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This is just a selection--

either

or else

To save space, this list starts from http://www.phy6.org/stargaze/StarFAQ17.htm
A full list is found at http://www.phy6.org/StarFAQsA.htm
and links arranged by subject are at http://www.phy6.org/stargaze/StarFSubj.htm.

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)

Reply

I looked up Wikipedia, as good a source as any, and it cites 71 km/s per megaparsec, give or take 4 km/sec. This is the average speed at which galaxies are receding from each other, due to the expansion of the universe. A parsec is about 3 light years--see end of section on "Parallax" in "Stargazers", and of course, a megaparsec is a million parsecs. More distant galaxies move apart faster, and the speed increases with distance, by 71 km/sec with each megaparsec.

The Hubble constant can be estimated using the Doppler effect and type 1A supernovas. When observing more distant galaxies, whose light originated billions of years in the past, smaller values of the constant are deduced, suggesting it has gradually increased since the Big Bang, i.e. the expansion of the universe is actually speeding up, rather than being slowed down by its own gravity. Such speeding-up implies that extra energy is continually made available, and this has been named "dark energy", because we cannot see its sources. This remains a major unexplored area in astronomy.

288. Are Summer Nights Darker?

Please help me understand why winter nights are (seem?) darker than summer nights?
Thanks
Ron (Hawaii)

Reply

Winter nights are of course longer than summer nights, as explained, in "Stargazers," for instance

http://www.phy6.org/stargaze/Sseason.htm

On Hawaii, however, there should not be any great difference in darkness. There the Sun goes down at a steep angle, and once it is 15 or 20 degrees below the horizon (you may look up "twilight" on a search engine) the darkness of the sky is determined by other light sources--the Moon, urban illumination etc. However...

If you get closer to the pole, the (apparent) motion of the Sun makes a much smaller angle with the horizon. The result is that even after it has set, for a long time it stays not far below the horizon, causing an extended twilight. St. Petersburg, the former capital of Russia, is famous for its "white nights" in midsummer, when the sky hardly gets dark. Fairbanks, Alaska, is a good place to see the polar aurora ("northern lights")--but not before the end of August or after the end of March, since in summer the sky does not get dark enough.

In polar regions, or course, winter nights last around the clock, and so do summer days. But again, summer nights may not be too dark if the Sun is below the horizon but close to it.

289. "Space Elevator"

I'm a journalist and I started a blog about the space elevator. Because of the recent articles about Van Allen Belt radiation killing space elevator occupants I looked up the Wikipedia entry on the belts which led me to your article on them.

Wikipedia says the belts are limited to +/- 65 degrees latitude (if I understand correctly). That makes me wonder if there is an anchor point on Earth that would bypass the Van Allen belts or at least minimise exposure to them.

Being a Canadian, I naturally think of our vast expanses of territory above that latitude.

Reply

The space elevator is a nice idea, but as in the legend of the mice trying to hang a bell on the cat which hunted them, when it comes to the details, the real problems emerges. We know of no material strong enough to do the job, and anything we have--carbon fiber, you name it--falls short by a big factor.

Your message suggests that you did not fully understand the "Space Elevator" idea: it uses the rotation of the Earth, and therefore needs to be anchored at the equator. Arthur Clarke, who used a space elevator as the central idea in "Fountains of Paradise," anchored it on a high mountain in Sri Lanka (where he lives). However (in the preface?) he apologized for the fact that in order to place his base on the equator, he "moved" Sri Lanka a few degrees. Which is why a base in Canada won't work at all.

The idea is essentially to have a massive satellite anchored by a strong but very light cable at the equator, placing the satellite itself a short distance outside synchronous orbit. The natural orbital period there is a bit more than one day (it's exactly one day at synchronous orbit). The cable drags the satellite and forces it to move faster than its natural speed, and that creates a centrifugal force which stretches the cable. I suspect the satellite cannot be too distant, or else the cable will tend to wrap around the Earth and bring it down, but that whoever did the calculation also figured out the right distance.

An attractive idea, if only it worked. Like the bell around the neck of the cat.

I would not worry about the radiation belt, much of it can be shielded out and if only a short time is spent there, the dosage is tolerable. Of course, instruments and fuel which are lifted are not affected.

290. Black Holes

Hello, I am a freshman at Shenyang International School, China, highly interested in astronomy. I was strongly intrigued by the power of black holes, and coming across your article on the black hole at the center of our galaxy, I was wondering if you could help me in answering few of my questions, which I had pondered upon, for so long.

First of all, are there really any black holes? According to your article (and this very article changed my perspective toward the universe), there is one-- at the center of our galaxy. Up until now, I had always thought that the black holes were mysterious, inexplicable matters, that absorbed everything that neared them. I was only in first grade when I first encountered this idea, and I actually had nightmares about these holes, approaching Earth and finally, swallowing the Earth. And frankly, up until now, I thought that these black holes would eventually swallow everything up.

What you're saying in your article, is that black holes do not actually pull everything into themselves, as we commonly think, but produces a gravitational force? This is a whole new idea to me, and it actually is quite hard to accept. This leads to my second question? What causes black holes? What are some forces that allow black holes certain properties they have? Lastly, are the black holes causing the Big Crunch, if Big Crunch is in progress at all? Or does the Big Crunch have something else that causes the universe to fold back? Those were some of the questions I was interested in, and please, if you're not too busy, can you give me some light on those problems?

Thank you.

Sincerely Yours,

Reply

Black holes seem real enough, and were predicted before other evidence about them accumulated. They are essentially collapsed stars.

It is actually very difficult for anything to be sucked down into a black hole--just as it is very difficult for any object to be pulled down by the sun. The same force is responsible in both cases, namely gravity. Comets approach the sun all the time, and some get very close and speed up enormously. However, it takes just a little sideways velocity for them to miss the sun, so that instead of hitting it, they loop around it and move out again in some different direction. It is very rare for a comet to hit the sun--only relatively recently, from satellites, have such events been observed.

What causes black holes? Gravity, obviously, extremely strong gravity. Usually, gravity is a fairly weak force--a very weak one, on an atomic scale. It does hold Earth together, but even in the center of Earth, it is believed, atoms and nuclei are not drastically modified, just somewhat compressed.

The Sun has about a million times as much mass, and if gravity could pull it together, its force could affect the sun's atoms (and also release a lot of gravitational energy, as matter falls together; I think Helmholtz estimated 150 years ago, as much energy as the sun produces in 20-30 million years). But it won't happen soon, since the Sun's hydrogen is being converted to helium by nuclear processes in its core, and the heat released this way not only keeps the sun hot and shining, it also keeps the gas inside it under pressure, not allowing it to collapse.

Some day the sun's fuel will run out and it will collapse, releasing its gravitational energy and going through some strange changes (red giant, etc), but ultimately it will collapse to as small a size as possible. Astrophysicists have calculated (I think the Indian Chandrasekhar was the first) that when this happens, atoms will be joined, their electrons will be tightly shared, and a star as massive as the sun will shrink to the size of the Earth, to become a "white dwarf" and some time later, presumably, a dark dwarf. For more, see

http://imagine.gsfc.nasa.gov/docs/science/know_l2/dwarfs.html

Bigger stars--I think Sirius would qualify--could collapse to even smaller size. Now gravity is so strong that nuclei are also forced together: electrons and protons combine to neutrons, and the neutrons join in one giant nucleus, forming a neutron star. A mass like the sun's may be only about 10 km across; see

http://imagine.gsfc.nasa.gov/docs/science/know_l1/pulsars.html

A star still more massive may collapse to a black hole. Gravity is so strong that light cannot escape, and rules of general relativity must be applied. It does no good to ask what is inside the black hole, because whatever it is, cannot be observed. For more, see

http://imagine.gsfc.nasa.gov/docs/science/know_l2/black_holes.html

Finally, about the "Big Crunch." The most recent belief is that there will be no "Big Crunch."

We know about the "Big Bang" which caused the universe to start expanding (e.g. see see the section on the Doppler effect and the expanding universe and also http://www.phy6.org/stargaze/StarFAQ16.htm#q267. As it expands, it must give up energy, to push stars apart against their gravitational pull. Early cosmologists wondered whether this would slow down the expansion. If the universe did not have enough energy to expand forever, ultimately none may be left and galaxies will stop expanding and fall back together again, ending up in the "Big Crunch," the reverse of the "Big Bang."

No one knows the future. However, astronomers who checked on the expansion of the universe in the past, using type 1 supernovas (all of which have very nearly the same brightness), found that in the past billions of years, the expansion of the universe has NOT slowed down--instead, it has been unexpectedly speeding up. Something--some sort of "dark energy"--is actually adding energy to the universe. As long as this goes on, there will be no "Big Crunch."

Questions are easy, answers are long and uncertain. Sorry!

Let me end by commending you on the way you write. You have a good style, and a good command of the English language. I wish you every success in school.

291a. Angle between ecliptic and Milky Way

Dear Dr. Stern: I wish to know what is the angle between the ecliptic and the axis of the Milky Way?

Thankyou!

Reply

I do not know offhand, but one can calculate. The angle G between two planes is the angle between the two vectors perpendicular to them.

Let the vector (X1, Y1, Z1) be of length 1 ("unit vector") and perpendicular to the ecliptic.

Let (X2, Y2, Z2) be similarly a unit vector perpendicular to the plane of the galaxy.

Then with dots denoting multiplication, the "scalar product" of the two vectors ("scalar" is a number without a direction, not a vector) is

X1.X2 + Y1.Y2 + Z1.Z2

This can be shown to equal cos(G), where G is the angle between the two vectors. That is:

X1.X2 + Y1.Y2 + Z1.Z2 = cos (G)

The system of coordinates has z pointing to the north pole, and (x, y) in the equatorial plane of Earth. The x axis is the intersection between the ecliptic and the equator, and the x direction points to the position of the Sun at the spring ("vernal equinox").

The axis of the Earth is inclined by an angle A = 23.5 degrees (approx) to the equator. It points perpendicular to the intersection of the equator and the ecliptic--that is, perpendicular to the x-axis. You may draw a sketch to convince yourself that in this case

X1 = 0
Y1 = sinA
Z1 = cosA

Now about the galactic plane. Here is what Wikipedia writes at
http://en.wikipedia.org/wiki/Galactic_coordinate_system

namely: In 1959, the IAU defined a standard of conversion between the Equatorial coordinate system and galactic coordinate system. Accordingly, the Milky Way's north galactic pole is exactly

RA 12h 51m 26.282s, Dec 27° 07' 42.01".

The RA (Right ascension) is like celestial longitude, and converting hours, minutes and seconds into degrees gives an angle B = 192.88°.

The declination is (converting the angular measure to decimal notation) D = 27.11667°, which is the angle of the axis to the equator. Then the unit vector to the pole of the galaxy has a Z-component

Z2 = sin D

and its projection on the equatorial plane is cosD. That projection has components (make a drawing if you wish)

X3 = cosD cosB Y3 = cosD sinB

So the components of the unit vector are

X2 = cosD cosB
Y2 = cosD sinB
Z2 = sinD

You can do the rest on your own! I think you get something like 70 degrees, unless, of course, I have made a mistake somewhere. Note that as discussed in

http://www.phy6.org/stargaze/Strig4.htm
sinB is negative.

Happy Winter Solstice!

291b. (continuation) -- About the year 2012

Thank you for answering me so quickly and so thoroughly. Let me explain to you the reason of my asking.

I live in Guatemala, the "land of the Mayas". As you must know, the Maya civilization is known for its great achievements in mathematics, astronomy and time measurement, especially for its very accurate calendar.

The actual aborigines of Guatemala believe that they are the descendants of the Mayas, and some have created a very strange mixture of "New Age" and "Maya spirituality." Some of them announce a new era, which is to commence six years from now (2012), when the axis of the Milky Way will form a "very beautiful poem" in the sky: a right angle with the axis of the ecliptic. In fact, I looked in Wikipedia for some information and I found that the angle must be greater than 20 degrees (I didn't do the accurate calculations that you showed to me).

Know, I looked for some information about the rate of growth of that angle, and the best I found, is that the star that moves fastest is the Barnard Star, whose velocity is about 10.3 seconds of degree per year. Assuming that this velocity is in part due to the rotation of the axis of the Milky Way about the axis of the ecliptic, I found that six years is a very short amount of time for these axis to get orthogonal. If this is not to abuse of your generosity, could you please explain to me if there is information about the rate of growing of the angle in question? Once again, thank you very much!!

Reply

Your second message made the picture much clearer, and in particular brought up the connection to the Maya Calendar, which starts a new cycle at the winter solstice of 2012--just as the year 2000 marked to some people a new beginning. About 4 months ago, a correspondent, an artist who only gave his name as "Rob" wrote to me about this, and I will attach his message and my response.

Now a few comments.

First, you should ignore Barnard's star: it is very faint--magnitude 9.56, whereas the eye can only see stars of magnitude 6 or less. The scale is logarithmic, so 9.56 is very dim: in no way could the Maya have seen it.

Note the star map given on that page, halfway down. It shows the Milky Way and the planets on 12-21-2012, they also outline the ecliptic. The equator is the straight line cutting through the middle of the map in the left-right direction, and you can see that indeed it makes an angle around 70 degrees with the Milky Way.

The only thing which makes 2012 special, to my thinking, is that Venus will pass in front of the Sun, Such transits occur in pairs, generally more than a century apart (one occurred in 2004, discussed on my "Stargazers" web site--see link above). Venus was very important to the Maya, but as it happens, the transit occurs in mid-summer, on June 6.

A happy new year to you, down in Guatemala, and Feliz Navidad! Answering mail from far away is always pleasant, making one feel that one has friends all over the world.

292. Don't use Diesel fuel in a gasoline car!

...on Sunday my sister filled her new car with diesel instead of gasoline, in a petrol car. The car ran for couple of miles and then stopped on a narrow strip of the freeway divider between the merging lane and the oncoming traffic. It was an exciting night....first, having the police stop the traffic flow so we could get a courtesy pull from a tow truck which cost 120 dollars. Then driving back to a Toyota garage for an overnight repair. Apart from the good stuff, I have a tough mechanics question for you.

How does a gas engine start? I understand that a mixture of air and gas is compressed by the piston so that the explosion will be greater. If the piston is stationary at the time of the car's start up, then how is an ignition achieved. I know that ignition occurs after when the air and gas is compressed. Then the piston moves upward so it can be lit by the ignition plugs. But if the piston is stationary at the bottom or midway then how does the engine start.

There are many engine diagrams with a moving crankshaft. I know how a moving car is kept constant by the linear motion of the piston. But I don't understand how a stationary piston achieves momentum during start up. Or could it be that a piston is not used during an initial start up, only gas, air and ignition flares. And the piston happens later. Can you explain?

Reply

...everybody should learn how a car works, in 7th grade or so, before learning to drive. Starting the car from any position is no problem. First of all, because cars have several pistons, which will be in different positions, and at least one of them is usually set to fire. But more important, all cars now have an electric starter motor, driven by the battery, which turns it over, also causing fuel to be pumped in. Small motors can be started by turning them by hand--lawn mowers have a rope to pull, and small airplanes can be started (or could in the past) by someone turning the propeller and then jumping aside. My father had once a car which you started with a crank stuck in a special hole below the radiator, in front. But today batteries and starter motors do the job.

However diesel engines and gas engines are QUITE different. In gasoline engines, the fuel evaporates easily, especially in contact with a hot engine. So a mixture of air and gas-fumes is created in the carburetor and sucked in by the engine--or in more recent models, gas is injected into the cylinder and evaporates there. Then the vapor-air mixture is compressed, and at the right moment, ignited by the spark plug.

Diesel engine use thick fuel which does not evaporate easily, they run hotter and at higher pressure, and have no spark plugs. Air is compressed by the piston until it is VERY hot, then at the height of the cycle, diesel fuel is injected by special pumps, and because of the heat, it bursts into flames immediately. Gasoline engines sometimes also have the fuel ignite on its own, because of bad adjustment of timing or dirty spark plugs with glowing carbon. This causes loud "knocking" in the engine, which is bad, both mechanically and for fuel efficiency. Your sister (and you too!) should read about these things in a book, after the garage cleans and fixes the engine. It may have run those few miles on diesel fuel because it used gasoline injection, and operated like a diesel (also, there may still have been some gasoline in the tank), but obviously, that did not work for long.

293 How bright is our Sun when seen from space?

How bright is the sun when observing it from outside of earth's atmosphere, like from the space shuttle or from the surface of the moon for example? I don't believe I have seen a photograph of the sun like this before.

Reply

Unless you specify how you assess brightness, "how bright" asks for a personal judgment. My answer might be "somewhat brighter, not exceedingly so," but it all depends what you observe.

One way of judging brightness is by the solar constant, the power beamed by the Sun on a surface of 1 square meter perpendicular to the Sun's rays, at the Earth's mean distance. The figure is usually given as 1.36 kilowatt, but by the time it reaches the surface of the Earth it may be 2/3 as much or less. A lot of the missing energy is scattered, giving us the blue of the sky, which is really sunlight coming from other directions. As you rise in altitude, the sky gets darker and then blacker, as less of the atmosphere is above you and less scattering occurs. The Sun seen from space dazzles, in part because the background is very black.

Dust and small particles ("aerosols") scatter a lot, too. And bets are off in cloudy skies.

All that for visible light. Ultraviolet gets scattered or absorbed by ozone in the atmosphere, infra-red by water vapor and carbon dioxide lower down.

Another way of looking at sunlight is by the graph in

http://www.phy6.org/stargaze/Q4.htm

You can see that the brightness of the Sun peaks around 500 micrometers (5000 Angstrom), which is blue-green (See "colors of Sunlight", sect S-4). Thus the eye is sensitive to most of the range of sunlight, but not all of it. The atmosphere cuts down a lot and there exist extensions to colors the eye cannot see. Some of these are important to the outer atmosphere (soft X-rays, way beyond the graph, may create the ionosphere) and to heating the Earth.

294. What is a "field"?

I teach "physics last" [In 12th grade rather than 9th]. Last week a very intelligent young man asked "What exactly is a field?" I didn't know how to answer that until I was working on my MASTERS degree in physics. It took me quite a bit of time to get the idea across to the class. Good luck to anyone who has just moved into the physics neighborhood from another area! Also, as Department Chair for many many years, I know that physics people are extremely hard to find --at any salary!

Reply

Teaching of physics is certainly NOT confined to solving a certain selection of problems, using mathematics. Such material is soon forgotten by the students after the final exam, and maybe rightly so.

No, teaching physics means to understand the intricate web of ideas which underlies the mathematics. If you understand that, it is relatively easy to add the math. Understanding physics means not remembering facts, but "how do we know?" those facts. It means, not citing obtuse concepts, but "what do they mean, and how were scientists driven to introduce them?"

Enough sermon. The concept in this case is "FIELD"

I have written a number of web sites where, I hope, anyone with good reading ability and enough curiosity can get a conceptual understanding. They stress astronomy and space, but a lot of physics is there too.

The term "field" grew gradually in the 19th century, and here is how I present it to the user. First, as noted in

http://www.phy6.org/Education/whfldlns.html

came Faraday's idea of magnetic field lines (his term was "lines of force"). They are no more tangible than lines of latitude and longitude, but to Faraday, it seemed that space with field lines was somehow not empty.

Then came Maxwell (following section there) who used the magnetic end electric vectors, abstract quantities representing electric and magnetic forces which could exist at some point, if any electric charge happened to be there. (If no such charges existed, the point was just empty space.) Maxwell showed that these insubstantial quantities could transmit an electromagnetic wave, which in every way behaved like light. He (and Poynting) suggested that space which contained light was not exactly empty, but could transmit energy and force.

Then came the struggle of "if not empty, what does it contain", and for a while the word "aether" floated around, as the substance filling space. But it was such a strange substance--if could not be localized, we could not tell if it was at rest or moving (see http://www.phy6.org/stargaze/Srelativ.htm for a superficial discussion)

It was finally decided that electricity and magnetism modify space, to become a "field." The old conundrum on gravity (whether it was a "force at a distance") was also answered, by endowing space with a gravitational field (due to masses in it), a subject later expanded by general relativity.

And to put a cap on it all, came quantum theory

http://www.phy6.org/stargaze/Q7.htm

and introduced an even weirder kind of field, a "probability field" giving the probability of finding a particle in some location.

Can you teach this to a class? I think so (especially if students can read those sections on the web). Will students think "physics is weird"? Probably, but then again, physics IS weird, constantly shaping and modifying our concepts. The concept of "mass", aka "inertia." The concept of "atoms." Concepts which are at the core of understanding physics. Weird? Maybe. But if students get the ideas, they might even conclude that physics is interesting.

Last point: teach physics with its history. All these changes happened in a certain order. First Oersted, then Faraday, then Maxwell, Hertz, Einstein, Heisenberg and Bohr (see http://www.phy6.org/stargaze/Ls7adisc.htm for a very quick summary). Unless you give the orderly framework, the sense may be lost. A timeline provided in this collection may help, too.

295. The outer limits of the Solar System

I am a high school student and I am currently doing a project concerning the solar system. I would like to ask you a few question:

How was the approximate boundaries of the solar system established, as well as the size of the planets?
Is it possible that very large planets will be discovered within the solar system using current-day equipment? Why or why not?

I would be most grateful if you could answer those questions.

Reply

The most distant objects observed in the solar system seem to be comets. The velocity with which they arrive, and the fact that they have very little "sideways" velocity (i.e. they barely miss the Sun, and a few even hit it) suggest they come from the very edges of the solar system. If any were truly interstellar (i.e. not bound to the Sun) some would move faster and would tend to have bigger sideways motion.

For this reason, it is believed that they come from a collection of icy objects at the very edge of the solar system (maybe a light-month away or so) called "The Oort Cloud" after the Dutch astronomer Jan Oort who proposed its existence.

If any large undiscovered planet exists, it must be on a very elliptical path, and currently very far from the sun. Otherwise, it would have been observed long ago.

The large planets we know all have near-circular orbits, so such a planet would be a real oddity. Still, we can never be sure--there is for instance the recently discovered Sedna. Also, some people postulate a distant planet "Nemesis" with a 22 million year orbit or so, deflecting asteroids to hit the Earth on its rare passages near the Sun. However, if I were asked to wager money on the existence of such a planet, I would definitely bet against it.

296. Gravitational Energy

In approximate terms, if a 200 lb weight on a tether was vertically dropped on a "load cell measuring device" from a freefall distance of 6 feet, and the same weight was extended and pulled taut at a 90 degree angle then dropped in an arc on an impact force measuring device (this time measuring the sideways impact), would the two impact numbers be the same amount, would one be more? less? by what percent or amount?

This has relevance in the fall protection industry where workers are wondering if vertical drop forces are equal to swingfall forces.

Reply

I believe the impact would be the same, or very nearly so. This is because the same amount of potential energy is converted to kinetic energy in both cases, and the kinetic energy is what determines the impact--vertical in case (1), horizontal in case (2).

The only point I am not sure is that in case (2), nothing keeps the string taut in the initial moments of the fall. Replace the string with a rigid rod and the case is much more clear.

This is discussed in more detail in
http://www.phy6.org/stargaze/Senergy.htm

297. Stresses on a Railroad Bridge

I am a railway engineer.We are faced with a peculiar problem. A train is to move on a down grade. The grade is 1 in 40. There are bridges enroute. Each engine is about 22m and with 6 axles. The longest bridge is of two spans of 30m each with tall piers. The train load is about 5300 tonnes.

Our problem is whether we should use 3 engines in front and two at the back, or all five in front. If there are 3 in front then the rear engines can keep the train in tension and partly take the load from the rear. This can of course cause a coupling snapping if sudden braking is there. In case all engines are in the front then rear train is in compression and in case of sudden braking from the front it may buckle. But a greater gray area is as to what will be the force(weight) transferred to the bridge pier, through the rail in a 5 engine consist assuming that at any time not more than 2.5 engines will be on the bridge.

I shall be obliged if you can give a thought to this problem of application of Newtons laws together with laws of motion and friction.

Reply

I am a physicist specializing in space, not an expert on railroad bridges! You should have such experts in the India Railway system, and you should consult some of them. Even they may want to look at the bridges or at least require more information about them.

Having said that, let me give you my opinions. I hope they are useful when you discuss the matter with your experts.

I would assume that your train has air brakes on every carriage, connected by an air pressure pipe through the train. And I also would assume that your train would always approach the bridge extremely slowly, especially during or after rain, because water on the rails reduces the friction. I remember crossing in 2002 a deep ravine near Talkeetna, Alaska, and the train just crawled, very very slowly.

Why go so slow? With a bridge like the one you describe, having a tall pier in the middle (and maybe some at the edges too), you must always ask, what are the forces. One force is the weight, pushing down. Piers of concrete or stone can usually carry an enormous weight, but still there may be a practical limit on what they can carry, because the foundation in the river and on its shore may have limited strength, especially if bedrock is too deep for the foundations to reach, or is in a relatively soft rock. The piers then won't break, but they could sink. I think the engines are the heaviest load here, but as you said, in any case only half their weight will be on the bridge at any time. Also, unless the bridge is brand new, any sinking would probably have been noted long ago.

However, the real problem are sideways forces, pushing the tops of the piers forwards or pulling them back: these can cause cracks, especially on tall piers. When the train arrives, coming down a 1:40 slope, it is braking, so it will be pushing the piers forward.

A complicating fact is that in adjusting the slow speed of the train, engineers alternately apply and release the brakes. Application of the brakes may be somewhat sudden, and that will cause the transfer of a certain amount of kinetic energy, from the train to the bridge. The slower the train, the smaller its kinetic energy, and the smaller that energy can be.

When the train is half way across, the tendency of its rear to roll down the slope is completely balanced by the opposite tendency of the front of the train, up the other slope, and after that moment the brakes can be gradually relaxed. But now the train must be pushed or pulled up the opposing slope. Locomotives pulling in front transmit the force to the ground (thorough rails, ties and ballast), but those on the bridge push the train and thus exert a backwards force on the bridge.

It may be a greater force than exerted by the braking before. When the train was on the bridge, perhaps 4 cars were braking simultaneously and pushing the bridge forward. At the end of the train, the two locomotives at the end not only push themselves forward against friction, but also push 40% of the weight of the entire train up the hill on the other side, at a 1:40 slope.

It thus seems less stressful to the bridge to put all 5 locomotives at the front. When the train is coming down, they do but a little pulling (gravity and brakes are the main factors), while when going up, they pull hard indeed, but none of this pulling stresses the bridge.

In any case, be sure to get the experts opinion on this! All sorts of other questions may arise. For instance, if you have 5 engines pulling a train up a 2.5% grade, how much stress is on the couplings between the engines and the train?

Would it be safer to place two engines, not at the end but in the middle? Then when the engines reach the bridge, they do not place much stress on it even if they help push the train up the other side, because the carriages behind push them forward. I am simply not experienced in such problems!

298. The constellation of Cassiopeia

I have come across your fascinating website in search for the answer to the question can Cassiopeia be seen in Alaska's night sky in December, and if so, where in the sky?

I live in Washington and can see Ursa Major clearly, and fairly high in the sky, which leads me to suspect that Cassiopeia may be below the horizon at this time of year. Are you able to shed some light on this question?

I thank you in advance for your time and for sharing your knowledge!!!

Reply

The answer is yes, you can see Cassiopeia from Alaska quite well, and also from Washington.

In fact, you can see it from any place from which Ursa Major is visible, but because it is on the opposite side in the sky from Polaris, you probably won't see both at the same time. If Ursa Major is at any point in the sky, Cassiopeia will be at the same location (roughly) 12 hours later (or earlier).

Of course, if you see Ursa Major at any time in the night, "12 hours later" may be in the daytime. Maybe in Alaska or even Washington (State) you can see them simultaneously--one low in the east, the other low in the west.

For a sky map showing the constellations, go to the left panel ("Looking North") of

http://www.bbc.co.uk/science/space/myspace/nightsky/observingnotes.shtml

Polaris is at the middle of the map, and taking this as the center of a clock dial, Ursa Major is around 4-5 o'clock, Cassiopeia around 10-11 o'clock, straddling the Milky Way.

299. Tracking of radioactivity carried by winds

Is there an account of following radioactive discharges around the world? Has radioactive discharge from one source point been followed up quantitatively worldwide? Any time line available on line?

Reply

A lot of work on this has been done, but you will have to conduct the search by yourself. One big effort of tracing the atmospheric spread of radioactivity followed the disastrous fire on 25 April 1986, which destroyed the Soviet nuclear reactor in Chernobyl, releasing huge amounts of radioactive fission fragments into the atmosphere. See
http://www,phy6.org/stargaze/Snuclear.htm

The Soviet government tried to quiet down the mishap, but air monitors (I think in Scandinavia and northern Europe) quickly picked up radioactive elements, forcing the Soviets to admit the extent of the disaster.

Another earlier detection of air radioactivity was on September 3, 1949, when a US Air Force aircraft picked up radioactivity east of Kamchatka, detecting this way the first Soviet nuclear bomb test which was conducted on August 29 in Semipalatinsk, Kazakhstan. See "Dark Sun" by Richard Rhodes, Simon and Schuster 1995, p. 371.

There probably exists a lot more, but you need conduct your own search

300. Why can't the space shuttle reenter "slowly"?

I am 50 years old and high school educated. I was recently engaged in a conversation with my step-father concerning why the shuttle needs to be traveling at such a high rate of speed upon reentry. He suggests that if the shuttle were stopped or significantly slowed, and then gently "nudged" that reentry could be accomplished without the excessive heat build up associated with reentry. I realize that during the Apollo missions, this wasn't an option but we wonder why gravity couldn't just "pull" the craft in now.

Reply

Your step-father suggests that the shuttle can be "stopped or significantly slowed," but actually that is not possible, for two reasons: first, the shuttle's speed is what keeps it in its orbit, and if it loses even a fraction of that, it starts losing altitude and moving down into denser air. And two, it has a lot of energy: at 24 times the speed of sound, weight for weight it has about 100 times as much energy as a rifle bullet. How are you going to bleed off that energy? The answer is by slowly losing velocity, slowly dropping into denser air and there creating a massive shock front which heats the surrounding air. It must all be done very carefully: enter too fast and too much heat is generated, enter too shallowly and too much speed remains, and at the very least, you land far from where you planned.

It so happened that a very similar question was asked before. Look up
http://www.phy6.org/stargaze/StarFAQ15.htm#q248

301. "The Standard Model of the Universe"

(From a high school teacher)

I want to teach my children about The Standard Model of the Universe. There is nothing about this in the textbooks, except that atoms have quarks in them. Well, I read that 60 years ago, muons were discovered. The Standard Model has been in practice for 35 years, I have also read. Furthermore, my students are visually impaired and blind and in the 9th to 12th grade. What do you think about this idea of teaching The Standard Model? Is it basically true or maybe not? What happened to gravity as one of the forces? Is gravity a force? Maybe there is only one force in all the Universe.

Reply

The question you ask is not simple (and is actually outside my science field). Even students able to read regular books may find it challenging!

The simple answer is that so far, the standard model of particles seems to work. It regards matter as made up of 4 basic stable particles--electrons, neutrinos (the kind associated with electrons), the "up" quark with the charge of 2/3 electrons and the "down" quark of charge -1/3. The latter two are always found in combinations (up, up, down) with charge +1 and known as protons, and (down, down, up) with charge zero and known as neutrons. (To these one may add anti-particles, which have similar properties, except for reversed electric charges),

Also, the model predicts that the quarks cannot be separated, because the force between them grows with distance (like the force of a rubber band and unlike that of a magnet), and most important, that two other foursomes of this kind exist, of higher mass (the muon is the one corresponding to the electron but at the next level). However all particles in those two extra groups are unstable and decay to their partners in the basic group in a small fraction of a second.

This is where science stands now, and there are still things we cannot explain--the weight of protons and electrons, the magnetism of protons and neutrons, and more. To properly appreciate the present state of science, students ought ask two more questions:

(1) How did science get to these conclusions?
(2) What can one expect in the future?

Concerning the first question, science reached its present-day understanding very gradually. In the 1800s chemistry and physics convinced scientists that matter consists of atoms, leading to the scheme of chemical elements: hydrogen, oxygen, carbon and so on... over 90 of them.

Also, matter seemed electrical. Chemical solutions in water, or molten salts, could be broken up by electric current (a technology useful in batteries, electroplating and the manufacture of aluminum, for instance) and the amount of current needed to separate a unit weight of any element was related to its chemistry.

Then it turned out that negative electrons could be boiled off a hot wire in a vacuum
http://www.phy6.org/Education/welect.html
and their mass and charge could be measured. Since matter in nature is electrically neutral, the rest of the atom needed a positive charge to balance the negative electrons. In 1911 it was recognized that this positive charge was concentrated in a tight atomic nucleus, which contained almost all of the weight. Some of this is in

http://www.phy6.org/stargaze/LS7adisc.htm

http://www.phy6.org/stargaze/Q5.htm

Since then our view of matter has been getting more and more complicated.

The weights of various nuclei (especially small ones) were very close to multiples of the weight of the hydrogen nucleus, known as the proton. Helium nuclei, for instance, weighed about as much as 4 protons, so since the helium nucleus had only the positive charge of two protons, the first guess was they contained 4 protons and 2 electrons (electrons have very little weight, and differences can be ascribed to the energy of the nucleus).

That turned out to be wrong. We now know that neutrons also exist (discovered by Chadwick 1932), similar to protons but with no electric charge. Atomic nuclei tend to have equal numbers of neutrons and protons--2+2 for helium, 6+6 for carbon, 7+7 nitrogen, 8+8 oxygen and so on (however, neutrons get favored in heavier nuclei--see "stargazers" section on nuclear energy).

Then after World War II, large electric machines were built to accelerate protons and electrons to higher and higher energies and see what happened when they were allowed to collide with atoms. What happened was that new particles were created, all unstable with very short lives, decaying (sometimes in several steps) to the familiar ones. It was hard to make sense of them.

Some were heavier than protons, and were believed to be "excited states" of the proton, states of higher energy similar to the higher energy states of atoms. But some were lighter than protons--the muon, for instance, which behaved like an electron but lasted only two microseconds before decaying into an electron and two neutrinos (of two different kinds, it was realized).

Neutrinos

The muon itself was the result of the decay of a pion, a slightly heavier particle produced in the collision. Some other "mesons" were also produced in collisions, particles with mass between electrons and protons, and also in decays of the new exotic particles, suggesting such particles were not simple variations of the proton. Theory (and experiments) finally suggested that the scheme which best explained this was the one based on quarks, connected by the standard model with its two extra levels.

You can find those levels listed in the books, with their quarks (which have fanciful names). Each particle has an antiparticle, so a pion was either an up quark plus an anti-down, or a down plus an anti-up. Also, you can read about the forces involved--but all that takes math to understand.

Why is it important? In everyday life, it is not. But very early in the universe--the first second, or seconds,, after the big bang--matter was so hot that high-energy forces played an important part.

The trouble is, we still don't understand the universe, which brings up the second question: what comes after this, still remaining to be understood? We don't know, but recent studies of the universe suggests it contains a lot of "dark mass" which we cannot see--more dark mass than the visible mass in stars--and we don't know what it is. All we can detect are effects of its own gravitational pull. See
http://www.phy6.org/stargaze/Sun4Adop3.htm

You asked about forces in the universe. When I went to school, 4 forces were recognized--gravity, electromagnetic, strong nuclear (binding nuclei together, even though their positive protons repel) and the weak nuclear force (converting neutrons to protons and vice versa). Today the force between quarks is fundamental and the strong nuclear force is supposedly a faint echo of that, and I am not sure about the weak nuclear force. Gravity is definitely not the only force, but it is still very much at the center of the picture, especially on the scale of the universe.

On that scale there seems to exist one additional important factor, named "dark energy" which is pushing the universe apart at greater and greater speed. At one time astronomers expected the expansion of the universe to gradually slow down, because gravity between stars tries to keep them together. We now know
http://www.phy6.org/stargaze/Sun4Adop2.htm
that the opposite happens, the expansion is speeding up. No one knows why.

I recently read and reviewed a book on all these--"Origins of the Future" by John Gribbin, at
http://www.phy6.org/outreach/books/Cosmology.htm but again be warned, it's not easy. Let me stop here--good luck to your class.

302. About the Maya Calendar

I live in the Netherlands and am interested in the Maya calendar, the old one and also one being proposed as a new system.

The new version was introduced on a number of artist sites around the world, among which is www.PAN-holland.nl, and it originates at www.tortuga.com. The sponsors of those sites wish to change our calendar to a 13 day (Mayan tone) month system of 20 days (Mayan seals) with 1 extra day july 25th which would be a day outside time, a day to share peace and happiness with each other. South and North hemisphere would be similar in season on that day, thus increasing equality (as compared to January season difference) as well.

My question is: how would that turn out on the long run in terms of so-called off being with respect to the sun cycle???? I am an artist with a background also as a biochemist and enjoy the area where science and art meets.

Reply

Your letter s seems to confuse two Maya calendars (this according to "A Traveller's History of Mexico," p. 37, by Kenneth Pearce, 2nd ed, 2004). The Mayas had a solar calendar, keeping track of the seasons, with 18 months of 20 days (20 was a basic number in the Maya numbering system) and FIVE extra days at the end. Presumably, one more extra day was added every 4th year or so, but that's just my guess.

In addition, they had a ritual calendar of 13 months of 20 days. This looks like what those web sites propose, but it won't stay in step with the seasons of the year.

If you have 13 months of 28 days, you get an extra two days. You won't easily get a single extra day, as you propose. And by the way, on July 25 (close to the summer solstice), seasons are opposite on the two sides of the equator.

Like the Maya, our society often has twin calendars. One is used in commerce and science (though astronomers use Julian days, a bit different) and forms the framework for most of our recorded material. In addition, different nations and religions use cultural calendars, and my web site describes some of these. I don't think you can introduce a new cultural calendar without a widely used culture behind it.

See also http://www.phy6.org/stargaze/StarFAQ16.htm#q264.

303. Are light sabers possible?

I'm impressed with the answers you put on the web, they are detailed and easily understood. Two questions here, arising from thoughts about a new product development:

(1) Can I focus a straight beam of radio waves (or any other waves like infra-red) with an intensity that can last for a distance of 1 meter? Yes. I am trying to develop a jedi lightsaber...
(2) When radio waves (or any other waves like infra-red) from 2 sources cross at an angle, will there be any reflected waves that bounce back to the transmitter that can be detected by a receiver? Essentially, I understand from my high school physics class that tradio waves will superimpose on each other and may result in a higher amplitude or cancel each other out. Radio waves will probably bounce off hard surfaces but I'm wondering if a wave can be reflected when it meets another wave in its path.

Reply

Sorry, no light sabers. You certainly can focus a wave into a beam, if the wavelength is short enough (for instance, visible light). However, I know no way of stopping the beam abruptly at a distance of (say) 1 meter.

Also, as your high school physics course noted--waves stay independent when they cross, at least in empty space. Take your radio as an example. It may perhaps be able to tune itself to any of 50 stations, but when it does, the other 49 stations have no effect on what you hear, even though their waves occupy the same space.

304. Can the heat of sunshine make the Earth expand?

We know, heat expands the volume or surface of any object. Therefore, does the heat of the sunshine expand the volume/surface of the earth? If so, how much surface expansion has occurred in a hot region? Kindly discuss with example and calculation of any region of the world.

In addition, please inform, what is the coefficient of expansion of (any one certain type of) soil and what is the temperature of sunshine in summer?

Reply

As you must have noted over the years, the Earth surface is neither heating up, nor cooling down, but stays at more or less the same temperature. The heat it receives from the Sun is balanced by the heat sent back to space. Here we ignore periodic changes due to seasons of the year and day-night variations, all of which average out to zero.

The process by which heat is returned to space is described in sections S-1, S-1A and S-1B of "From Stargazers to Starships." It is also the process which drives Earth's weather and climate.

The expansion of soil I don't know, but in any case, it would be the rock under the soil which affects what happens on the surface. Most soil is more strongly influenced by the water it contains than by heat--and when it dries out, it cracks.

305. About mountains

Dear Dr. Stern,

I would be very grateful if you answer my following questions in details?

Do mountains stabilize Earth?
How will be the Earth without mountains?

Reply

What strange questions! your first question--I would say "no," except that I really do not know what you mean. Stabilize against what?

Some things should be understood. Compared to the size of the Earth, mountains are not at all high. They provide less surface variation than the markings on a coin. What they do is provide evidence for forces inside the Earth which deform its surface--throw up volcano peaks, crumple sections of surface which are pressed or stretched sideways (just look at a relief map of Nevada, with its north-south ridges) or raise parts of continental plates as one plate pushes beneath another.

This last process is responsible for some high mountains--for the Himalayas, raised by the plate of India (which I have read started as an island south of the equator and migrated north) pushing beneath the Asian plate. In Alaska, Mt. Denali (or McKinley) is similarly produced as the Pacific plates pushes northwards beneath the American plate and lifts it. Both processes create earthquakes.

Mountains on Earth are just about as high as they can get: unless pushed up or held by pressure below, they would sag under their own weight and gradually flatten. Mars has a giant volcano, Olympus Mons, nearly 3 times higher than any mountain on Earth: but then again, Mars only has 0.39 times our surface gravity, and no oceans (measuring Earth mountains from the sea bottom shows greater height).

And how would Earth be without mountains? Depends. We have continents of lighter rock, which float on top of denser rock and poke out above the oceans. If that floating did not exist, Earth would be one big ocean and dry-land plants and animals would have no chance. How would Earth look without mountains? The icy satellites of Jupiter have all sorts of surface markings, e.g."ghost" craters from long-ago impacts. But unlike Moon craters, they are just markings on a flat surface ("palimpsests") because ice is weak and easily sags, even under low gravity.

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

Last updated 27 March 2007 Edited 2 November 2016

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284. "Iridium" flares

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285. Discovering Planets outside the Solar System

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286. Landing speed of airplane

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287. Hubble Constant

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288. Are Summer Nights Darker?

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289. "Space Elevator"

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290. Black Holes

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291a. Angle between ecliptic and Milky Way

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291b. (continuation) -- About the year 2012

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292. Don't use Diesel fuel in a gasoline car!

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293 How bright is our Sun when seen from space?

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294. What is a "field"?

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295. The outer limits of the Solar System

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296. Gravitational Energy

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297. Stresses on a Railroad Bridge

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298. The constellation of Cassiopeia

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299. Tracking of radioactivity carried by winds

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300. Why can't the space shuttle reenter "slowly"?

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301. "The Standard Model of the Universe"

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302. About the Maya Calendar

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303. Are light sabers possible?

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304. Can the heat of sunshine make the Earth expand?

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305. About mountains

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