2. Can the Earth's field be used for spaceflight?
Dear Mr. Stern:
I am an Industrial Technology teacher at a middle school
and one of my students is dreaming of a space propulsion system based on
magnetic repulsion of the earth's magnetic field. Could you possibly
squeeze in a moment for us and provide some information on the strength of this field and how it has been measured and maybe a relative comparison? Tyson, my student, is really excited about the Internet and will be enthralled to
have an answer from a NASA scientist. Perhaps you could steer him to
other references as I certainly will explain to him how busy a schedule
you must have. Thank you.
Reply
I am afraid it won't work. First of all, the magnetic field is very
weak. Compared to fields in electric machinery, where appreciable forces are
exerted, it is a few thousand times weaker.
But there is a more fundamental reason. Magnetic poles always come in pairs, equal and opposite: if a field attracts an N pole, it repels the attached
S pole. Similarly, if we generate the field by a current in a loop of wire
--say, shaped like a rectangle--for each side in which the current flows
in one direction, there exists a side where it flows in the opposite direction,
and the magnetic field exerts opposite forces of equal strength on the two
sides.
From the preceding one would guess that magnetic forces always cancel,
and no net force is exerted. So how come magnets are attracted to each
other, or pins to a magnet (same thing, really, since each pin in the magnetic
field turns into a small magnet)?
The answer is that the forces on the N and S poles (or on the opposing
currents) are not exactly equal, if one pole, or one wire, is closer to the
source of the field than the other. This can be put into a mathematical
formulation and the bottom line is that a suitably oriented magnet may be
attracted by a magnetic field, moving towards the greatest strength of that
field. But the force is proportional to the rate at which the field changes with distance, which in the case of the Earth, is very small.
The idea of magnetism as anti-gravity has come up before. Your student may
look up "Gulliver's Travels" by Swift, where in the third voyage, in a spoof
on science and learned societies, Gulliver arrives at an island floating
in the air, held there by the repulsion of a large magnet. Swift even
gives an explanation, except it's all gibberish gobbledygook, as befits a book
of satire. (I won't cite here the name of Swift's island, since too many
people in Texas speak Spanish!)
David Stern
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3. The Sun's Magnetic Poles
Dear Mr. Stern:
I have a question about the sun that I was hoping you might be able to
answer for me. A friend of mine recently returned from a new-age conference where it was presented that the magnetic poles of the sun were about to reverse, and cause a number of changes.
The idea of the sun having magnetic poles seemed counter to what I remember
learning about the sun, and your web page seems to dispel the idea that the
sun has actual poles. My guess is that the presenter was taking a dose of
creative license with the 11 year cycle of sunspot activity.
Is it true then, that:
1.) There are no magnetic poles on the sun.
2.) Is the change in sunspots related at all to a reverse of polarity of
magnetic fields?
Thank you.
If you can provide reference to a college-level text as a reference, it would
be appreciated.
Reply
Actually, your friend was right: the Sun does have polar
fields, and they do seem to reverse their polarity each sunspot cycle.
The Sun's most concentrated magnetic fields are of course in sunspots, but
people have long suspected there might also exist polar fields, because during
a total eclipse of the Sun one often sees streamers coming out from the polar
regions, looking very much like the pattern of iron filings near the poles
of a magnet.
But there was no good way of measuring such diffuse magnetic fields: the
field of sunspots affects the light emitted from them ("Zeeman splitting")
but the effect elsewhere is very weak. Then in the 1950s (if memory serves
me) the Babcocks pushed the technique to its limits and found the polar field.
This revealed the reversal of the polar magnetic field and suggested this field
was somehow coupled to that of sunspots (which also reverse each cycle--they
come in pairs, and the leading spot, in the direction of the Sun's rotation,
has north or south polarity, in alternate cycles), a sort of a cumulative
effect of the distant field of many spots. Theories exist by Horace
Babcock and Robert Leighton, though they are somewhat qualitative.
The fact the magnetic field lines at the poles stick straight out means they
do not hinder the escape of the solar wind in any way, and indeed the Ulysses
spacecraft which recently passed above the Sun's poles confirmed (as was
predicted) that the solar wind there is faster. There seems to exist no great
effect of the reversal on Earth, though one might expect a bit more magnetic
storminess when the polarity is opposite to that of the Earth.
For more on the Sun, see:
Yours,
David Stern
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4 Synchronous Satellites
Dear Dr. Stern:
I have been told, and read, that in order for a satellite to remain in a
fixed position relative to the earth, it must be in a synchronous orbit, and
that this type of orbit is best for communication purposes. All of the
other orbits I have read about are used by satellites with goals other than communication. Satellites in orbits other than synchronous are not fixed in position relative to the earth.
This being the case, it seems to me that all satellite dishes for reception
of TV signals would face the equator - south east, south west, or somewhere
between. My observation of satellite dishes does not seem to support this
concept. Many dishes do have a southerly inclination, but others do not.
Further, here, where we are close to the equator, it seems to me that in
order to focus on a satellite, the dish should be aimed high - higher, at
least, than one located in the USA or Canada where the angle between the
earth and the satellite would be smaller than here in Barbados. Many dishes
here seem to follow a line of sight that is barely above the horizon.
So, my question - are all communication satellites in fixed orbits above the
equator, and if so, why don't all reception dishes face the same way?
As I said at the outset, I know that I am being brash in writing you, and I
would appreciate your indulgence. Over the past year or so, I have asked at
least a half dozen engineers for an explanation, and received little more
than a blank stare in response. Access to other resources here is not
always easy. If you are unable to take the time for an explanation, perhaps
you would direct me to a source that could satisfy my curiosity.
If you do reply, please bear in mind that I am an accountant, not an astronomer.
Reply
I am very glad to hear from you, to find someone as far
away as Barbados interested in satellites, but I have no good answer to
your question. It is absolutely true that all commercial communication
satellites orbit above the equator, at a distance of 6.6 Earth radii,
with a 24-hour period, which keeps them above the same station. You know
probably that the space shuttle and other low-altitude spacecraft
complete one orbit in about 90 minutes: the further out you go, the longer
it takes, until you reach the moon, which takes one month. So it stands
to reason that somewhere in that range the orbital period is exactly 24 hours.
If a 24 hour orbit is inclined to the equator, the satellite does not stay
above the same spot but wanders back and forth: so it must be an equatorial
orbit. Only then can the antenna on the ground be fixed in one position.
It is true, however, that not all satellites tracked from Barbados are
at the longitude of the island. To receive phone calls from Europe, say, it could be that a satellite is tracked which is orbiting at the longitude of Europe, and then the dish should point towards the southeast.
I do not know how you reached my name; maybe you were directed by a search engine to the file.
http://www.phy6.org/Education/wsynch.html
I hope you are aware that this is only one part in a much larger exposition, the Exploration of the Earth's Magnetosphere, dealing with the Earth's magnetic environment, with its home page at
http://www.phy6.org/Education/Intro.html
You might look it up. Also try:
http://www.phy6.org/Education/wlagran.html
dealing with satellites keeping a fixed position (or staying close to one)
relative to the Earth in its orbit around the Sun.
David P. Stern
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5. Magnetic Field Lines
Mr. Stern,
I am enjoying your presentation on magnetospheres very much and I am
finding it most interesting and informative. However, I have one
question that I have not found an answer to yet.:
If the earth's magnetic lines of force are in fact "lines" upon which
electrons and protons can collect like "beads on a wire", what is the
spacing between these lines say, at the altitude of the recent Tethered
Satellite experiment?
Some co-workers and myself have had a rather heated discussion on this
matter (i.e. whether the magnetic lines are "lines" or a "field"). We
would be most greatful if you would enlighten us about these magnetic
lines of force around our planet just a little more than you have in
your presentation on the Goddard Home Page on the WEB.
Reply
Be very careful here! Magnetic field--space modified by
magnetic forces, so to speak--is one thing, and magnetic field lines are something else again. They are a mathematical description of that field, no more tangible than lines of latitude and longitude which describe the surface of the Earth. One never asks how close THOSE lines are; you can draw any number of them, depends how tightly you are willing to space them.
Magnetic field lines are defined as lines that point everywhere along the magnetic force (in a fluid, a complete analogy is given by flow lines or "streamlines"). They can be described by formulas, in terms of quantities known as Euler potentials or Clebsch functions.
But there also exist intuitive properties: particles threaded by a common
field line, tend to share that field line later on as well. Say we have 10
ions numbered 1... 10 sitting on a common spot on the Sun, and therefore
sharing there a field line, and destined to come out in the solar wind
one day apart. The Sun rotates, so make a drawing with a circle representing
the Sun and 9 radial lines coming out about 15 degrees apart. After 10 days,
particle #1 is 2.5 inches along the first line, particle #2 2.25 inches on
the 2nd one, and so on, down to particle #10 still on the surface: the line
conecting the particles is a spiral, so we expect interplanetary field lines
to have a spiral shape, and we derived this from intuitive concepts alone
(though the same thing can be derived from formulas).
The details of this excercise are described in http://www.phy6.org/stargaze/Simfproj.htm.
The spacing between field lines is not meaningful (though some engineers speak of "density of magnetic field lines" to describe a quantity commonly known as "flux density.") Suppose you draw two
field lines of the Earth, reaching Earth 1 meter or 1 foot apart. Each can
have electrons or ions trapped around it. The meaningful question is what is
the radius of the circle these electrons or ions describe around their guiding
line, and that depends on their energy, and how strong the field is (the circle
gets larger in the weak fields far from Earth), but it is generally much more
than 1 foot or 1 meter. No problem: densities are so low that such ions or
electrons rarely collide, and their orbits can easily overlap. The radius of
gyration of auroral electrons can be 100 meters, which is why auroral "curtains"are so thin. On the other hand, solar wind ions entering near the "nose" of the magnetosphere have radii of the order of 500 kilometers, or (say) 350 miles, because the field there is much weaker, and that is therefore the order of the expected thickness of the magnetopause, the boundary between the solar wind and the magnetosphere.
David P. Stern
6. The Solar Wind
To David P. Stern:
Hello David, I liked the WWW article on The Solar Wind-History. In the
article it said:
"Not everyone accepted Parker's theory of the solar wind when it was first
published in 1958, and it was debated until observations confirmed it."
Have you ever heard of the book OAHSPE by John Ballou Newbrough copyright 1882? Oahspe means Earth, Sky, and Spirit. Oahspe contains much scientific information that was discovered many years later, such as the earth's magnetosphere, Van Allen Radiation Belts, the SOLAR WIND, the origin of stars in nebula, the configuration of galaxies, the beginning substance of
life(DNA) in nebula, the cycle and age of galaxies and the stars they
contain, interstellar and intergalactic Unseen matter(Dark matter). Oahspe
says the Sun has a vortex that streches throughout the solar system.
Scientist have some knowledge of the Sun's vortex, they call it the "Solar
Wind'. .... (most of the letter omitted)
Tell me what you think about it. Please send me a reply email. Hope to hear from you soon.
Reply
I am sorry to have to disagree with you, but just coming out with a
statement which is later verified is not a prediction, unless it is supported
by cogent arguments, which distinguish it from similar predictions which
were not verified. That's the essence of the scientific method: what we believe
to be true is based on a tight interlocking web of observed evidence. The first
evidence for the solar wind came from comet tails, whose behavior had been
explained by sunlight pressure: it took a lot of physics to understand why
this process worked on dust tails, but not on ion tails. Parker's theory
was based on the high temperature of the corona, discovered in 1939 or so,
and again involved some intricate physics.
The solar wind, by the way, is not a spiral: it flows straight out. Only
the Sun's magnetic field lines are spiral, because the sun rotates: they
tend to act like continuous strings, and since their "roots" rotate with
the Sun, they get twisted into spirals.
David Stern
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7a. Explaining the Geiger Counter
Hi, I am a 10th grader ...I came across a web site ... in my search for how a
geiger counter meter works. I was hoping you could give me a relatively simple yet good explanation of how it works (preferably, really simple). I'd appreciate it very much.
Thank you.
Reply
And I thought "Exploration" did give a simple explanation!
Imagine a fast ion or electron going through the tube. On its way it hits atoms
of the gas in the tube and ionizes them--knocks off electrons and leaves
positive ions. Usually, such electrons recombine soon. But if there is a
voltage difference (electric field) in the tube, before they can do so, the
electrons will start moving towards the positive wire and the ions towards the
negative walls.
As they move, they gain energy. This is particularly true near the wire,
where the electric field is concentrated and its force is strong. (One can draw
electrical field lines just like magnetic field lines, and near the wire they
bunch together, like magnetic field lines near the poles of a magnet.)
If the energy gained by the average electron is enough to knock out additional
electrons from atoms of the gas with which it collides, the number of
electrons will multiply. As the electrons move towards the wire
and the field gets strong, this process grows quickly: one electron frees up two, two release four, and by the time the wire is reached, many more electrons arrive than were released by the initiating particle, enough to draw a measurable current and create a signal in the circuitry attached to the counter.
There is much more, of course, e.g. ultraviolet light which spreads the
process away from the wire as well, which could cause the current to continue
without stopping even after all the initial electrons (and the additional
electrons caused by them) have reached the wire. Special gas filling takes care
of that.
The counter is usually charged by just a trickle of current from a high
voltage source, so that the current taken by the discharge is easily measured.
If too many particles pass through the tube, too much current is drawn, the
voltage drops and the discharges get smaller, until the electronic circuits
supposed to count them don't do so any more. I think that's what happened on
Explorer 1.
David Stern
7b. Building a Geiger Counter
Hello!
I found your web-site in the internet. But I have still two questions.
1. Which gas is suitable?
2. Which pressure is in the metal tube(vacuum?)?
Please can yuo send me a wiring diagram from a geiger counter.
Best regards
Matthias
Reply
Dear Matthias
I did my thesis work with Geiger
counters, but that was 40 years ago and my memory of that time is
sketchy. If you have a local university with a physics department,
it (or at the very least, its library) could provide you with much
better and much more up-to-date information. Here is what I remember
- You should understand, of course, that if the Geiger counter
is a metal tube, the end plugs must be glass, with a tight
metal-to-glass seal, because the central wire must be insulated
from the tube. Or else, the whole thing is inside glass, and
the tube nowhere touches the wire.
- When a particle passes inside, it creates ions and initiates a discharge.
But you don't want the discharge to get too big. As noted, the counter has two main parts, insulated from each other--a cylindrical metal tube and a thin wire through its middle. The two act like a small capacitor, a device that holds an electric charge when a voltage exists between its two parts. For example, the tube may be connected to the ground (voltage zero) and the wire may be charged through a lerge resistor (which only allows a small trickle of current to flow) to some high positive voltage, say 1000 volts; the exact number depends on the design of the counter.
- Now when the counter discharges, the electric charge from the wire jumps over to the tube, and the voltage between the two momentarily drops down--not to zero (the discharge is never complete) but by a few hundred volts. A small additional capacitor can transmit that jump to an external circuit, which registers a "count." Afterwards the counter is "dead" (insensitive) for a small fraction of a second, while the capacitance between the wire and cylinder refills to its operating voltage of 1000 volts.
- The trick with the counter, if I remember, was for it not to
go into a continuous discharge. The filling, at a pressure of a
few tens of milibars, was either alcohol vapor or halogen.
Alcohol stopped the discharge by itself, but was gradually
broken up by the discharges, so that the counters had a certain
lifetime. Halogen--I don't remember what it was--chlorine?--
lasted longer but needed an external electric circuit to give
it a large negative pulse and shut it off, after each discharge.
In either case, the voltage was critical--too big, it went into a
continuous discharge, too small, the pulses were small, too, in
what is known as the "proportional counter" regime. Today many
people prefer proportional counters, since the electronics can
amplify the pulses very well. But 40 years ago it was good to
have a detector whose output pulse was big enough without any
amplification. The pulse was carried out through a small
capacitor, which let the pulses through to whatever counting
circuit was used, but kept out the high voltage.
I hope all this is useful. Sometimes simple questions lead to complicated
answers!
Yours
David P. Stern
7c. Who was Hans Geiger?
Hi
My name is Matt and I am a High School student in Corona, CA. I was recently assigned to do a report on a scientist. I found Hans Geiger interesting, and I picked my topic to be about his work.
Reply
Hans Geiger was a young German assistant to Ernest Rutherford (about whom you might have found and written much more!). Together with Ernest Marsden he helped Rutherford in his famous experiment which established the existence of a heavy, positive nucleus at the center of each atom. That was in Manchester, in 1909, and you can read about it in "Giant of the Atom," a biography of Rutherford for young readers by Robin McKown, first published in 1962 (your library may have it).
You might also find some about his work in the beginning chapters of
The Making of the Atomic Bomb" by Richard Rhodes and "From X-rays to
Quarks" by Emilio Segre (look him up in the indexes).
Later he devised the "Geiger counter" instrument and helped deduce
laws of radioactive decay.
#7d Questions connected to the Geiger Counter
Hello Dr. Stern,
Please answer to my following questions. My father couldn't help me. I am very happy now to know you.
- The initial electrons create an avalanche in Geiger Counter. I don't want to disturb the avalanche. Will this avalanche remain even when the initial electrons are stopped, providing enough atoms are existing in the tube?
- Geiger counter need over 1000 volts. How is it possible to create this high voltage in a small handy counter. What is actually the electrical consumption of these counters?
- I assume the avalanche is a mixture of electrons and ions. Using two different metals, installed in the Geiger Tube, can I separate the electrons and ions out of each other? In other words absorbing two opposite charges using two different materials. How sounds it if I use a magnet for separation and direct the opposite charges to those different metals?
- How many electrons or ions roughly create an avalanche?
- If "Z" is the number of electrons in an avalanche then I can say there is a negative charge of Z x 1.602 x 10–19 which I can use it as a potential energy(?)
- If in vacuum the alpha particles strike a metal, this metal gets positively charged?
Your answers will be greatly appreciated. These questions bother me every night when I lie in bed.
Reply
Your message was very much appreciated. You must be fairly young, or else you might have asked not your father but your physics teacher or professor. Yet what you ask are demonstrate thought and understanding). I hope you will continue to pursue your science interests, because you seem to have what it takes. I will try to answer, but please remember, I am no expert.
- You can assume enough atoms exist in the tube--after all, their number does not change. As some get electrons separated to become ions, other ions recombine.
The avalanche is complicated. It occurs mainly near the central wire, where the electric force is concentrated in a narrow region and is therefore strong (similarly, if a metal object has sharp spikes and you charge it electrically, the electric force is strongest near the spikes, and that's where sparks are most likely). The process also involves ultra-violet emissions, and these can make create a "continuous discharge," for a long time. You of course do not want that to happen.
All sorts of effects can be used to end the discharge. If the capacitor which stores the high voltage is only filled by a small trickle (through a big resistor), the discharge may drain it and lower its voltage, to where the avalanche stops. Or else, an electric circuit can sense the discharge and forcibly lower the voltage. This has the same effect, but produces less "dead time," during which the counter waits for the capacitor to fill up again and is therefore temporarily inactive (I built such circuits as graduate student, at the time of Sputnik 1, in 1957). Or else, a filling gas (alcohol or chlorine, I vaguely recall) absorbs the ultra-violet and stops the discharge.
- To produce 1000 volts, you usually need (a) an oscillator circuit to create a high-frequency alternating current (AC); (b) a transformer converting the AC to a higher voltage (with smaller current flow); and (c) a rectifier, which only lets current flow in one direction and converts 1000v AC to single-direction 1000v current. That current still has fast ups and downs, but as noted, it is only used to fill a capacitor, and once that is full--like a cup filled to the brim--its voltage stays almost at the same level.
The electric current needed is very small--just to fill and empty a relatively small capacitor. The problem is that both transformer and capacitor need pretty good electrical insulation.
- Look up some book about electrical discharges and discharge tubes. A neon light is such a tube--nothing more than a glass tube with some low-pressure gas in it, and two electrical contacts at the ends.
If you connect one end to the ground and the other to a voltage of (say) +1000volt, a current will flow (and light will be emitted). That is more like the situation you address in your question--it keeps going, does not operate in pulses. The fluorescent tube is also similar--see
http://www.phy6.org/Education/wplasma.html
http://www.phy6.org/Education/wfluor.html
In the tube ions and electrons are constantly separated. Electrons then travel to the (+) contact and ions to the (–), where they pick up an electron and become normal atoms again (the electrons at the (+) help complete the circuit). Appreciable numbers of ions and electrons, however, cannot stay separated without an enormous voltage to keep them apart.
- I don't know. Many.
OK, let me try a rough estimate. However, I will have to use scientific notation and electric terms which you may only learn later.
Say the size of the capacitor is about 1000 picofarad, or 10–9 farad. It is charged to 1000v, so multiplying the two we get the electric charge, 10–6 coulomb.
If the capacitor gives up (say) 10% of its charge, dropping from 1000v to 900v before the discharge stops, then the counter releases a charge of 10–7 coulombs.
The charge of a single electron is about 1.6 10–19 coulomb (see your next question). So the number of electrons needed to carry the charge is obtained by dividing
[10–7 / 1.6 10–19] = 6.25 1011 = 625,000,000,000
That is, 625 billion: the estimate may be inaccurate, but whatever it is, the number is obviously BIG.
- You also need multiply by the voltage--coulombs times volts gives energy in joules. Strictly speaking, the voltage drops during the discharge, so if you use 1000v, you have a slight overestimate.
- If an alpha particle strikes an insulated body in a vacuum, the body's positive voltage will indeed rise. In practice, if an appreciable stream of alphas is hitting, the voltage quickly gets positive enough to pull electrons from the surroundings, and the effect quickly levels off. (If somehow not enough electrons are available--theoretically possible, practically unlikely--the voltage will rise to where arriving alphas are repelled, and no more charging takes place.)
In space (best vacuum we have) the problem is not so much arrival of ions but of electrons. Spacecraft can then charge up to 50 or 500, even 5000 volts (in the aurora). That may not only confuse scientific instruments, but also damage electronics, when different parts charge to different voltages and a surge jumps between them.
OK. Now sleep soundly!
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8. Measuring the Earth's Magnetic Field
I am doing a sixth year studies project on magnetism in and was delighted to
find the question and reply page with topics similar to what I had thought of
studying.
I was wondering if there was a practical method for measuring the strength and direction of the Earth's magnetic field at different geographical locations.
Any help or inspiration would be greatly appreciated.
Reply
Is your "sixth year" in school or 6th year in college? It is not easy
to tailor an answer to fit either level!
In any case, the electronic gizmos nowadays used in space are too complicated
for a quick discussion, so let me instead describe earlier, simpler methods.
The direction of the magnetic field is of course given by the compass needle:
but that is just the horizontal part of the force, Actually the magnetic force
also points i n t o the Earth (or out of it, in the southern hemisphere).
To find the angle at which the force points down ("dip angle") people used a
needle similar to a compass needle, but on a horizontal axis, allowing it to
swing in the various directions to which the hands of a wall clock might point.
That is a bit harder to arrange than a compass needle: if one end of such a
needle points at an angle downwards, how is one to know whether the magnetic force is responsible, and not, say, that the needle is not quite balanced on its pivot, but that one end is slightly heavier and therefore points downwards? To avoid this problem one starts with an unmagnetized needle, balances it very
carefully, and only then magnetizes it. When in 1831 the expedition of John
Ross searched for the north magnetic pole, it carried along a dip needle, and
when it pointed straight down (while the regular magnetic needle showed no
preference for any direction), that was it .
Measuring the strength of the field is harder. Take a thin long bar magnet
and hang it by a thin thread, then wait until it points north-south. After it
does, push one tip slightly left or right and let go: it will swing back to
north-south, but will overshoot to the other side, then turn back to the right
direction, swinging back and forth like a pendulum, gradually quieting down to point steadily. The average length of each swing depends on two things: the
strength of the bar magnet and the strength of the magnetic force. With a
stopwatch, measure 20 swings or so and figure out how long each swing takes.
Then put a small compass needle on a table, and put the small magnet nearby,
in such a position that it tries to line up the compass to point east-west.The
small magnet and the Earth's magnetic force obviously compete fordetermining which way the needle points, and by looking at the actual angle of the needle, and its distance from the small magnet, we again get an observation that depends on how strong are (1) the small magnet and (2) the magnetic attraction of the Earth. Using these two observations and some calculation, the physicist can find both these unknown quantities.
This method was proposed by Carl Friedrich Gauss in Germany around 1835. It
obviously won't work on an orbiting satellite--but how measurements are made there is another story altogether.
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9. The Strength of the Earth's Magnetic Field
Could you please send me any information regarding the current field strength of the earths electromagnetic field? My data is current as of 1975 which is by far outdated. My reading from that time were 30,000 gammas at the equator. If possible could you please send information on the current decay of the earth's magnetic field.
Any information would be greatly appreciated.
Reply
I am not sure at what type of information you need, or to what
use you put it. The most complete information on the Earth's internal magnetic field is in form of a set of coefficients, to be plugged into a mathematical representation--the so-called spherical harmonic expansion. The coefficients generally used are the so-called IGRF set (International Geomagnetic Reference Field) chosen by a committee every 5-10 years and based on the "best available" observations. You can find them on the world-wide web at
http://fdd.gsfc.nasa.gov/IGRF.html
Some of these models also include the annual change of the field (but not in the above files). You might like to search the web using (say) the Altavista or
Yahoo search engine, on the term IGRF.
If you just want maps of the field, for instance those describing, the variation of its strength over the globe, try
http://swdcwww.kugi.kyoto-u.ac.jp/igrf/index.html
Clicking on the map of horizontal intensity in Mercator projection (use GIF format, which web browsers read) will show you that the horizontal intensity around the equator varies quite a bit. but 30,000 gamma (or nanotesla, same thing) is a reasonable value. A central dipole field would be horizontal at the equator; the average total intensity is somewhat larger (32500 is a good average) but that may be due to by non-dipole components.
The field has been weakening since Carl Friedrich Gauss measured it around 1836, by about 5% per century, recently accelerating to 7%/century. The decrease in the dipole field is however accompanied by a growth of the non-dipole (=more irregular) components, as shown by Benton and Voorhies. This means that the field is not really weakening, just reshuffling its field linesy, reducing the "main dipole" (=north-south bar-magnet pattern, declining as noted by about 7% per century) and reinforcing the more complicated parts.
These tend to contribute a weaker field, because the magnetism originates in
the Earth's core, about half an Earth-radius down: all magnetic fields at the
surface are weaker than those in the core, because of the distance, but the more complicated fields decrease faster.
Whether the main dipole will reverse in about 1300 years is anyone's guess.
Geological evidence suggests it has happened in the past, but odds are against
it, because the mean frequency of such reversals in the past seems to be about
once in 500,000 years.
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10. Solar Eclipses
I'm working on a science project about the solar eclipse.
My first question is, how can you figure out exactly when the next
eclipse will come?
The next question is: What are the main theories about the incredible
heat of the corona? How can it be so warm when it's so far away from
the sun's center?
Reply
Dear Lars
Predicting eclipses is relatively straightforward, you just need
to know the motion of the Sun and Moon across the sky, and when they
occupy the same area, you get an eclipse.
By now we have pretty good formulas for the orbital motion of the Earth
around the Sun (which determines where the Sun is in the sky) and of the moon around the Earth, and can predict eclipses quite accurately. The journal
"Sky and Telescope" usually carries accurate maps of where the eclipse can
be seen (if the sky isn't cloudy) and the times when it should happen. The
journal also maintains an eclipse page on the web, at:
http://www.skypub.com/eclipses/eclipses.shtml
The heat of the corona is still a great mystery. I can describe to you
one theory, but it is probably not the right answer.
When you walk along a beach, you usually see fairly large waves, breaking
on the seashore. If you take a boat past those waves, you are likely to
find that in deeper water the waves almost disappear, or anyway are much
smaller. Why?
It happens because a traveling wave carries a certain amount of energy,
which causes the water in the wave to rise and fall again. As the wave moves
into shallower water near the shore, the same energy now moves a smaller
amount of water: if energy is conserved, the motion must be bigger, which is
why waves become higher. Finally, the water is not deep enough for the
wave to keep going, and the wave breaks, giving up its energy all at
once to irregular swirling of the water.
Some scientists have speculated that waves, perhaps similar to sound
waves, rise from the surface of the Sun into the corona. They carry much
less energy than sunlight, but as they rise, the density of the gas
around them quickly decreases, until finally they reach a height at which
not enough gas is left to carry the wave: it then gives up its energy,
and since that energy is given to the surrounding gas, and there is very
little such gas left at those heights, that remaining gas gets very hot.
That at least was the theory some time ago: however, scientists now know
what sort of waves can move in the atmosphere of the Sun, and they say
that such waves get reflected back downwards before they reach high
enough for this process to happen. So we really don't know.
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12. Cosmic Rays
After reading your cosmic rays report, my friend and I decided that I
would like to do a science project on cosmic rays.
However, we are only eighth grade students, and therefore do not have much background on the subject. It would be much appreciated if you could provide us with some background on cosmic rays, and perhaps with a science project we could perform.
Reply
Actually, you can find quiet a bit of material about cosmic
rays in "Exploration," including material you need to understand more
advanced discussions of cosmic rays.
I would recommend that you and your friend use the "index" file and
reach from there the following files, in the order listed here:
Electrons, Positive Ions, Energy, Energetic Particles, The Geiger
Counter, Cosmic Rays, High Energy Particles, Solar Energetic Particles.
Copy them on paper, if you can. Of course, if some items are not comp-
letely clear, you will need to look up other sections as well.
In general, our study of cosmic rays can be divided into two phases.
The first started in 1912, with the discovery that some unknown radiation,
similar to the one emitted by radioactive materials, was reaching Earth from
space. Gradually, it was identified--first as electrically charged
particles, by the fact the Earth's magnetic field excluded some of it
from near the equator (around 1922). Then it was found that the particles
had positive charge--because the field affected unequally those coming from
the east and from the west (around 1936). Finally, around 1947,
photographic plates in balloons at high altitudes recorded tracks of
individual particles, finding they were familiar ions--mostly hydrogen,
some helium, and a scattering of heavier stuff, not too different from
the composition of the Sun.
Scientists also found out much about the fragments produced when
these particles hit the atmosphere (what we get on the ground is almost
entirely fragments) and measured the particles' energy distribution. It
turned out that some of them had phenomenal energies, raising the question of what process could provide them. But looking for the source of the rays proved elusive: it was like trying to observe the Sun in a heavy fog. In a fog
sunlight gets scattered until it comes evenly from all directions, leaving no
clue about where the Sun actually is. Similarly, cosmic rays seem to
be thoroughly scattered in space, arriving equally from all directions. It
is true that it is hard to bend the path of particles with such high
energies, but the energies meet their match in the great distances of space:
even a weak magnetic field can bend the path of a cosmic ray proton, if
it acts gradually over cosmic-scale distances.
So these days the emphasis is on tracing the source of x-rays and gamma-rays, high-energy relatives of visible light, which move in straight lines no matter what happens and therefore tell where they come from. It takes a high-energy particle to produce a high-energy gamma-ray, so observing the sources of such rays tells us where in the universe high-energy particles are plentiful, and perhaps these are cosmic rays near their sources. The catch is that (1) these gamma rays do not penetrate the atmosphere well, so the observation must be done from satellites, and (2), their intensity is much weaker than that of cosmic rays. Still, we have been looking, and discovering (e.g. see the story of gamma ray bursts in "Exploration"). Currently NASA has a gamma-ray observatory in orbit, doing a nice job. This area of research goes by the name of high energy astrophysics.
I don't know how much beyond this an eighth-grader can go. The "Resources" section lists some files you might look up, e.g. on high energy astrophysics, and a book "Moments in the Life of a Scientist" by Bruno Rossi, Cambridge 1990
Bruno Rossi was a pioneer of cosmic ray research and this is his own story.
He began in Italy as part of the talented group which included Enrico Fermi
and Emilio Segre, and died a few years ago as a much-honored professor at
the Massachussetts Institute of Technology.
Another book, by a pioneer of x-ray astronomy which covers that aspect
as well as the rest of astronomy, is "The Astronomer's Universe" by
Herbert Friedman, W.W. Norton, 1990.
Finally, your own country of Canada has contributed significantly to the
study of cosmic rays. Perhaps the science museum in Ottawa can help you.
Good luck!
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