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For a list including questions 28--324, click here.
396B Posssibility of Asteroid Hitting Earth (2)
420. Earth crossing Galactic Equator?Dear Dr. P. Stern
I ran across your name while searching the Web for information on the Van Allen belt. I am wondering what the impact of the earth and the sun passing through the Milky Way galactic equatorial plane in the next few years will be for life on earth. Is it something to be concerned about? Can you tell me where I can find reliable information about this? Thanks so much.
Your letter reflects yet another aspects of the growing lore about 21 December 2012, when the "long count" Maya calendar is due to enter a new cycle. For more see letters linked at the end of
Never mind now the scientific content of anything we infer from Maya astronomy, product of the stone age. The Milky Way Galaxy, we know (unlike them) is a giant wheel of stars a few thousand light years thick. Our solar system is about half a light day wide, if that much. How could we tell when it crosses the middle to the galactic disk, and where that middle would be (and never mind what the effect would be)?
In analogy, the angular momentum plane of the solar system is near the orbital plane of Jupiter. When Earth crosses that plane, about twice a year, does anything special occur? I doubt it.
421. Is the geocentric theory ruled out?Hi
It is said that the earth rotates around the sky and there are scientific calculations trying to prove this. Any possibility that the Earth stands still and the sky moves around it?
NO, at least under the rules used in ordinary science. If the sky rotated and Earth stood still, you would see the same motion of stars at night--but the FORCES associated with that motion would be quite different.
By Newton's 3rd law, Earth pulls the Sun with the same force as Sun pulls Earth. If Earth stood still, there could be NO force on it from the Sun, while to hold the Sun in a daily orbit, Earth would have to exert a HUGE pull on the Sun.
Experiments confirm Newton's 3rd law, so this possibility must be ruled out, even though it creates similar appearance .
422. Does the Southern Sky have a Pole Star?Dear Dr. Stern,
I was reading about Henry the Navigator and the use of the Cross Staff with my son. I thought it might be a good project to make a cross staff and read the latitude. But the book talks about reading latitude using the Pole star. What would the equivalent be in the Southern Hemisphere? We live in Cape Town, South Africa.
No star is right now close to the southern celestial pole, to play the role the pole star serves in the north. The best I can suggest for your son is to locate the southern pole using other stars. One reference is
http://www.dibonsmith.com/downunder.htm I was asked about this pole in
and you might look up that page. Unfortunately, the references cited there no longer exists.
423. What is the fate of starlight energy?What has happened to Radiant Energy which has been emitted into space by our sun and every other sun (star) for the past 13 to 14 billion years?
I am no astronomer or cosmologist, but I think it just keeps on spreading forever. It is not going to hit an "end of the universe" because the universe is also expanding, in a way possible only if it behaves as if it were embedded in a 4th spatial dimension (not time, which is something different again).
Because it is expanding, a certain "burst" of light (or "photon", if you will) emitted in a specific second will occupy a bigger and bigger volume. However, its energy is conserved (not taking now into account "dark energy" and other recent observations which we do not yet understand), so its wavelength has to be red-shifted (red photons have less energy than yellow-blue ones), in proportion to its age.
The oldest "light" which we observe was emitted when the universe was about 300,000 years old, very dense, and first became transparent. Today we identify it with the cosmic microwave background observed from all directions. More about it mear the end in
That "light" is between 13 and 14 billion years old--and it too is still expanding
424. Double-slit diffraction of particlesDear Dr. Stern,
When the double-slit experiment is done with more than one particle, is it only the first particle that makes an interference pattern? Or does each particle make an interference pattern? If the latter, is it the same one or different ones? Or the same one over time?
I understand that the particles arrive in random order. Is that after the first one, with each going through and making an interference pattern, (either each the same, or different, or the same in the long run?) Or is that only when their wave-functions are apparently collapsed?
Warmest regards, Alex
Visible light builds up an interference pattern on a film behind a double slit, even if it is so dim that only one photon at a time passes the instrument. You would think that photon passes either the slit on the right or the one on the left, and if so, there is no interference expected. But no, the light passes the slits as a wave and only when it hits the film is the photon created, according to a probability distribution described by the diffraction pattern. With particles hitting a double slit, if you send just one electron, you won't get any interference pattern--you will just register one electron, somewhere. The position where you observe it, however, has a probability distribution guided by the wave function (I think, by its amplitude squared). One electron gives no distribution; but if you beam a million or a billion electrons, the distribution of their arrival points follows the interference pattern. This holds even if the electrons do not move simultaneously, i.e. each wave function interferes only with itself.
You may also look up what the master wrote--chapter 1, vol. 3 of the Feynman Lectures.
425. Does the Sun overhead reduce effective weight?I am from India. In the morning the sun is directly over head and is pulling in the direction opposite to that of earth's gravitational pull. At night, both the earth's gravitational pull and sun's gravitational pull are in the same direction. So does this mean at night our weight increases?
ReplyThe effect of the Sun's pull (and that of the Moon, slightly stronger) is complicated, because the Earth on which you stand is also pulled. In any case, the pull is too small to observe (the effect of the Earth's rotation is also small but much bigger. See "Stargazers", section 24a). The result are tides of the ocean (and also of the land, less noticeable). Since the tide is a wave traveling around the world, it is very much modified by coastlines.
426. Evidence for Global Warming ?Quite by accident this evening I came upon your website. I am truly astonished by your depth of knowledge and didactic skill.
I wonder whether you would be willing to help us?
I and some colleagues, all professional engineers of one kind or another, reaching (or past!) retirement age, are currently attempting to get beyond the hype of global warming science and look at the basic physics (without prejudice one way or the other) associated with the so-called greenhouse gas effect. Our interest is in the concept of radiative balance in the atmosphere and whether this is a genuinely useful way of assessing the influence, if any, of CO2 and other greenhouse gases on the mean surface temperature of the planet.
There are many contrarian physicists out there who regard the idea of radiative balance as a pernicious fiction. See for example the attached papers by Gerhard Gerlich and Heinz Thieme. The latter, in particular, takes an interesting didactic approach (not unlike your own) whereas the former I find somewhat less digestible. And yet I have a feeling that a better formulation of what they are both saying might be needed to get at the truth.
I therefore plan to analyse the issue in depth - because, if Gerlich, Thieme and others are correct, there is a monstrous misunderstanding being propagated widely by the IPCC that should be easy to refute by presenting the basic physics. On the other hand, if they are charlatans and/or incompetents, it is best to understand why their arguments are wrong because this would then strengthen the case that man-made greenhouse gases really do represent a significant threat to mankind.
Would you be interested in corresponding with me on this subject?
(further parts omitted)
If you seek enlightenment about global warming, you should probably ask someone who has actually gone into the nitty-gritty of the physics, calculations, data and simulation, which Thieme has not done. My own background is in magnetospheric plasmas. You also wrote that you have "come upon my website." Which one? There exist hundreds of pages, even not counting translations--see
The web pages you probably want are
and the two that follow it; also the related lesson plan
Professional atmospheric scientists have simulated and calculated radiative transfer until there is no doubt in its main properties. The situation is complicated by clouds, distribution of water and humidity, and by global climate patterns, but observations seem to show that indeed, the global temperature is slowly increasing. It is a small effect, but our climate is in delicate balance, and a shift may greatly affect our style of life and that of our descendants.
There is also no doubt that polyatomic gases impede the radiative cooling of the Earth's surface: instead of solar heating being radiated back to space as infra-red (IR), the IR travels only short steps before being absorbed and reradiated, diffusing towards space until, in the stratosphere, radiation is finally able to leave. I think you agree with that. By the way, I have read that the main "greenhouse gas" is water vapor and that without it, Earth would actually be too cold for our style of life. So the "greenhouse effect" is actually beneficent: we just do not want too much of it.
Even if you doubt the observations and theory, there is one important consideration. If humanity knows a bad outcome is possible, even if not certain, it should play it safe: a shift in climate would be hard to undo quickly. Just for this I would prefer to reduce carbon emissions and concentrate on conservation and alternate energy resources. (And remember, theory predicted stratospheric ozone depletion long before it was observed, warning of a slow long-term process which cannot be reversed in a hurry.)
But in a/ddition, an effect has been observed which suggests global warming is real--namely, the rapid thawing of polar ice.
My section S-1B
stresses that our climate is shaped not only by the vertical heat transport to the base of the stratosphere, but also by horizontal global air flow. Solar heat is deposited most effectively in the tropics, and global flows--wavy air currents around the globe whose core is defined by the "jet streams"--help spread it to wider areas in the middle latitudes.
Suppose some factor such as "greenhouse gases" impedes the vertical return of heat. One way global circulation can react is by extending further poleward, spreading the distribution of heat poleward and thus involving a larger part of the globe in its return to space. The polar thaw seems to indicate this is actually happening.
Please read the cited sections, but remember I am no climate scientist. Find one and get into details. I do not think the references you sent qualify.
427. Distances to the EquatorHi Dr Stern,
Hope you are doing fine. I have a very simple yet urgent query.
1) What is the shortest distance from the equator line to India ?
2) What is the shortest distance from the equator line to the UK ?
Please any help will be highly appreciated.
ReplyShortest distances on a sphere are always along a "Great Circle" whose center is the center of Earth itself. Lines of longitude are all great circles, and define the shortest distance between their points and the equator. You will find more in
I will not give you the numbers, you should find them yourself, using maps in an atlas and the radius of the Earth.
To the reader: if you want, stop reading here and figure the answer for yourself
Response:Well I have tried but seem to stuck somewhere. Could you please let me know? It will be highly appreciated
ReplyPlease calculate! Lines of longitude are approximately circles (the Earth slightly flattened by its rotation, but let's ignore that).
The meter was originally defined as 1/10,000,000 of the distance from pole to equator (today's definition is slightly different, but ignore that too).
The arc from pole to equator covers 90 degrees.
Can you do the rest?
ReplyThe southernmost point in England is "The Lizard" at approximately 50 degrees north, the one in India is Cape Comorin at about 8 degrees. These are also the lengths of arc along a line of longitude from those points to the equator.
Pole-to-equator covers 90 degrees and equals about 10,000 kilometers.
8 degrees is 10,000 times (8 / 90) or about 889 kilometers.
428. Weight on the Equator and at the PoleWill an object weighing 1 ton at the north pole still weigh 1 ton at the equator?
I am a member of a small group who "put the world to rights" on a Friday night in our local. Thanks in anticipation.
ReplyThis can be a confusing problem. At the pole, all you observe is weight, the force of gravity. At the equator, viewed in a rotating frame of reference, you need subtract the centrifugal force. Viewed from a non-rotating frame, the weight is still the same, but now a small part of it is "occupied" in maintaining rotation with the Earth. Calculating either way, the result is the same.
The "weight" you observe depends on the instrument you use. Suppose you weigh yourself at the pole and get 170 pounds. What do you get at the equator (assuming your scale is accurately calibrated for the pole)? If your use balance-beam scales which compare your weight to that of a standard weight inside the scales, you still get 170 pounds: the centrifugal force has reduced the effective downward force on you, but it also has done the same for the standard weight used for comparison.
On the other hand, if you stand on a spring scale, it will register slightly less. The downwards force on you is smaller at the equator, but the springs are not affected.
Gravimeters used by geophysicists searching for (say) oil use a very accurate spring balance to measure the variation of gravity from place to place. See Wikipedia.
429. Why doesn't gravity overcome buoyancy?Good morning, Dr. Stern,
I "googled" the following question: If the law of gravitational attraction is a physical law which governs the behavior of objects above the earth's surface, why does it not "over rule" the "less dense than air" explanation for the rising of a helium balloon in the atmosphere?
Your website, get a straight answer, was listed and I chose it because I simply want a straight answer to this question. I would have asked my physics professor, but my past experience, warns me that the question would not be asked directly and I would still be "wanting" an answer after he had "explained" it.
ReplyGravity IS the reason why a helium balloon rises.
Consider first a simpler case: objects in water. Rather than calculate forces (which is the rigorous way of doing so), let us examine buoyancy from the angle of energy.
(1)   We all know mechanical systems evolve in the direction of LOWERING the amount of potential energy: A stone falling in air lowers its potential energy, which is proportional to its elevation.
(2)   A stone in a bucket of water will also fall to the bottom: in doing so, it displaces a volume of water (equal to its own volume), which is added to the top layer (the water rises). The water which rises INCREASES its potential energy, being lifted the same distance as the stone is lowered.
However, the stone is denser and weighs more than the water it displaces, so the potential energy it LOSES is more than the energy gained by the rising water.
(3)   Instead of a stone, use a block of wood, starting at the bottom of the bucket, held there by a long metal rod in your hand. If you remove the rod, the wood will float to the top. WHY? Because even though the block GAINS potential energy (as it is lifted), water rushing into the space it has vacated, LOSES potential energy. Since water is heavier than wood, there is again a net loss.
More generally--anything heavier than water sinks, anything lighter than water floats. Ships made of iron also float, because the interior filled with air also pushes away water--as a whole, the SHIP pushes away ("displaces") more weight of water than its own weight.
(4) A helium balloon is like that piece of wood: the air it displaces weighs MORE than it does, so as the balloon rises, the air rushing to fill the place it occupied weighs more than the balloon, and LOSES MORE potential energy than the balloon GAINS by rising. The process of exchanging helium low down with air higher up lowers the gravitational potential energy--the change due to the air "falling" downwards outweighs the change due to the lifting-up of helium.
(5) Now something not related to gravity: You have a car with a helium balloon floating in it, tied by a string to the floor. The car accelerates and its passengers are pushed backwards. What does the balloon do? Surprisingly, it moves FORWARD (yes, there have been physics students who actually tried it). EVERYTHING in the car is pushed back, including passengers, air and helium balloon. However, volume for volume, the air weighs more (or "has greater mass") than the balloon and therefore it gets ahead in the backward push, forcing the helium forward.
430. The Prime MeridianJust looked up in the internet and wanting to know the history of Longitude and latitude and the name or names of people who came up with it And if possible who came up zero at Greenwich. It is my brother in law who is really asking this question for quite some time. Many thanks in advance.
OK Tire & Auto Service
I do not have all the answers, though I found on
that the Royal Observatory at Greenwich was chosen as the location of the prime meridian in a conference in 1884. Before that, some countries preferred the longitude of their own capital cities, and I vaguely recall reading in a book by Jules Verne (probably 20,000 Leagues Under the Sea) of an offer by a captain to his French guest, to calculate his longitude from prime meridian of Paris (maybe that convention explains why France abstained in 1884). I vaguely recall that the meridian of the US Naval Observatory in Washington may also have been considered.
But the system of latitude and longitude probably started in astronomy, from what we call declination and right ascension, the equivalents of latitude and longitude on the celestial sphere (see
http://www.phy6.org/stargaze/Slatlong.htm#s10 and other parts of "Stargazers"). That started with the Babylonians dividing the circle into 360 degrees (so the Sun's position shifts by about one degree per day). Hipparchus and Ptolemy made star charts, and presumably used those units. On Earth however the corresponding system of latitude and longitude evolved only slowly--in part because measuring the Sun's elevation at sea only evolved slowly (see section #5b of "From Stargazers to Starships"), in part because of uncertainty about the true size of the Earth (section #8 there).
431. Is L2 in the Earth's Shadow?(from a Listserve discussion)
After our discussion of the Planck satellite and its position at the earth-sun Langrange point L2, and my conjecture that whether or not the earth totally shields the sun there depends only on the ratio of the densities of the earth and the sun (actually true only for fixed earth-sun mass ratio but very nearly independent of that ratio when it is very small, as it is for the earth-sun), I got curious what the ratio of densities has to be for a planet to shield a star at L2. I quickly worked it out...
... Thus the earth should block about 84% of the sunlight at L2. Perhaps astronomers should lobby for reducing the density of the earth by about 23.4% or so, which would then make the sun totally eclipsed by the earth at L2 for future WMAP and Planck satellites.
I did check the Wikipedia article on Lagrangian point and found it said about the earth-sun L2, "It is, however, slightly beyond the reach of Earth's umbra, so solar radiation is not completely blocked," though it did not say what fraction is blocked. ...
ReplyDear Don, Dmitry et al.
The distance to L2 is practically the same as for L1, derived in
It depends of the mass ratio m/M of (earth/Sun); that ratio can be derived from astronomical observation, and from that the average density can be calculated. We cannot measure density of Sun or Earth directly, since we cannot probe directly what is deep under the surface.
it is shown that the Earth's shadow forms a cone with apex angle equal to the angle subtended by the Sun. That angle changes slightly over the Earth's elliptic orbit (it's a bit greater in mid-winter, when the Sun is closer), but a value often cited is 1/2 a degree. If the solid Earth has a diameter 2R, the distance to the apex is approximately
2R/tan 0.5 deg = 229 R
The average distance to L1 or L2 is 236 R, so the statement in Wikipedia is borne out.
432. In what direction is Israel from NY?Hi:
New York is approximately at latitude 42° and Israel is approximately at latitude 30°. Logically, someone standing in NY and facing Israel should be facing southeast. A friend suggested that since the earth is a sphere he would be facing northeast. Is that correct?
Your friend is probably right--just look at some map showing how airlines fly from New York to Europe and Israel. They all start out in the north-east direction, following the coast as far as Newfoundland, and then gradually curve over to east and southeast.
Why? Intuitively, if latitude and longitude were like perpendicular (x,y) coordinates, you would expect the path to be directed to the southeast--like a straight line between start and end points on a world map in a Mercator projection. One COULD fly along that line, too, but because the Earth is a sphere, the curved path starting towards northeast is actually shorter.
The shortest path between two points on a sphere is a "great circle" whose plane passes through the center of the Earth. The path cuts the globe into two equal halves, and therefore half of it is north of the equator and half south of it. The path between New York and Israel is north of the equator, so it is in the northern half, which curves away from tits equatorial crossing towards the north pole, then past its middle curves back.
One could calculate the path exactly using vector products, but this is probably too much for you. There exists however a map projection--the gnomonic one--in which all straight lines are portions of great circles. It is not widely used, because it greatly distorts shapes; however, look up
and trace there the straight line from New York to Israel!
(The line from New York to Mecca is not much different: one wonders in which direction Moslems in the USA pray!)
ResponseFrom Wikipededia entry "Rhumb Line":
"Some Muslim groups in North America take the rhumb line to Mecca (southeastwards) as their qibla (praying direction) instead of the traditional rule of the shortest path, which would give a northeastward direction."
433. Is the World Overpopulated?(From a Listserve discussion)
Isn't it illogical to assume the carrying capacity of the earth is less than 6.5 billion? We're all here and still existing. If the planet is over capacity then the population would be decreasing due to over-capacity issues, but it's not. So, hunger, poverty, crime, drugs, and even health care problems are the result of something other than over capacity (probably greed for both money and power, which will only go away when the last human dies).
If we intelligent souls convince our peers to quit having children, then the only population growth will be among the ignorant that don't know or care about over-population. These are the ones most easily recruited by radical militant groups that would like to take away our freedom to be intelligent and forcibly enslave us to their belief system. Be careful what you promote, it may backfire on the human race (and the earth).
I am not sure if society can feed 6.5 billion mouths--and feed them well--without fertilizers and without the energy needed to create them (e.g. in fixing nitrogen). Maybe; but the problem could be more subtle.
Over 40 years ago an ecologist named John B. Calhoun
conducted an experiment. He created an environment in which laboratory mice had all they needed--food, clean water, straw for nests etc.--but were limited to a fixed space. For the 4 breeding pairs introduced to this "mousery", it was mouse paradise. But the population grew, doubling every 55 days, until more than 600 mice crowded the cage. Mice then grew neurotic, actually refused to reproduce and the population crashed.
In today's mega-cities--Mexico City, Cairo, Mumbai, Jakarta, Accra etc.--plain food may be available, but life is increasingly stressed by crowding. Remembering Dr. Calhoun's work, I wonder if such a mode of life is sustainable on the long run.
434. Magnetic energyI would like to ask one question.
Suppose we have magnetic coil (solenoid) or magnet. What will happen with the magnetic energy if we suddenly destroy (blast) the magnetic coil or the magnet? Is it going to work like a magnetic bomb (ELECTRO-MAGNETIC PULSE: EMP) or the magnetic energy will transform to other energies?
Thank you and waiting to get your reply...
ReplyYour question is simple, but its answer is not. What will happen depends on the way the coil is destroyed, and I am not completely sure of the details...
Plasma confinement machines (such as ITER) use very strong magnetic fields produced by coils which carry large currents. Such currents exert as strong outwards force, trying to stretch the coil: as you know, parallel currents attract, opposing currents repel --see story of Oersted and Ampére in
and each section of a circular coil faces a current flowing in the opposite direction, pushing it away.
For that reason, the conductors of large currents (including cold superconductors) may need strong supports to hold them in place. You might think that if those supports break, the sections of wire would fly outwards and the magnetic energy would become their kinetic energy.
Only... the moment the current stops, the force on the conductors also ends. The current won't stop immediately, because breaking it creates an enormous induced voltage
which tries to keep the current going. If the wire is torn (with air around), that voltage will create a spark across the opening, then a plasma (an electric arc), which will continue carrying the current, at least for an instant--somewhat like the arc which occurred when the space tether broke
( http://www.phy6.org/Education/wtether.html )
The air in that plasma is heated, and ultimately that heat energy also comes from the magnetic field. And a spark also radiates strong radio waves (which is why lightning crackles on AM radio).
It is complicated!
435. Magnetic Carnot CycleTwo questions about magnetism:
(1) Magnetic fields have energy, and different fields have different energies. In the very same way the warm body has bigger energy compare to a cooler one, so is it possible to make a Carnot cycle with magnetism? One magnet with lower magnetic field corresponds to cooled body and one with higher magnetic field corresponds to warm body.
(2) Is it possible to make magnetic batteries instead of electrical batteries?
ReplyCarnot cycles based on magnetic energy exist, generally using hysteresis, the "memory" of magnetic materials which makes the demagnetization curve different from magnetization. I looked up "Carnot cycle for magnetic materials" and articles exist, but they are usually not free, and I suspect they are not elementary. Am not sure whether hysteresis motors which drive (for instance) electric clocks may or may not use such cycles.
There do exist magnetic refrigerators, for cooling materials near the absolute zero temperature, difficult to do by other means.
About "magnetic batteries"--please remember that not much magnetic energy can be stored in, say, one kilogram of material. A one-kilo ballast coil in a fluorescent fixture stores enough magnetic energy to carry the lamp through half an alternating-current cycle (say, 1/120 second), but that is a rather short time. A one-kilogram battery stores much, much more energy. The biggest magnetic storage I remember was of the magnetic energy of a big particle accelerator in Brookhaven, New York, which exchanged energy with a heavy rotating wheel--see item #4 in
436. Defining the EquatorIs the definition of the Equator a convention or not? I'm writing to you from Brazil.
Geodesists say it is a convention because "it is given by definition" but in a website on astronomy, a teacher wrote to his pupil that it is not a convention, because it is "given".
Now, if the Earth's axis is imaginary, the poles are also a convention, as is cutting the planet in half by an equatorial plane perpendicular to the axis. One could cut the planet with diagonal or vertical imaginary lines, too.
So what is your definition, please?
ReplyWe are discussing here language, not science. All our concepts, and all words in the dictionary, are generated and defined by humans. Is "beauty" a convention, or is it "given by definition?" To some extent it is both, and so is the equator.
The Earth is shaped very close to a flattened sphere (a spheroid or ellipsoid), which has axial symmetry. This means, if you rotate all points by some angle around the axis, at the end they occupy the same positions. There exist two points where the axis cuts the surface ("the poles"). If you take the halfway point between the poles ("center of the Earth") and draw there a flat plane perpendicular to the axis ("equatorial plane"), the line where that plane cuts the surface is the equator.
That line existed even before humans were around to define it--but humans gave it a precise definition. To quote Humpty Dumpty (an egg-shaped character in a children's song, who also appears in a whimsical book by Lewis Carroll):
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