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Angle between ecliptic and Milky Way

(Continuation)--About the year 2012

396A Posssibility of Asteroid Hitting Earth (1)
396B Posssibility of Asteroid Hitting Earth (2)

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Response to reply:

thanks but my assignment was due like three days ago and i kinda didnt get your answer in time so thanks anyway. love jane

191. Re-entry from orbit

I am 17 years old. I go to school at Father Lopez Catholic High School where I run cross-country and track and play soccer. I have a few questions for you:

What concept of physics causes the space shuttle to get so hot that it almost burns up when returning to earth? 2
What one word describes this concept?
What kind of energy is present during reentry?

Reply

You probably mean "process', not "concept" (concepts are in your mind, processes occur in nature). The process involved is a shock, a piling-up of air around the shuttle, since the shuttle moves too fast for air to flow out of its way. The shock heats the piled-up gas, but luckily, most of the heat is then radiated away, since anything hot glows and radiates light--e.g. a flashlight filament. Only a small fraction of the heat reaches the heat shield tiles, although, since radiation is beamed in all directions, some of it will hit the shuttle, too.

The amount of kinetic energy which must be given up (as radiation) is tremendous. The shuttle starts at 24 times the speed of sound, while a rifle bullet may have twice that much, maybe 3 times. So pound for pound, the shuttle may have 100 times more energy. Lead bullets melt when they hit a sandbag, so getting rid of that energy is a tricky feat indeed.

192. Effects of weightlessness on one's body

I was wondering how does going up into space have an imapct on your body if you are up there for a certain amount of time. How does it affect your health? what changes occur for males and what changes occur for females and both?

Also how are these problems fixed if nessecary?

Reply

Dear Australian friend

Many of these problems were addressed on the space station "Skylab". Astronauts tend to lose weight, muscle tone and bone--in a way which somewhat resembles problems of patients who are bedridden for a long time. Exercises help prevent these from occurring. I am not sure about more subtle effects--you will have to search on the web.

About weight loss, see http://www.phy6.org/stargaze/Sskylab.htm

The principles used in measuring the mass of astronauts in a "weightless" environment, see the end of the section preceding
http://www.phy6.org/stargaze/Smass.htm
and perhaps the one following
http://www.phy6.org/stargaze/Smasscom.htm

193. Blimps on Mars

I'm trying to figure out lofting capacity for various gases on Mars, so I can more realistically visualize a lighter-than-martian-atmosphere-craft. What with the different gravity, different atmospheric pressure, and different atmospheric composition, I figure that the lofting capacity of various gasses would be different.

Unfortunately, I'm getting hung up on that lifting gas. I suspect that Helium will be in short supply on Mars. On earth, it is a byproduct of natural gas, but on Mars, there should be little, or no natural gas, and helium would have to be mined by itself.

My idea however, is that since the atmosphere is mostly CO2, blimps with much heavier gasses could be used. I would expect hydrogen, oxygen, and nitrogen blimps to be common, since these three gasses are highly useful commodities in their own right on a world with little water, and no breathable atmosphere.

Reply

Flying a balloon on Mars is not easy. The ground-level atmosphere is (I believe) 1/140 times as dense as ours, and even with 1/3 of the gravity, it may be equivalent to flying a balloon at 25,000 meters on Earth or at 80,000 feet. It can be done, but takes a big balloon. With the fierce storms of Mars, one also wonders how long such a balloon would last.

About the lifting power--it equals to the weight of the displaced atmosphere, minus the weight of the gas inside the balloon, required to keep it inflated. Whether that is hydrogen or helium should make little difference, because either gas weighs much less than the air (or on Mars, carbon dioxide) which is displaces. Hydrogen should be available on Mars, if only a little water can be extracted there, which seems likely. Hydrogen was of course used in all the Zeppelins in WW-I and with proper caution is quite usable.

Oxygen and nitrogen are rather heavy, cutting the lifting power by a factor of about 4: considering how marginal any balloon is on Mars, they are clearly unsuitable..

Scientific high-altitude ballooners on Earth prefer helium because of the way its temperature changes as the balloon rises and the gas inside expands, but on Mars a balloon probably won't rise far. Rubber balloons launched to probe the weather are filled with hydrogen, which is much cheaper: they rise quickly and explode at their maximum altitude, but by then all required data have been transmitted by radio.

194. Planet Mars "huge" in the sky, in August 2005?

Is there a terrestrial phenomenon occurring this month with Mars? I've heard form a few "wannabe" astrologers that the planet Mars will be "huge" is the sky and look as big as the moon with the naked eye. This is an event that has happened every 5000 years or so. Mars is to come within 34,649,589 miles to Earth. I have not seen any television reports on this (maybe due to the recent NASA landing). Could you expound upon this for me ? Thanks,

Reply

Note: The above turned out to be a false rumor, which had quite wide circulation

Beats me. The average Mars-Earth separation is 0.5237 AU, and with 1 AU equal approximately to 150,000,000 km or 93,000,000 miles, this comes to 48.8 million miles. The actual closest approach may be larger or smaller, because of the ellipticity of the orbits (mainly the one of Mars),

In any case, Mars seen by the unaided eye is never as big as the Moon. It is true, though, that viewed through a telescope, Mars appears to be about as big as the Moon seen by the unaided eye (although, unless seeing conditions are very good, the image may shimmer and distort).

After writing the above I looked up Google for some more precise facts--see
http://www.imcce.fr/en/observateur/support/opposition_mars/index.php.

The next closest approach is October 30, 2005, and will bring us within 43,000,000 miles of Mars. The closest approach your friend mentions happened 2 years ago and was indeed unusually close.

195. Astronomy and telescopes for ones' own children

Having looked at the elementary school texts my children have been assigned, I have been disappointed. Some of the most enthusiasm they have shown recently toward learning more about the physical world and doing a bit of thinking, is during a recent discussion of "how to point a telescope." But they do not get those kind of examples, or anything that seems remotely stimulating from their textbooks. Unfortunately, that kind of motivation seems only to come from strictly extracurricular activities.

If they do continue to show interest more than a few days in the telescope project, then I hope to help them build (instead of buy) a set of telescope drive controls. So far their enthusiasm has not waned, and they are asking a lot of questions about how to find objects in the sky and point the scope. My experience doing some controls engineering will help, but I want to let them do some of the programming to make the telescope follow the right target. My challenge will be to keep their challenges at the right level.

Your pages provide a nice balance. Appropriate examples, and reasonable approximations that make some of the fundamental calculations of motion of celestial objects trackable. I think if I can learn that art of finding and sharing simple examples, then the telescope project will generate several fun and useful lessons. Otherwise, it will become just another project.

Thanks for your contributions in making physics, astronomy and earth sciences fun for non-scientists.

Reply

I do not know your children--what ages, what interests, what school. Nor do I know the limits of your budget.

Textbooks are generally uninspiring--they are produced to sell, not to inspire, and are often the result of committee work. If your kids would like to know about the universe, here are two books they may like
"Seeing in the Dark" by Timothy Ferris
"A short History of Nearly Everything" by Bill Bryson.
I reviewed the 2nd of these in an article later picked up by "Eos", on
http://www.phy6.org/outreach/books/Creation.htm

As for telescopes, I might have a different philosophy here--give the kids an instrument with minimal hassles, to let them go right away and observe. For our son's birthday (32nd, I think) we gave him a Meade 3.5" telescope. We scrimped and did not buy the computer controlled model, and that was a mistake--I think he would have used it more if he had the one with built-in star catalog. On advice we also bought for it a 90-degree elbow eyepiece (easier to look at objects high in the sky), a better eyepiece and a subscription for "Sky and Telescope" (he had a tripod already, and he crafted his own camera attachment).

If your kids are not yet in that league, they have plenty to read in my web pages. I can also send you solutions to the problems, if you want to teach them that way. They should keep in mind, though, that no one will care as much about their own education as they themselves. If they want it, it's theirs for the taking.

196. Does the solar wind have escape velocity?

Your site claims the particles in the solar wind are leaving the Sun at about 400 km/s. This is less than the escape velocity which is about 600 km/s. Does it mean many of these particles will eventually fall back to the Sun? Is there any evidence of such as behaviour?

Also, what are the leading "hot" topics on Solar Physics now?

Reply

The solar wind starts not from the Sun's surface, but from the corona, and is accelerated somewhat gradually. Obviously, it has to overcome solar gravity, which I suspect is one of the conditions needed for accelerating the solar wind--maybe like a lid on a pressure cooker, holding down the hot corona until it can just barely escape.

You might want to look up http://www.phy6/org/ Education/FAQs6.html#q82

Incidentally. NASA has been toying for years with the idea of a solar probe, approaching the Sun within 4 solar radii--following boost from a "hairpin" orbit around Jupiter (mentioned briefly here and in the page following it). It would be shielded from the Sun's intense heat by an "umbrella" of tungsten or similar material, and would study the solar wind in its source region. How can it do so with a metal barrier between it and the Sun? Simple: at closest approach is moves at about 300 km/s, perpendicular to the line to the Sun, so in its own frame of reference, solar wind particles (unlike sunlight) would seem to arrive from the side, at an angle. They would seem to have the vector sum of their own velocity and that of the corona relative to the fast-moving probe.

"The leading hot topics"? I am only slightly involved in solar research, but the big question there seems to be what happens beneath the surface--where do sunspots originate and how, what are they, and what creates the uneven rotation of the Sun (which drives sunspots and magnetic fields). When I got into the space research, it was proposed all these were shallow phenomena, in the outermost layers of the Sun, but current study suggests they actually extend to appreciable depth. If you have a science library nearby, try to find

Parker, E.N., The physics of the Sun and the gateway to the stars, Physics Today, 53, p. 26-31, June 2000

197. Astronomy for cliff-dwellers of New York City

I live in NYC (have all my life) and I became a lunatic (yes, I know the prefered term is lunarian..but ..) because you could see the moon.(I was an adult before I was any place dark enough to see the milkyway--NYC is not a good place for astronomers.

'I've read, and taken advantage of places like the Hayden planetarium, and I have made (and continue to make) my own observations.

I am blessed now to live in a high rise, with a clear south and west view.--more or less.. (I live close to Flushing Meadow park,)

My observation is: at the winter solstices, the sun sets in Brooklyn.. and by now, its getting close to down town Brooklyn, soon it will set in Manhattan, and by summer, it sets in midtown.. (certain building of the NY skyline are my personal stonehenge!)

But the moon, oh , the fickle moon.. there must be a pattern.. but in the 18 months I have lived here, I haven't worked it out..

Sometimes it sets in downtown, some times in midtown.. but it doesn't seem to move in a smooth pattern, (a sine wave say) but its all over the map! I can't tell from one month to the next were the moon will set.

I am sure information about the moons patterns and movements (or perceived movements) must be documented. I 1 read about the sun's movements and began as a child to note were it set (and more often where it rose, since my childhood home had clear eastly views.) observation and reading have brought me a clear sense of the movement.

But the moon.. can you suggest some reading?

Reply

I loved your e-mail message! You are truly observant. I don't know what you do for a living, what your age or education are, ... but you have the soul of a good scientist. Brings to mind what a friend ones said: The most powerful phrase in scientific discovery is not "Eureka, I found it" but "Hmmm ... that's funny!" (He did not known who had said it, but I cited it anyway.)

The Moon is not fickle, just a bit harder to predict. To understand, you should know what the ecliptic is--"Stargazers" has a section about it--the plane of the orbit of Earth around the Sun.

The ecliptic cuts our visible sky in two halves (half the stars are north of it, half, south of it), and the dividing line (also called "the ecliptic") is where the Sun is in the sky, it goes once around the ecliptic in one year. The constellations along the ecliptic are "the zodiac," so dear to astrologers.

The ecliptic is inclined to the plane of the equator by 23.5 degrees, because the rotation axis of the Earth does not point perpendicular to the ecliptic, it is off by 23.5 degrees. Actually, it nowadays points almost exactly towards a fairly bright star, the pole star Polaris (there's a section on that, too). Because of that inclination, the Sun is further north (up to 23.5 degrees closer to the pole star) in the summer, and more distant (up to 23.5 degrees) in the winter. That tells why now in January the Sun is lower in the sky and days shorter (that is on the web site, too), while around midsummer, it's the other way around. And why the apparent motion of the Sun at sunrise or sunset migrates north and south in a yearly cycle, as you have noted (and ancient astronomers have before you).

Still with me?

Now the solar system is flat. Other planets all orbit the Sun in planes rather close to the ecliptic, and our Moon does too (about 5 degrees off, I think, and we'll ignore that). That means that the imaginary line around the sky where the Sun makes its path is also the only place where we are likely to see the planets (when close to each other, they are clearly strung out in a row), and the Moon too.

Think about it: the path of the Sun around the sky is also (almost) the path of the Moon around the sky. With one big difference: the Sun makes its circuit in one YEAR, while the Moon does so in each MONTH. They both follow the same path (almost), so that yearly north-south dance of the sunrise (Brooklyn-Manhattan-midtown and back), the Moon completes it in one month. No wonder you find it irregular!

But if you track only the full Moon you might see the reverse of the Sun's cycle--north in winter, south in summer, because the full Moon is always opposite the Sun. It better be REALLY full, because the Moon shifts its position across the sky 12 times faster.

That's as far as you can go. Let me add that the actual motion of the Moon, to the precision astronomers need, is rather complicated. In the nautical almanac, "low precision formulas for the position of the Moon" take about 50 terms (each with its sine or cosine; I had to use them once), while precise ones take many more. That complexity arises because many factors disturb the Moon's orbit--the Sun, the equatorial bulge of the Earth, maybe Jupiter too is important enough. In the 1800s the French astronomer DeLauney spent 20 years calculating the orbit of the Moon, yielding a formula so long it filled an entire book. In modern times this was checked by a computer, which only needed minutes, and it found everything was correct, except for 3 small errors which did not change anything important.

Enjoy your Stonehenge! Alas, two big menhirs it used to have are now gone.

Response--with a bit of personal confession

I am not in modern way of thinking a scientist (having a piece of paper), but yes, I think of myself as one.. (I like too, to think of myself as a polymath.. but truth is, I lie somewhere between a dilletante and polymath.) and my piece of paper says I have mastered the art of business administration (is that really an art?).

I am getting to be 'of a certain age'-- that is, I admit to being 47, but don't discuss how long I have been 47! 47 is a prime number, and well, I am in my prime.

Now that I have an idea of the motion, I will begin a more studied observation of the moon.

I had great fun last year, and the year before stopping neighbors and passersby and insisting the look at the lunar eclipse--and on a language board I frequent, when the word camera came up, I was the one of a few who know the origins of that words, (alas, I do not really know Latin.. just a smattering of words, no real declensions,) -- I remember making camera obscura's to watch a solar eclipse as child.. (and again in 1990's -- I watched that eclipses in Times Square--on an extended lunch hour)

NY skyline as a Stonehenge has some limits.. (geology is the underlying factor, ha) I would have only been able to see the very tops of the towers from my current vantage point (there are some tall building close by that block some of my skyline view) -- I moved here, after 2001 and never saw them from here. I worked close to them in Manhattan in 2001, (close enough to be evacuated) , and unlike many NYer's I had been to the top several times.

I have no trouble with the math in your explanation, -- I was blessed as child, and went to an all-girl school, with well educated nuns, who had no truck with math phobias. In elementary school, I was introduced to the geometry of classical curves. It was great fun, and occasional, when watching the coverage of those early space flights, I could actually understand some of the 'formula's'--they were the same ellipses, parabola, hyperbolas and circles we were plotting for math homework. I also learned octal and binary in elementary school-- as an adult I have picked up hex. I taught all three systems to my kids, it took with my son, and since he had an immediate use for the knowledge.(we had a home computer in the early 1980's--a 16 bit one that used hex)--for me, these numbering systems were stupid number games. He has far surpassed me --I can do simple math in binary, he can think in binary! I do still read math and science for fun--which puts me definitely into the nerd category, but I think "nerd" is a rather complimentary term!

My knowledge of the world, is miles wide, and microns thin, with an occasional pot hole and one or two sink holes! and being a child (and adult) raised on concrete, tides and nautical tables are an area where my knowledge is stretched to vapor thinness.

I do have a parochial view,--I KNOW NYC*-- and have learned a bit about the tides, (rule of 12) because the tides, while they are rather small (only about 4 foot on average between high tide and low), they do interesting things in parts of the estuary, especially were they 'meet' in the Harlem "river' at Sputendival, and in the east 'river' at Hellgate.

[*My knowledge of geology is rather specific.. I know NY geology well, and geology in general less well, same with botany, I know NYC botany quite well, but trees and plants of the tropics.. hardly at all, and so on for must subjects.. I am lucky that I live in an area with interesting geology and diverse plant (and animal) life, and great building, and wonders of engineering, and museums and other cultural institutions!]

But now, thanks to your kindness, and pointers of where to look and why, in another year or two, I'll have a new pothole full of knowledge about the movement of the moon.

Thank you, thank you, thank you!

Reply

I enjoyed reading your letter. Maybe your "piece of paper" is an MBA, but you are not among those yahoos who pride themselves on never having understood science, or cared for it. Gone are the days when no one was accepted as well educated who did not at least have some understanding of nature!

If I may direct you to some of my web pages... a very good book (OK, with some errors, but it's still great fun) is Bill Bryson's "A Short History of Nearly Everything," whose paperback version has been on the top 10 list of The Washington Post for about 6 weeks. I reviewed it among others at
http://www.phy6.org/outreach/intbook.htm
The above is a link to the entire list, because you might like other books listed there, too, Another collection is
http://www.phy6.org/outreach/intedu.htm
from which your son may find that the Romans made use of the binary system, even though they were not aware of it.
And a highly recommended book on astronomy is "Seeing in the Dark" by Timothy Ferris.

Have fun with any or all of these.

David

198. Portable star finder

I am looking for a hand held display which, when held facing north, can help an individual locate visually the different constellations, stars, & planets, visible with the naked eye at that time of year in the northern, mid-western sky. I intend to use it to help youngsters & new observers locate the wonders of the sky. I hope what I am seeking exists.

Reply

What you want is a map of the sky. I typed "Sky map" into Google and got a long list, starting with
http://www.fourmilab.ch/yoursky/
Give it your location and it will give you a map of the sky for tonight's date. Click on any point on the map and get a magnified view of the sky around it. You enter your location and get a sky map for today's date. I guess you can print the page and use it outdoors.

A useful trick which someone told me requires fast-drying "whiteout" paint used by typists to blot out mistaken letters or words, which are then overtyped correctly. Draw the stars in the constellations which you want to watch on a fairly large sheet of paper, put on top of it a sheet of saran wrap from the kitchen, and with the white-out brush mark on it the stars you want to identify--bigger marks for brighter stars.

Then take a wire-hanger used for clothes, pull it apart to a square, wrap the edges of the saran sheet around the wire and maybe secure them with tape. You now have a transparent star map you can take outdoors and hold against the sky.

199. What if the Moon was closer? (A)

My name is Korey and I am a high school student looking for an answer to the question of my project: If the Moon was to get closer to the earth what would happen to the tides?

Reply

The tides would of course be higher.

In fact, the Moon WAS closer to Earth in the past, and is even now gradually receding. This is a side-effect of the tides, which may be viewed as a world-wide system of waves, losing energy as it hits continents and islands. This takes away energy from the Earth's rotation, which slows down (days get longer, but at a very slow rate). Because of conservation of angular momentum in the Earth-Moon system, this causes the distance of the Moon to gradually increase.

How close was the Moon originally? The answer depends on the way the Moon originated--was it formed with the Earth, captured by the Earth or somehow torn off the Earth? George Darwin, son of Charles Darwin

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Darwin.html

who was a well-known scientist in his time, believed in the last possibility. He claimed that originally the Earth rotated too fast to be stable, a bulge formed, and it was torn off by the rotation, to form the Moon. In this view the Moon was originally "within touching distance", but the action of the tides (which initially must have been huge) caused it to recede to where it is now.

More careful studies showed Darwin's theory cannot hold. I think most astronomers feel the Moon and Earth were created together, as a double planet, though other views persist--see "The Big Splat", a book by Dana MacKenzie. If you can find the old book "Biography of the Earth" by George Gamow (written about 50 years ago) you will find he still supported Darwin's theory. It's a delightful book, even though not everything in it has stood the test of time.

What if the Moon was closer? (B)

Today in physics class, my teacher talked about the moon. He said that the moon is moving away from Earth each year by a certain distance. Can you tell me the actual annual movement of the moon away from Earth? Thanks

Reply

The average rate at which the moon recedes is 3.8 cm per year, about an inch and a half. See
http://www.talkorigins.org/indexcc/CE/CE110.html

This happens (and your teacher might have said so already) because of the tides in the oceans. The moon pulls the water into a wave which tries to remain pointing at the moon; the moon also pulls the entire Earth, leaving behind a second crest of the tide-wave on the opposite side of the Earth.

The two crests try to line up with the Earth-Moon direction, but the rotation of the Earth under them causes them to collide with shorelines. Such collisions slow down the rotation of the Earth and give up energy, whose ultimate source of that energy is the rotation of the Earth and the motion of the Moon.

However, by Newton's 3rd law, if the Moon produces a force on the ocean tides, those tide-waves must also produce an equal and opposite force on the Moon. The result may be best explained using the conservation of angular momentum. The total angular momentum of the Earth-Moon system must be conserved, so if the Earth loses some, the Moon must gain some, and it does so by moving further out.

200. Why doesn't the Moon have an atmosphere?

Dear Doctor, I was wondering if you could answer a question of mine. If the moon's gravitational pull is strong enough to affect water movement here on earth (by creating tides), how can it not be strong enough to hold on to its own atmosphere. I know this question might sound dumb so forgive me.

Reply

The two problems are quite different. If the Moon were big enough to hold an atmosphere but (say) 3 times as distant, tides might have still been as big: one effect does not inform about the other.

How exactly are atmospheres held? By gravity of course, but note that the density of the atmosphere decreases with altitude. With Earth, it drops to one half about every 5 kilometers in altitude (temperature can modify this). If you rise 5 kilometers, only half the atmosphere is above you, with only half its weight compressing the air, so density and pressure are down to 50%. Rise to 10 km, and it's only 25%, and so on. At 100 kilometers you are down to about one part in million, and collisions between molecules become more rare, so that they rise and fall like stones tossed upwards.

The "halving distance" could be more than 5 kilometers, or less. If gravity were smaller (as it is on the Moon) and temperature higher (as happens at high altitudes), it would be larger--and the atmosphere would rise higher. The somewhat early loss of the space station "Skylab" in 1977 was helped by higher sunspot activity, which caused the upper atmosphere to heat up and expand (from more solar X-rays), with more air resistance in low orbit.

Also, above 100 kilometers, sunlight may break up molecules (e.g.) of water, and the atmosphere is no longer evenly mixed, in constant proportions. Lighter atoms (e.g. hydrogen) then rise higher than heavy ones (e.g. oxygen), because their velocity is larger, at the same temperature.

The velocity is still much less than escape velocity--but in a hot gas, a spread of velocity exists (a "Maxwellian" spread, named for James Clerk Maxwell who first derived it) and a few atoms or molecules always move fast enough to escape. On Earth, over geological time spans, all the helium has escaped (the helium we get from natural gas was produced as alpha particles by radioactive elements such as uranium). As the attached graph shows, on the Moon all common gases are expected to be gone.

The graph is from
http://abyss.uoregon.edu/~js/ast221/lectures/lec14.html

Hope this answers your question. If a comet rich in water were to hit the moon (as may happen--a small comet may have hit Siberia in 1908), the Moon would have a watery atmosphere for a thousand or maybe a million years, but it won't last.

201. Telling a 3-year old about the atmosphere (A)

Hi-- My three year old daughter, Sarah, would like to know . Any help you can provide would be appreciated

Reply

Hmmm. Questions have come from all ages, and from all over the world. Some 8-year olds have asked quite profound ones--but Sarah is probably the youngest yet. I'll try to answer, but YOU are the one who has to make it clear to her.

First of all, it is a GOOD THING there is no air in outer space! Outer space is SO BIG, if our air could spread out over all of it, almost nothing would be left for us to breathe.

Luckily, air has WEIGHT. (You don't feel it, but the air in a room weighs more than Sarah).

Without weight, everything would FLOAT FREE, like astronauts in a spaceship (I hope Sarah has seen pictures). Weight is what keeps tables, chairs, people, cats, dogs, cars and so on standing on the ground, also keeps down the water in oceans and lakes. And it also keeps our air from floating away.

Weight tries to keep everything as LOW DOWN as possible. Water flows downhill. In the winter, sleds slide down a hill by themselves, but need to be pulled back. Weight also keeps air attached to the ground.

Weight is caused by GRAVITY--the pull which any piece of matter has on any other. The pull is very weak: any two stones pull each other, but so weakly, you can never feel it. But the EARTH is such a BIG piece of rock, that it has enough pull to keep all of us, and all things around us, safely on the ground.

It even has enough pull to keep the MOON from running away. As well as all the satellites NASA and others have launched, which like little moons go around the Earth..

Please let me know if the above is good enough for a 3-year old!

Telling a 3-year old about the atmosphere (b)

Thanks so much! This answer did seem to satisfy her (mostly, anyway). Now she just wants to know where the air came from in the first place Thanks again for such a thoughtful and speedy response--it was really helpful!

Reply

It is probably hopeless to try keep up with the questions of a 3 year old! On the long run, it may be easier to teach her to read--as we have done--see

http://www.phy6.org/outreach/misc/ilana.htm

and then let her find answers in the library.

Let me still try answer this one. Where did air come from? Hard to say. I guess it came with the Earth. There exist other "worlds" in space, a little like ours (some smaller, some bigger), called "planets." They look like stars in the night sky, though stars are different (stars stay in fixed groups, planets move among them). Some planets have "air", others (like the Moon, still another "world") came without it.

OUR air is different, however: we can breathe it! Air on other planets is too hot (if they are closer to the Sun), too freezing cold, if more far away. But in addition, hot or cold, we COULD NOT breathe it, we would choke. It would be the wrong kind.

For breathing, air needs to contain something we call OXYGEN. That is the part of the air which we breathe, the rest just goes in and out. Sick people in hospitals, who can't breathe well, sometimes get oxygen from special metal bottles.

Our planet at first had "bad air", too. It has oxygen only because we HAVE GREEN PLANTS. Trees, grass, green leaves everywhere, with the help of sunlight, change air we cannot breathe, and make oxygen out of parts of it. If our world stopped growing trees or grass, our air would slowly become bad. So we should thank plants for our good air!

202 Three-Color Vision

I have heard somewhere that three colors are not enough to reproduce ALL colors which the eye can see. Is that true?

(Adapted from question asked on Physhare, a list server of physics teachers)

Reply

It is true.

I have looked up this question in the writings of the true master, Richard Feynman, who dealt with color vision in chapters 35 and 36 of "The Feynman Lectures", volume 1. It is remarkable how far his interests have ranged, how few were the topics he did NOT look into. My own field of magnetospheric physics is unfortunately one of those few, and that only because his sister Joan (who is still with us) worked in it. When her brother showed interest, she told him to butt out, leave something for her to do. He did, and now we are stuck with all sorts of unresolved problems.

You should read Feynman's exposition, in particular chapter 35, which I tried to flesh out a bit here. Feynman is so much more articulate than I can ever be, and what I wrote below is anyway my own interpretation, not necessarily the same thing.

The important thing to do is to pose the proper question: what exactly do we want to claim? There is no question that the normal eye has 3 kinds of receptors, which we may designate (R,G.B) for (red,green,blue), although each is sensitive to a wide spectral range beyond the "pure" rainbow colors of red, green and blue.

When we look at some colored object, with some standard brightness (I choose here a standard brightness for all colors, so that only relative intensity matters), if the (R,G,B) sensors detect intensities (a,b,c), we will see SOME color, and that color will be characterized by the 3 numbers (a,b,c). The range of values for (a,b,c)--say, from 0 to 1 for each, after we have standardized intensities--covers ALL colors the eye can see. There exists nothing more.

The real question to ask is--is it always possible to "fake out" the color (a,b,c) by presenting the eye with a superposition of 3 colored sources, of three standard colors (U,V,W). These can be pure spectral colors, or not. (Red, Green, Blue) are a good choice, though, because each stimulates primarily one kind of receptor. Therefore, by twiddling with their intensities, we can make each type of receptor receive an EQUAL intensity, and the result registers in our mind as white. Let this be an assumed restriction on the choice of "primary" colors, requiring that we CAN get white; three different hues of green may never be able to do so.

Let the color U create responses (a₁, b₁, c₁) in the 3 receptors of the eye. Similarly:
--the color V creates responses (a₂, b₂, c₂), and
--the color W creates responses (a₃, b₃, c₃)

These numbers (a₁ . . . c₃) are all COMPLETELY determined by our choice of reference colors (U,V,W).

Suppose we want to illuminate a white surface with a combination (a', b', c') of the 3 sources, in such a way that the eye will be made believe that it sees a GIVEN color (a,b,c). Then

a = a₁ a' + a₂ b' + a₃ c'
b = b₁ a' + b₂ b' + b₃ c'
c = c₁ a' + c₂ b' + c₃ c'

It is now necessary to invert the equations: (a,b,c) are given, (a', b', c') are to be determined. (You can write it in matrix notation if you wish, and you then need invert some matrix). There always exists a solution (unless the equations are dependent--e.g. the 3rd is the sum of the first two), so it SHOULD be possible.

Having reached that point, Feynman raises a warning. A solution exists, but do we have a guarantee that (a', b', c') are all positive? They have to be if we add light from three sources--we cannot subtract (except maybe by using a colored screen, something he briefly discusses).

If we choose (U,V,W) wisely, the coefficients will be positive for a wide range of color combinations (a,b,c), all of which can be represented by combinations of our reference colors. But there may exist some oddball combinations (a,b,c) where the solution gives some negative coefficient. NO combination of (U,V,B) can then fool the eye to believe that it sees that color. Feynman claims that there will always exist such colors, and at this point I tend to believe him.

Unless there is some flaw here, you may pass all this to your class. Let them see Feynman's book, too!

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Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: stargaze("at" symbol)phy6.org .

Last updated 10 May 2005 Edited 1 November 2016

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