands there perhaps. I would certainly expect some new plate shifting dynamics, tides etc, but with a DnD game you don't really need a computer and lots of data to sort all that out though. --Modocc (talk) 00:17, 25 February 2012 (UTC)

You seem to be all out of paragraph breaks, so have some, on me: ¶¶¶. :-) StuRat (talk) 00:25, 25 February 2012 (UTC)

Done. :-) Yep. I wrote up more than I intended or thought I had. Sometimes, I need to step back and revise for readability, but when I'm in thick of it and adding details, that does not always happen. Thanks. --Modocc (talk) 01:50, 25 February 2012 (UTC)

Hmmm, since this is fantasy, how about saying that the intelligent comes from another dimension with "incompatible gravity"? Whatever means of propulsion the planet uses to get next to yours, it could just sit there without affecting or being affected by your gravity. (It might have to match the course of your planet around the sun... unless it's the sun that revolves...) Earth material would fall to Earth, Planet material would fall to planet, so if you rode a dragon up to their surface you'd still feel "upside down" until you drank enough of their water; maybe your heavy Planet-made armor would hold you down in the meanwhile. ;) Wnt (talk) 17:00, 25 February 2012 (UTC)

Jules Verne's novel Off on a Comet considers a comet that temporarily gets very close to the surface of Earth but luckily doesn't go under the surface. The comet does steal some water from Earth. – b_jonas 17:38, 25 February 2012 (UTC)

Unfortunately, Jules Verne's science was rather iffy, even for his day. He had Martians launched to Earth in giant cannons, for example, which would kill the occupants both when launched and when they struck Earth, due to massive g's. StuRat (talk) 20:26, 25 February 2012 (UTC)

Well, there's no guarantee the Martians aren't sturdier, and actually, a giant cannon might not have that high an acceleration. I'm also not entirely unwilling to allow them some parachuting or aerobraking to their pods, since after all, if you can land a Space Shuttle safely I'd think the Martians could think of something.

The weirdest idea though is something I remember from one of those Earth to the Moon movies, where drastic acceleration from a gun was countered by spinning people around really fast in little tubes. My feeling is that the centrifugal force should rapidly become worse than the acceleration from the rocket, yet I haven't entirely convinced myself that this couldn't work. But I don't think this was suggested in the original story. Wnt (talk) 19:46, 26 February 2012 (UTC)

The portrayal of the ships leaving craters where they struck the Earth makes it clear they were going entirely too fast. As for countering gravity with centrifugal force, I don't see how, since centrifugal force constantly changes direction. At best, they wouldn't effect each other at all, while, at worst, the centrifugal force would add to the gravity at one point in the spin. I suspect they are misinterpreting the common carnival ride, where people spun inside a cylinder "stick to the walls" instead of falling down when the floor lowers. This isn't because the force of gravity is reduced, but because the "cylinder" is more of a conical shape, which narrows at the bottom, so the centrifugal force pushes them upward. However, the total g force isn't reduced, it's just in a different direction. StuRat (talk) 20:03, 26 February 2012 (UTC)

Well, what I'm thinking is, if the gravitational force pools blood to one side of the body, pulls the bones toward the other side, and then you change orientation 180 degrees, the process reverses. Sort of like running an electrophoresis gel in reverse to get all the bands to come together again - but more like a sedimentation gradient. ;) But - the gravity also probably very quickly applies tension/pressure to some cell membranes which could burst, and a 180 degree rotation won't fix that. Also, if the spin is too slow, the bones have already ripped off the meat before you pull them the other way. I don't know from first principles how important all such processes are. Wnt (talk) 23:31, 26 February 2012 (UTC)

Rapidly reversing your g-forces sounds very unhealthy, to me, resulting in nausea, at the very least. StuRat (talk) 23:35, 26 February 2012 (UTC)

Um, where does Verne consider Martians launched to Earth in giant cannons? I don't think he does. What he does write, however, is Earthmen launched towards the Moon from a giant cannon in From the Earth to the Moon. Here he describes a mechanism for reducing acceleration forces that obviously wouldn't work in real life (see Chapter XXIII in an English translation). – b_jonas 10:23, 28 February 2012 (UTC)

Pressure and the nonmetal-to-metal transition

I was just doing some editing on a topic that I don't know very well (yes, that's bad, but it can be interesting ;) - Nonmetal#Metallic allotropes. The table is all new; if you see something stupid, many thanks for singing out! But I have some more general blue-sky questions about this.

I'm thinking that our planet's atmospheric pressure is arbitrary, so where we see the boundary between metals and nonmetals should be arbitrary. If it were 40-20000 times denser, we'd have fewer than 18 nonmetals. But does that apply in the opposite direction? If you do all your metallurgy at 0.0001 atmosphere, do many of the poor metals form nonmetallic allotropes? Aside from some obvious ones like alpha-tin I haven't had so much luck finding these, nor did I find clear sources linking them with low pressure - I don't actually know that the metals don't just straight sublime to gas, even if you work at lower temperatures.

Is there any distinction between an allotrope of an element and a "phase" of the element, as commonly used to apply to forms of the element with different crystal structures or chemical formulas?

If a high-pressure phase of an element is shown to be a superconducting metal, at a few kelvins, does that guarantee that above the T_c it is still a metal, or could it go straight to being something else without a change in structure?

Some properties of a metal are defined in terms of the properties of compounds, and others in terms of the physical properties of pure allotropes. These are not interchangeable, and the allotropes depend on the environmental pressure. Does that mean that in some broad philosophical sense, for those who can move freely between any environments in the universe, being a "metal" is actually two entirely different concepts, one dependent on pressure, one not?

Wnt (talk) 22:33, 24 February 2012 (UTC)

There is a difference between phase and allotrope, look at sulfur - one of its allotropes can exist as either solid or liquid. Plasmic Physics (talk) 04:41, 25 February 2012 (UTC)

Good point. The situation here can be surprising - to quote one source:^[7] "Gallium melts at 30^oC and can be easily supercooled to ~3^oC below the melting point. On melting, the covalent bond and the well-defined lattice of α-Ga are destroyed and the DOS minimum disappears, resulting in more metallic properties and free-electron behaviour for the liquid [Hafner90]. Gallium’s behaviour does not seem to change after subsequent meltings and solidifications, but does depend on the annealing temperature that it is heated to. That is, the liquid seems to have a memory of the α phase in its structure, but annealing it above 45oC changes this structure towards a more β-like one, resulting in a significant decrease in the temperature at which it solidifies [Kofman79, Wolny86]." Wnt (talk) 22:04, 25 February 2012 (UTC)

The main effect that you would see at very low pressures is that some metals would be considered as a gas, for example mercury is a gas at 0.8 Pa at 40°C but that is below your stated low pressure. At even lower pressures your alkali metals will be gas, eg potassium at 13 microPascals at 40°C. Graeme Bartlett (talk) 20:35, 27 February 2012 (UTC)

I'm more interested in what that gas might condense into, if it is cooled enough. Are we really at the very bottom of all possible pressures in the cosmos, so that with higher pressure nonmetals become metals, but at lower pressures metals never become nonmetals? Wnt (talk) 05:13, 28 February 2012 (UTC)

The chemical bond energy is much greater than atmospheric pressure, as you can look at the pressure needed to drush something, or the negative pressure to stretch a material. It gets much less likely that there are two allotropes extremely close in energy to each other that would be changed by a low pressure. Even if there was a change in temperature would probably change the equalibrium point any way, and change may be slow, for example with tin. There are likely to be large negative pressure regions that have not yet been explored. Graeme Bartlett (talk) 06:04, 28 February 2012 (UTC)

An astronaut on a very small moon...

• An astronaut standing on Thebe (moon) - would he be able to push himself off (jump off) the surface to "escape" the gravitational pull of the mini-moon?
• Asked the other way round: What would be the smallest size moon (assuming density 3 g/cm3) where this would be possible? Thanks! 213.169.162.159 (talk) 23:00, 24 February 2012 (UTC)

The Escape velocity in that article is reckoned to be some 20–30 m/s. Even a Soviet athlete on steroids would have trouble achieving that. So I'd say no. This is a bit of an odd question to my mind. Why are you asking. Are you writing a sci-fi novel or sommit? It would help us focus our response --Aspro (talk) 23:08, 24 February 2012 (UTC)

There are no odd questions, only odd answers :-) Background: At the surface points closest to and furthest from Jupiter, the surface is thought to be near the edge of the Roche lobe, where Thebe's gravity is only slightly larger than the centrifugal force. As a result, the escape velocity in these two points is very small, thus allowing dust to escape easily after meteorite impacts, and ejecting it into the Thebe Gossamer Ring. So - even there "he" would not be able to "jump away" ?? Grey Geezer 09:15, 25 February 2012 (UTC)

That's different. Both tidal forces and centrifugal force (yes, it does exist, despite what lots of ignorant pedants may have told you!) can cancel out some, or all, of the gravitational force. There are irregularly shaped asteroids where the bits furthest away from the centre are rotating so fast that surface gravity is effectively negative - you would have to hold on tight to avoid being thrown off into space. The formulae we've been talking about are for escape velocity taking into account only the gravity of the object you are standing on. Once you take other factors into account, it can get very complicated. --Tango (talk) 14:19, 25 February 2012 (UTC)

As for how small it would have to be, it's not that straightforward. You might think a moon with 1/10th the mass would have 1/10 the escape velocity, but it's not so, since the mass near you has far more effect, and with a smaller moon more of the mass is close to you. The angle also matters, since mass out to the sides of you doesn't pull you down much. And the density also changes, with smaller masses having generally denser elements, because they don't have the gravity to keep the lighter elements from blowing away, but also being packed less densely. Finally, irregular shapes must be considered. In the mass range we're talking about you no longer get a spherical shape. Considering all this, a moon with 1/100th the mass of Thebe should be safe to kick off from. Also note that Thebe has a density around 0.86 g/cm³, so your assumption of 3 g/cm³ seems a bit high. StuRat (talk) 23:21, 24 February 2012 (UTC)

Thebe has a density around 0.86 g/cm³, so your assumption of 3 g/cm³ seems a bit high. NASA is wrong? 213.169.162.159 (talk) 09:09, 25 February 2012 (UTC)

I wonder why our article says the lower value, then. StuRat (talk) 20:19, 25 February 2012 (UTC)

What angle matters? The angle your trajectory makes with the ground? That doesn't matter at all, as long as it is doesn't make your path to infinity go through the asteroid. You can see that the angle doesn't matter by thinking in terms of energy. Whether you can escape or not depends on the sum of your gravitational potential energy (which depends only on height) and your kinetic energy (which depends only on scalar speed), so angles don't come into it. (It gets a little more complicated if you take things like rotation or irregular shapes into account.) --Tango (talk) 00:39, 25 February 2012 (UTC)

I refer to the angle of the ground beneath you. On a large body, much of the mass near you is almost out to the side, so it contributes little to the downward pull of gravity. This is one of several factors making the escape velocity not proportional to the mass of the body. StuRat (talk) 01:55, 25 February 2012 (UTC)

I guess that's one way of thinking about it, but it isn't a very useful way. If you are standing on the surface of a 2m radius sphere with mass 100kg or you are hovering 1m above the surface of a 1m radius sphere with mass 100kg then the gravity you feel is the same (see shell theorem). More of the 1m radius is directly below you, but it is further away. Those two factors exactly cancel out. The reason escape velocity is not proportional to mass is simply that you are further away from the centre when standing on the surface of a larger object. (Of course, if the object is sufficiently massive then adding more matter to it would actually cause it to shrink due to increase pressure, so surface escape velocity would increase by more than the increase in mass. See Jupiter#Mass for one example. Neutron stars are another example.) --Tango (talk) 14:19, 25 February 2012 (UTC)

I'm more interested in why it can be modeled as a point mass, and the angle of the ground beneath you is one of the reasons. StuRat (talk) 20:21, 25 February 2012 (UTC)

E.g. on Deimos (moon), it should be possible, you just need 6 m/s to escape. --Roentgenium111 (talk) 23:54, 24 February 2012 (UTC)

Escape velocity is straight-forward to calculate. As the article mentions, the formula is $v_{e}={\sqrt {2GM/r}}$ for a spherically symmetric body. If your density is ρ = 300 kg/m³, then M = ρ(4/3)πr³, so in terms of radius $v_{e}=r{\sqrt {8\pi G\rho /3}}\approx r\cdot 0.0004\;\mathrm {s} ^{-1}$. The part I'm missing is that I don't know what a reasonable velocity from a jump is. Rckrone (talk) 17:00, 25 February 2012 (UTC)

Does the speed you can jump at depend on gravity? I'm not really sure... Assuming it doesn't, then we can use our experience of jumping on Earth. A typical person can probably jump roughly 0.5m in the air (that's increase in centre of gravity - you can get greater clearance from the ground by lifting your legs up, but that's not useful to us). As we know, $v^{2}=u^{2}+2as$. Substituting in v=0 (you are at rest at the peak of your jump), s=0.5m and a=-9.8m/s/s, we get u=3.13m/s. So, let's take a jumping speed of 3m/s (the 6m/s Roentgenium mentions for Deimos is looking a little high - that would require an Earth jumping height of 2m, while the world record for high jump is 2.45 metres, using a technique that doesn't involve lifting your centre of gravity over the bar and wasn't done wearing a spacesuit!). That would give r=7,500m, compared to Deimos' mean radius of 6,200m, (but its density is only 1.5g/cm³, so that's doesn't make sense... ah, your density is wrong - 3g/cm³=3,000kg/m³. That means the radius for 3g/cm³ would be more like 2,400m.). --Tango (talk) 17:54, 25 February 2012 (UTC)

Thanks for your calculations. I was assuming that a human can reach a similar vertical speed as he can reach a horizontal speed (>10 m/s for the world record, and presumably more without air friction), but apparently that's not possible. Still, you could probably reach an orbit just by running fast... --Roentgenium111 (talk) 19:39, 25 February 2012 (UTC)

Of course you would have trouble gaining the required traction and would probably leave the surface due to curvature, before obtaining escape velocity, only to fall back with a less useful velocity... But if you could find a suitable staircase to run up, you might be able to do it. Rich Farmbrough, 20:04, 25 February 2012 (UTC).

Yes, leaving the surface due to curvature would definitely be a problem. Orbital velocity is ${\frac {1}{sqrt{2}}}$ times escape velocity, so you would reach orbital velocity (and leave the surface, although you would come back the surface after one full orbit so you could try and gain a little more speed at that point). That's assuming a spherical planet, though. An irregularly shaped asteroid could be a lot like the staircase you mention (you don't need steps, just an inclined ramp should be enough). If you are moving towards a bit of the asteroid where the surface is further away from the centre, then you are effectively moving up hill. Whether that could ever be enough for you to reach escape velocity, I'm not sure... the rotation of the asteroid would be important to consider. --Tango (talk) 21:10, 25 February 2012 (UTC)

Given that such a small moon's gravity is very small, I'm thinking even a steep incline is inadequate because of the Earth-based tendency to push away from the surface and so one's inertia will not be falling back towards the incline or stairs very rapidly. A suitably long concave incline might work well though. --Modocc (talk) 22:22, 25 February 2012 (UTC)

I'm skeptical of this. I think of one person running up a staircase on Earth and not stopping at the top, versus the other standing on the top step and tensing for as high a jump as possible, and I just can't picture the one running making the higher jump. Wnt (talk) 22:28, 25 February 2012 (UTC)

There is practically no gravity to work with here. For Thebe its only .004g or only four thousands of our gravity. The gain with running is similar to pole vaulting, because running permits the accumulation of kinetic energy. Its counter-intuitive with inclines though, because we lose this energy when running up steps here due to our stronger gravity. Because the g force is so small, the incline does not much effect the outcome other than it is the general direction that you want to be heading... which is away from the rock. One could even run the interior rim of a shallow crater in circles only to exit the crater at the last moment. --Modocc (talk) 22:46, 25 February 2012 (UTC)

I haven't thought too much about it, but I think neither curvature nor the inertia in falling back would be much of a problem: As long as you haven't reached escape velocity, you will get back to the ground to make another "step" in your running. Each "step" may ultimately take you a kilometre or so to make, but you keep your horizontal speed during this kilometre due to the lack of air friction, and can accelerate with each step just as you would in an Earthly running, until you finally (after maybe ten steps) leave the surface continuously for a complete orbit, and then push yourself off the "takeoff" point a bit higher when reaching the ground after completing the first orbit (as described by Tango), to stay in the orbit indefinitely... --Roentgenium111 (talk) 22:49, 25 February 2012 (UTC)

True, although obstacles such as running into boulders or crevices might present this runner with some difficulty. I'm assuming that the OP has some important place or ship that some stranded guy or guys must reach on their own. With any such attempt, one may end up in a perpetual orbit about the rock that takes a very very long time to decay and that could be a lonely place to be. Maybe they just need the exercise, or more likely, working on a mineral excavation. --Modocc (talk) 23:36, 25 February 2012 (UTC)

Some of the details described in Arthur C. Clarke's 1949 short story 'Hide-and-Seek' may be of some interest and relevance here. {The poster formerly known as 87.81.230.195} 90.197.66.166 (talk) 00:20, 26 February 2012 (UTC)

Seems like I read that story, although its been decades, so I don't remember the details. One problem with trying to simply "run" off the moon as suggested above is that its more likely that one will simply reach some arbitrary orbital velocity, but not the desired escape velocity because the difference between these is too large. When "running" along the surface with progressively longer strides one will get very close to a sustained orbital speed which then only allows for a single last "jump" or "step" to either an orbital or escape velocity with no second chance of increasing one's speed further. But if one runs the rim of a crater and spirals outward, they can check their speed to ensure the velocity they need is attained (should they know what this is of course),and they can even stop at any point due to any problems with their equipment or intended trajectory. --Modocc (talk) 01:24, 26 February 2012 (UTC)

There isn't a problem there - you would always come back to the ground unless you reached escape velocity. An orbit always goes through the point where you last had any thrust, so if your only thrust occurs when in contact with the surface your orbit must always intersect the surface at at least one point. If you pushed off every time you reached that point, you would gradually extend of apoapsis (furthest point in your orbit) while your periapsis (closest point) stays the same. Eventually, you would achieve escape velocity and that is when you would stop coming back to the surface. --Tango (talk) 01:53, 26 February 2012 (UTC)

I see and when reflecting back on the previous comments, they make more sense now, and I may want to study up on the reason for this dynamic which I'm sure has everything to do with the conservation laws. Since the OP's only request was whether or not an escape velocity could be reached, the running off bit works fine then. Of course, if one needs a particular velocity that exceeds the escape velocity to perhaps get to a nearby ship then a controlled run makes more sense. --Modocc (talk) 02:43, 26 February 2012 (UTC)

This method of running seems sufficiently difficult to turn the OP into a QWOP. -- ToE 12:50, 26 February 2012 (UTC)

(Outdent) Orbital mechanics à la Newton's cannon becomes complex in two-body interaction problems, where a larger planet (say, Jupiter)'s Roche boundaries influence the local gravity on a smaller moon. You'd need to take into account the Hill sphere around the smaller object. Maybe the person jumping off will assume a horseshoe orbit with respect to the moon and its larger planet, or interact with the Lagrangian points in some way - the end result appears similar to a set of resonance frequencies by which the astronaut will have an easier or harder time jumping off said moon at different angles and different times. ~AH1 ^(discuss!) 21:27, 26 February 2012 (UTC)