Get a Straight Answer

    My daughter is conducting a science project on "Does the weight of gases effect the length of time a balloon will stay inflated?" She used medical oxygen, medical nitrogen and helium. She had thought the helium (being the lightest) would stay inflated the longest.) Not the case - helium deflated first, oxygen- 2nd, and nitrogen stayed inflated the longest. Oxygen is the heaviest of the 3 according to atomic weights.

    What's up??

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    I do not know why oxygen and nitrogen should be very different (a balloon filled with air would make an interesting comparison), but I am not surprised that helium deflated first.

    Your daughter should ask herself--why does a balloon deflate at all? I guess she was using identical rubber balloons and the answer is, that what to our eyes is a continuous surface, actually has a lot of little holes, and occasionally a molecule of the gas inside finds it can escape through such a hole. Helium has much smaller molecules, so it "diffuses out" much faster. Mylar balloons hold helium much longer because they have fewer (or smaller) holes.

    During WW-II, when the US was secretly building the first nuclear bombs, it needed to separate two types of uranium, which differed just slightly in weight--U-235 was bomb material (atoms weighing 235 times as much as those of hydrogen), U-238 was not.

    The uranium atom combines with 6 atoms of fluorine to form a gas, uranium hexafluoride, UF₆. In Oak Ridge, Tennessee, a huge factory was built with thousands of linked containers, each of which divided in the middle by a porous wall. UF₆ was pumped to (say) the right side and diffused to the left, and what emerged on the left was a TINY bit richer in U-235, because the lighter molecules of UF₆ containing U-235 had just a VERY SLIGHTLY higher probability of getting through than the heavier ones of UF₆ with U-238.

    Imagine now thousands of such units connected end to end (with some in parallel, too)--the enriched part was sent forward to be enriched still more, the depleted part was send back to be reprocessed so as to extract a bit more U-235. The highly enriched U-235 coming out the left end was used to fuel reactors, and for other uses we better not mention. The "depleted" uranium is now used in armor-piercing shells--it is very dense (heavier than gold even) and its dense mass helps breach armor.

    Your answer to the question

"If June 21 is the day when we receive the most sunshine, why is it regarded as the beginning of summer and not its peak? And similarly, why is December 21, the day of least sunshine, the beginning of winter and not mid-winter day? "

( Blame the oceans, which heat up and cool down only slowly. By June 21 they are still cool from the winter time, and that delays the peak heat by about a month and a half. Similarly, in December the water still holds warmth from the summer, and the coldest days are still (on the average--not always! ) a month and a half ahead).

    However, it's interesting that in East Asia, it has long been a tradition to observe the winter solstice as indeed the mid-winter day, the spring equinox as the mid-spring day etc...That's why, the celebration of the New Lunar Year (normally falls between late January and early February on the Julian calendar) is considered also a celebration of the beginning of Spring and not the middle of winter... Sincerely,

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    What you describe as "East Asia" may mean mainly China--and there, if global winds (like here) come from the west, they blow from dry land, from the deserts and high lands of Gobi and Tibet. The oceans may have very little influence on them, so yes, it is possible that (say) December 21 is "mid-winter" and not the start of the cold season.

    Originally, February was the last month of the year, which is why the variable date (February 29, every 4 years) was placed at its end. Supposedly the Roman New Year was originally in March, on the Spring equinox, so March was the first month, September the 7th (Septa, seven) and so on to December, the 10th month (compare "decade" and "decimal system"!).

    The ancient Romans had rather arbitrary ways of adjusting their calendar and adding leap years, and by 46 BC it was badly in error (compared to the positions of the Sun and stars). Dates were shifted far from where they were supposed to be, so Julius Caesar reformed the calendar, and one provision of his reform was to set the start of the year at January 1.

    When you stick your hand out of the window, it will usually emit or receive heat. Some possible processes:

•     It is cooled or heated by the air passing by it, through conduction of heat.
•     It is heated by the resistance of the moving air (overcoming resistance absorbs energy).
•     It radiates heat or receives heat by radiation.

    Let me start with conduction. What is the temperature of the air outside? Here in Maryland it is February right now, the air temperature is close to the freezing point and if you stick your hand--which receives blood at about 98 deg. F--out of a car window, it is likely to be cooled, Stick it out on a summer day in Baghdad, when the air is at 120 deg F., and I am not sure what will cool what.

    And which side of the car will you be sitting there? All warm objects radiate heat, including your hand, and this cools them down--but meanwhile, they also receive radiation. If you sit on the sunny side (in Baghdad), your hand probably receives more than it gives out. If it is in deep shade, maybe not (though if hot walls are nearby, heated by sunlight, they radiate towards you, too).

    And heating need not be evenly distributed. Consider a bullet. A pistol bullet flying below the speed of sound pushes air out of its way and encounters resistance, which heats it up. A rifle bullet is supersonic, and in addition also compresses air in its front, creating much greater heating. But the heating is not evenly distributed, the tip gets much hotter than the rest (in either case). It is not just "what speed", but what part of the object, too.

    A practical problem: an airliner at 35,000 feet. The outside air there is very cold, say 40 below zero, and the airplane skin is quite cold--in spite of the friction of air rushing by, at close to the speed of sound. But I read somewhere that in airplanes going at 3 times the speed of sound, their skin can get warm enough to be weakened (at least at the front edge). Sticking out a hand from such a plane would not be a good idea--besides, the force would be so high, even at jetliner speed, your hand would be ripped off before it could get much heating.

    From my understanding the North and South poles can spend months without seeing the sun drop below the horizon, that is they have 24 hours of daytime. My question is would it be possible for someone to spend one year in daylight without seeing the sun drop below the horizon? I appreciate that one would have to move from the north to the south or vice versa in order to do this and was hoping that it wouldn't require an aircraft moving faster than Mach 2 or a space shuttle. Basically, could someone with the will and the ability, move around the planet usng conventional travel in such a way as to avoid seeing the sun set for one full year?

    I hope that makes sense, and thank you for your time.

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    With the overwhelming increase in cell phone towers and the now constant exposure to radiation and electro magnetic waves, is there any blocker that one can easily create and use in one's home to make it a clear/clean space?

    I realize that there is no direct evidence as yet that these microwaves are dangerous (just as some would say there is no evidence of global warming), but I am of the opinion that accumulation and unrelenting exposure could be harmful to humans, and I'd like to err on the side of caution. Since the announcement that Philadelphia will become a "wireless" city in the next year by placing antennas on every street pole, I have been searching for some way to at least minimize the level of waves passing through our homes. Do you have any ideas?

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    Electromagnetic waves are kept out of any enclosure which is entirely enclosed in a good conductor of electric current. Such an enclosure is known as "Faraday Cage" after the scientist who first devised it in the middle 1800s, and it needs not be completely enclosed--it can tolerate openings, as long as these are appreciably smaller than the wavelength of the wave.

    One example is a microwave oven (it keeps radiation in, not out, but the same principle applies). Inside it a very high density of microwave energy exists, but none escapes, because walls are of aluminum and the window, too, has a mesh of aluminum or copper embedded in it, with openings too small for the waves.

    Laboratories use enclosures, frameworks over which everywhere a copper screen is stretched--like window screens, but of copper (insect screen made of iron does not have sufficient conductivity at high frequencies). Doors are tricky--they may need copper frames, with foils of a copper alloy (phosphor bronze?) all around to seal the crack between door and frame. If you walk into such an enclosure and close the door behind you, your cell phone will probably not detect anything. Cell phones do work in cars, because their windows are large enough to let the radiation in--also iron may not be such a good shield, and anyway, the car's frame is not grounded.

BUT WHY? how can we show all the reasoning in one mathematical equation?
thanks for your time.

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    Newton had an elaborate proof. However, if you know more advanced math, the use of the potential function –GM/r (developed by Gauss, Laplace, Poisson, Green and others) gives you the result immediately.

    So suppose you stand on the Earth's surface, your R is one Earth radius, and you moved to a location at distance R/2. The attractive force, inversely proportion to the distance squared, should be 4 times larger, since you are twice as close to the center. However, if the density of the Earth is uniform throughout, the amount of attracting matter is only what is contained in a sphere of radius (R/2), and is therefore only 1/8 as much. So the force of gravity is weaker, only half the one at the surface (4 times 1/8).

    However, the Earth gets denser towards the middle, due to all the weight piled up on top--also, much of its core is iron, denser than rock. So it is just possible (mathematically, at least) that the matter inside the sphere of (R/2) has twice the average density of the Earth as a whole. In that case, the attraction is doubled, and as a result, gravity is the same at R/2 as on the surface.

    If the average density is more than double, the gravity is stronger. I don't think that happens, but in theory at least, it is possible.

Continuation of the question

The Earth has a radius of 6370 km, and a mass of 5.98 x 10²⁴ kg.

---The thickness of the crust is 25 km and it weighs 3.94 x 10²² kg.
---The thickness of the mantle is 2855 km and it weighs 4.01 x 10²⁴ kg.
And finally:
---The radius of the core is 3490 km and it weighs 1.93 x 10²⁴ kg.

Show that g has a local minimum within the mantle; find the distance from the Earth's center where this occurs, and the associated value of g.

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    Forget about the crust: the point you seek is in the mantle, and the crust exerts no gravity pull there--it's a hollow sphere, and you are inside it.

The volume of a sphere of radius R is taken as 4.189(R³) The outer radius of the mantle is then 6.375 10⁶ meters, and the volume is 1.07 10²¹ cubic meters.

The radius of the core is 3.49 10⁶ meters and its volume 0.178 10²¹ cubic meters, so the mantle contains 0.892 10²¹ cubic meters

The density of the mantle is then DM = 4.5 ton/cubic meter (or kg.liter) The density of the core is DC = 10.84 ton/m³ , and the ratio is K=DM/DC = 0.415

Suppose the radius of the core is R and we are observing gravity at a distance R+r.

The pull of the core is 4.189 G DC (R³) / (R+r)²

4.189 G DM [(R+r)³ – R³]/(R+r)² =
4.189 G K DC [(R+r)³ – R³]/(R+r)³

Combined

F = {4.189 G DC}{K [(R+r)³ – R³] + R³}/(R+r)² =
      {4.189 G DC}{K (R+r)³ + (1-K)R³}/ (R+r)²

    My sister and I have been surfing the web to find out whether or not the sun has an axis. So far we've found nothing concrete. If it does have an axis, we want to know how it turns, how long is it's revolution, and if it's not the center of this galaxy, how it and our planets turn in our own rotation?

Thank you!

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    I am doing a piece of coursework on orbital planes of the planets, about the creation of the solar system and how the planets came to be in the same plane. How do the planets (apart from Pluto) stay in the same plane? I found something about repulsion and gravity particles coming out of the sun at

            http://www.grantchronicles.com/astro10.htm

but am not sure if this is just one man's theory or the best theory scientists have today. (Sorry, but I'm sometimes a bit skeptical about website theories.)

    Could you also tell me why Pluto orbits the sun as it does? I found some strange theory about a 10th planet that entered our solar system ages ago and brought into our solar system Pluto and its moon Charon, but then broke off and became part of our solar system. Is this a reasonable theory? And if so why doesn't Pluto re-adjust into the same orbital as the other planets?

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    As for orbital planes... they are of course fixed by conservation of angular momentum. Those planes may be very slightly affected by the attraction between planets, but they seem all roughly follow the plane of the original cloud from which the solar system was formed. Their inclinations differ slightly, perhaps because at the time of their formation, collisions between big clumps of matter (which later joined up to form planets) were still occuring. Planets do not share exactly the same plane, they only do so approximately.

    However, be careful about "repulsion." I looked up the web page you cited. Its mention of "gravitational particles" reminds me of the theory of George-Louis LeSage (1724-1803), described at

            http://en.wikipedia.org/wiki/LeSage_(gravity)

    LeSage (like others of his time) tried to explain all Nature in terms of mechanics, and gravity's "action at a distance" was a challenge. (Today we have a broader view of space, believing that "fields" exist which are modifications of space, and which explain such phenomena as electromagnetic waves. I have mentioned some of that is section S-5 of "Stargazers" and in the sections that follow it.)

    LeSage's explanation was that space was filled with "ultramundane particles," very fast particles which carried momentum and could easily penetrate matter, a bit like neutrinos. However, occasionally they collided with matter and rebounded elastically, so that two material objects close to each other would be driven towards each other. They would shield each other to some extent and therefore be hit asymmetrically, with more hits on their hemispheres pointing outwards than the ones facing each other.

    The trouble with LeSage's theory (among other things) is that it assumes a select frame of reference--the one in which all "gravity particles" are equally distributed in all direction. If an object starts moving in relation to that frame, it encounters more "head-on collisions" than "rear-end collisions" (and even if all those particles move at the speed of light, head-on collisions carry more momentum) and therefore its motion is resisted, as if it moved in a viscous medium.

    As for Pluto, it seems now to be not an isolated planet but part of a growing family of distant icy asteroids, the "Kuiper Belt." It isn't even the biggest or the most inclined among them--see the last part of the section on the ecliptic

    My son says his teacher doesn't believe men landed on the Moon. Eric and I used to chase parts at our Air Museum for the old engineer who built Saturn V; that guy would have loved to strangle my son's teacher, not that it would solve the problem. I had Judy Resnik's help early in my career and as a boy [She was an astronaut who perished in the "Challenger" disaster].

    Col. Aldrin and his friends at NASA would likely take a very dim view of this. Any other constructive ideas on how to get them pointed in the right direction?

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    Generally, a craft suspended above the ground (excluding balloons) stays up in one of two ways. Either it has enough velocity (looking at it one way) for the curvature of its fall to match the curvature of the round Earth. Or else, it gets lift from the air its motion encounters, the way airplanes do.

    At orbital speed, at least 8 km/sec, the shuttle keeps its height the first way. However, once it enters the atmosphere and slows down, its fall no longer matches the curvature of the Earth, and instead it gets lower and lower. It could have entered more gradually if it could have used the atmosphere to keep its height, the way an airplane does. But at 15-20 times the speed of sound, wings create more resistance than lift, and anyway, presenting a wing edge-forward as an airplane does would concentrate too much heating and pressure on its front.

    Other tables I have seen reverse these values. I would like to know the reasoning in each case!

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    The situation is similar with gravitational energy--say, planets around the Sun, or satellites around Earth: all bound orbits have negative energy. If you add energy to (say) a satellite), it climbs to a higher orbit with a less negative (total) energy. If the total energy is zero, it is just escaping on a parabolic orbits, and any spacecraft with positive total energy is unbound.

    We can determine positions of celestial objects fairly accurately by telescope, A fix within of one second of arc (1") means an error of 0.78 km at a distance of a million kilometers--nearly 3 times the distance of the Moon.

    But actual accuracy is even better. We have sent space probes to (say ) Jupiter, and from the delay of radio signals can judge distances quite accurately. The gravity of Jupiter itself is determined by the well-known periods of its satellites. The gravity of the Sun is known (for instance) from the length of the year. The size of planets and the Moon was determined from occultations of stars, but now we have data from probes which have encountered them, took images and even orbited them, all giving more accurate information.

1. Defining what you want to achieve through the lesson,
2. Identifying your source material--text, chapters... maybe more, even web sites, remembering not every kid has a web connection (though public libraries do)
3. Identifying what examples, stories, diagrams etc. you will use to get your ideas across,
4. Identify potential stumbling blocks. Where may students become confused, and how do you avoid it? One way is to present an idea (where that is possible) in several ways, or using several different example applications.
5. Decide how you will make it interesting
6. Decide how you will test the students' knowledge, and perhaps also:
7. Identify what is optional and may be omitted, also what more advanced parts are optional but may be given as a special challenge to students who feel the class is too slow.

    I do not particularly like state standards--they tend to stress memorizing "facts" and not to learn the reasoning behind them--e.g. the "fact" the Earth orbits the Sun instead of vice versa, rather than the reasoning why we believe it is so (which is actually more interesting). I once wrote a draft standards list of my own and it is on the web:

    As the Moon goes around the Earth, the amount of the bright side which we see changes, and that determines the "shape" of the Moon. When the Moon is in a direction close to that of the Sun, we see most of the dark side, and only a small crescent that is bright. (Actually, the "dark" part of the Moon is not completely dark at that time. An observer on the Moon at that time will see the Earth almost completely lit-up by sunlight, and the bright "earthshine" brightens up the dark side of the Moon a little.)

You say

An astronaut floating in a space suit cannot shift his position without involving something else, e. g. pushing against his spacecraft. The center of gravity--or "center of mass"--is a fixed point, which cannot be moved without outside help (turning around it, however, is possible).

    I don't see any engines firing to the side of the rocket to maintain its course.

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    I am aware of three active control methods used in the past to maintainin an alignment ("attitude") monitored by gyroscopes.

1. In some rockets, small auxiliary rockets provide thrust to the side, firing downwards but at an angle. Early Atlas rockets had such stabilization. Check some launch pictures--occasionally, they show those small rockets firing!

2. The main rocket motor can sometimes be swiveled in different directions (around two perpendicular axes, using "gimbals"). I am not sure, but think the shuttle can do so. I vaguely recall pictures of the rocket engine being tilted this way and that before launch, as a final test.

3. Carbon vanes in the exhaust of the rocket can deflect its jet. I think the early "Redstone" used this, and Dr. Goddard's rockets also had deflecting vanes.

    It all started with a conversation between a friend of mine and myself. We understood that at higher altitudes water boils at less than 100 degrees C, and I was interested to know that mountain climbers used to use this theory to determine how high they were.

    I have searched the Internet for an answer, all currently to no avail, and I was hoping that you could shed some light for us.

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            http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/vappre.html

    Vapor pressure of a liquid (or even a solid, though its value may be vanishingly small) is a measure of how much its molecules "want" to convert to gas in the surrounding space. For instance, suppose you pump out all the air in a big bulb. The bulb is connected to a reservoir of water, and you let a cupful of water at room temperature, 27 deg C, be sucked into it. What will happen?

    The water will boil, and as it does, part will be converted to water vapor. The process will stop when the pressure of the vapor reaches the value of the vapor pressure of liquid water at 27 degrees. At this point, an equilibrium exists--the rate of evaporating molecules is exactly balanced by the rate at which others consense out of the vapor.

    Let's say that pressure equals P atmospheres (you can find tables of P against temperature in handbooks). If instead the bulb already contains air at pressure P, the water will be just at its boiling point. Heat it to 40 deg and it will boil, until the steam released adds enough pressure to P for the sum to equal the vapor pressure of water at 40 deg. At 40 degrees the vapor pressure of water is larger than P, because vapor pressure of a liquid increases with temperature.

    The rule is, then--water will boil at the temperature where the external pressure equals its vapor pressure. The vapor pressure of water at 100 deg. C is one atmosphere, so at sea level, it boils at 100 C. On a mountaintop where the external pressure is only 0.8 atmosphere, it boils at a lower temperature, the one where the vapor pressure of liquid water only equals 0.8 atmosphere.

    And in space, where the external pressure is zero... water boils at any temperature at which it has some vapor pressure. Which in principle means, any temperature above absolute zero.

    Suppose an astronaut vents water to the outside. It will always evaporate, but not immediately, because there is also energy to consider. Turning water from liquid to gas requires about 236 calories per gram, more than twice the heat it takes (on the ground) to warm it from near freezing to boiling. That's why sweating on a hot day cools your body: as the water evaporates, it needs extra energy, and by supplying it, your skin gets cooled.

    If water is vented to space, part of it immediately boils away, but the rest is cooled to where it freezes, into a sort of instant snow. Ultimately the frozen part also evaporates, since no equilibrium can exist between water (in any form) and a vacuum, but that happens more slowly.

    Comets are apparently mostly ice, so they are expected ultimately to evaporate. However, they are so far from the Sun, and therefore so cold, that I would not be surprised if (as long as they stay distant) "ultimately" turns out to be much longer than the age of the universe.

    Short question, long answer. If you know any better way, please tell me; but at least, I hope you and your friends have now learned a little more physics, and also have a bit more appreciation for the complexity of nature..