Tag Archives: Mars

Why the earth is magnetic with the north pole heading south.

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The magnetic north pole, also known as true north, has begun moving south. It had been moving toward the north pole thought the last century. It moved out of Canadian waters about 15 years ago, heading toward Russia. This year it passed as close to the North pole as it is likely to, and begun heading south (Das Vedanga, old friend). So this might be a good time to ask “why is it moving?” or better yet, “Why does it exist at all?” Sorry to say the Wikipedia page is little help here; what little they say looks very wrong. So I thought I’d do my thing and write an essay.

The motion of the magnetic (true) north pole over the last century; it's nearly at the north pole.

Migration of the magnetic (true) north pole over the last century; it’s at 8°N and just passed the North Pole.

Your first assumption of the cause of the earth’s magnetic field would involve ferromagnetism: the earth’s core is largely iron and nickel, two metals that permanent magnets. Although the earth’s core is very hot, far above the “Curie Temperature” where permanent magnets form, you might imagine that some small degree of magnetizability remains. You’d be sort of right here and sort of wrong; to see why, lets take a diversion into the Curie Temperature (Pierre Curie in this case) before presenting a better explanation.

The reason there is no magnetism above the Curie temperature is similar to the reason that you can’t have a plague outbreak or an atom bomb if R-naught is less than one. Imagine a magnet inside a pot of iron. The surrounding iron will dissipate some of the field because magnets are dipoles and the iron occupies space. Fixed dipole effects dissipate with a distance relation of r-4; induced dipoles with a relation r-6. The iron surrounding the magnet will also be magnetized to an extent that augments the original, but the degree of magnetization decreases with temperature. Above some critical temperature, the surrounding dissipates more than it adds and the effect is that the original magnetic effect will die out if the original magnet is removed. It’s the same way that plagues die out if enough people are immunized, discussed earlier.

The earth rotates, and the earth's surface is negatively charged. There is thus some room for internal currents.

The earth rotates, and the earth’s surface is negatively charged. There is thus some room for internal currents.

It seems that the earth’s magnetic field is electromagnetic; that is, it’s caused by a current of some sort. According to Wikipedia, the magnetic field of the earth is caused by electric currents in the molten iron and nickel of the earth’s core. While there is a likely current within the core, I suspect that the effect is small. Wikipedia provides no mechanism for this current, but the obvious one is based on the negative charge of the earth’s surface. If the charge on the surface is non-uniform, It is possible that the outer part of the earth’s core could become positively charged rather the way a capacitor charges. You’d expect some internal circulation of the liquid the metal of the core, as shown above – it’s similar to the induced flow of tornadoes — and that flow could induce a magnetic field. But internal circulation of the metallic core does not seem to be a likely mechanism of the earth’s field. One problem: the magnitude of the field created this way would be smaller than the one caused by rotation of the negatively charged surface of the earth, and it would be in the opposite direction. Besides, it is not clear that the interior of the planet has any charge at all: The normal expectation is for charge to distribute fairly uniformly on a spherical surface.

The TV series, NOVA presents a yet more unlikely mechanism: That motion of the liquid metal interior against the magnetic field of the earth increases the magnetic field. The motion of a metal in a magnetic field does indeed produce a field, but sorry to say, it’s in the opposing direction, something that should be obvious from conservation of energy.

The true cause of the earth’s magnet field, in my opinion, is the negative charge of the earth and its rotation. There is a near-equal and opposite charge of the atmosphere, and its rotation should produce a near-opposite magnetic field, but there appears to be enough difference to provide for the field we see. The cause for the charge on the planet might be due to solar wind or the ionization of cosmic rays. And I notice that the average speed of parts of the atmosphere exceeds that of the surface —  the jet-stream, but it seems clear to me that the magnetic field is not due to rotation of the jet stream because, if that were the cause, magnetic north would be magnetic south. (When positive charges rotate from west to east, as in the jet stream, the magnetic field created in a North magnetic pole a the North pole. But in fact the North magnetic pole is the South pole of a magnet — that’s why the N-side of compasses are attracted to it, so … the cause must be negative charge rotation. Or so it seems to me.  Supporting this view, I note that the magnet pole sometimes flips, north for south, but this is only following a slow decline in magnetic strength, and it never points toward a spot on the equator. I’m going to speculate that the flip occurs when the net charge reverses, thought it could also come when the speed or charge of the jet stream picks up. I note that the magnetic field of the earth varies through the 24 hour day, below.

The earth's magnetic strength varies regularly through the day.

The earth’s magnetic strength varies regularly through the day.

Although magnetic north is now heading south, I don’t expect it to flip any time soon. The magnetic strength has been decreasing by about 6.3% per century. If it continues at that rate (unlikely) it will be some 1600 years to the flip, and I expect that the decrease will probably slow. It would probably take a massive change in climate to change the charge or speed of the jet stream enough to reverse the magnetic poles. Interestingly though, the frequency of magnetic strength variation is 41,000 years, the same frequency as the changes in the planet’s tilt. And the 41,000 year cycle of changes in the planet’s tilt, as I’ve described, is related to ice ages.

Now for a little math. Assume there are 1 mol of excess electrons on a large sphere of the earth. That’s 96500 Coulombs of electrons, and the effective current caused by the earth’s rotation equals 96500/(24 x3600) = 1.1 Amp = i. The magnetic field strength, H =  i N µ/L where H is magnetizability field in oersteds, N is the number of turns, in this case 1, µ is the magnetizability. The magnetizability of air is 0.0125 meter-oersteds/ per ampere-turn, and that of a system with an iron core is about 200 times more, 2.5 meter-tesla/ampere-turn. L is a characteristic length of the electromagnet, and I’ll say that’s 10,000 km or 107 meters. As a net result, I calculate a magnetic strength of 2.75×10-7 Tesla, or .00275 Gauss. The magnet field of the earth is about 0.3 gauss, suggesting that about 100 mols of excess charge are involved in the earth’s field, assuming that my explanation and my math are correct.

At this point, I should mention that Venus has about 1/100 the magnetic field of the earth despite having a molten metallic core like the earth. It’s rotation time is 243 days. Jupiter, Saturn and Uranus have greater magnetic fields despite having no metallic cores — certainly no molten metallic cores (some theorize a core of solid, metallic hydrogen). The rotation time of all of these is faster than the earth’s.

Robert E. Buxbaum, February 3, 2019. I have two pet peeves here. One is that none of the popular science articles on the earth’s magnetic field bother to show math to back their claims. This is a growing problem in the literature; it robs science of science, and makes it into a political-correctness exercise where you are made to appreciate the political fashion of the writer. The other peeve, related to the above concerns the game it’s thoroughly confusing, and politically ego-driven. The gauss is the cgs unit of magnetic flux density, this unit is called G in Europe but B in the US or England. In the US we like to use the tesla T as an SI – mks units. One tesla equals 104 gauss. The oersted, H is the unit of magnetizing field. The unit is H and not O because the English call this unit the henry because Henry did important work in magnetism.  One ampere-turn per meter is equal to 4π x 10−3 oersted, a number I approximated to 0.125 above. But the above only refers to flux density; what about flux itself? The unit for magnetic flux is the weber, Wb in SI, or the maxwell, Mx in cgs. Of course, magnetic flux is nothing more than the integral of flux density over an area, so why not describe flux in ampere-meters or gauss-acres? It’s because Ampere was French and Gauss was German, I think.

Chaos, Stocks, and Global Warming

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Two weeks ago, I discussed black-body radiation and showed how you calculate the rate of radiative heat transfer from any object. Based on this, I claimed that basal metabolism (the rate of calorie burning for people at rest) was really proportional to surface area, not weight as in most charts. I also claimed that it should be near-impossible to lose weight through exercise, and went on to explain why we cover the hot parts of our hydrogen purifiers and hydrogen generators in aluminum foil.

I’d previously discussed chaos and posted a chart of the earth’s temperature over the last 600,000 years. I’d now like to combine these discussions to give some personal (R. E. Buxbaum) thoughts on global warming.

Black-body radiation differs from normal heat transfer in that the rate is proportional to emissivity and is very sensitive to temperature. We can expect the rate of heat transfer from the sun to earth will follow these rules, and that the rate from the earth will behave similarly.

That the earth is getting warmer is seen as proof that the carbon dioxide we produce is considered proof that we are changing the earth’s emissivity so that we absorb more of the sun’s radiation while emitting less (relatively), but things are not so simple. Carbon dioxide should, indeed promote terrestrial heating, but a hotter earth should have more clouds and these clouds should reflect solar radiation, while allowing the earth’s heat to radiate into space. Also, this model would suggest slow, gradual heating beginning, perhaps in 1850, but the earth’s climate is chaotic with a fractal temperature rise that has been going on for the last 15,000 years (see figure).

Recent temperature variation as measured from the Greenland Ice. A previous post had the temperature variation over the past 600,000 years.

Recent temperature variation as measured from the Greenland Ice. Like the stock market, it shows aspects of chaos.

Over a larger time scale, the earth’s temperature looks, chaotic and cyclical (see the graph of global temperature in this post) with ice ages every 120,000 years, and chaotic, fractal variation at times spans of 100 -1000 years. The earth’s temperature is self-similar too; that is, its variation looks the same if one scales time and temperature. This is something that is seen whenever a system possess feedback and complexity. It’s seen also in the economy (below), a system with complexity and feedback.

Manufacturing Profit is typically chaotic -- something that makes it exciting.

Manufacturing Profit is typically chaotic — and seems to have cold spells very similar to the ice ages seen above.

The economy of any city is complex, and the world economy even more so. No one part changes independent of the others, and as a result we can expect to see chaotic, self-similar stock and commodity prices for the foreseeable future. As with global temperature, the economic data over a 10 year scale looks like economic data over a 100 year scale. Surprisingly,  the economic data looks similar to the earth temperature data over a 100 year or 1000 year scale. It takes a strange person to guess either consistently as both are chaotic and fractal.

gomez3

It takes a rather chaotic person to really enjoy stock trading (Seen here, Gomez Addams of the Addams Family TV show).

Clouds and ice play roles in the earth’s feedback mechanisms. Clouds tend to increase when more of the sun’s light heats the oceans, but the more clouds, the less heat gets through to the oceans. Thus clouds tend to stabilize our temperature. The effect of ice is to destabilize: the more heat that gets to the ice, the more melts and the less of the suns heat is reflected to space. There is time-delay too, caused by the melting flow of ice and ocean currents as driven by temperature differences among the ocean layers, and (it seems) by salinity. The net result, instability and chaos.

The sun has chaotic weather too. The rate of the solar reactions that heat the earth increases with temperature and density in the sun’s interior: when a volume of the sun gets hotter, the reaction rates pick up making the volume yet-hotter. The temperature keeps rising, and the heat radiated to the earth keeps increasing, until a density current develops in the sun. The hot area is then cooled by moving to the surface and the rate of solar output decreases. It is quite likely that some part of our global temperature rise derives from this chaotic variation in solar output. The ice caps of Mars are receding.

The change in martian ice could be from the sun, or it might be from Martian dust in the air. If so, it suggests yet another feedback system for the earth. When economic times age good we have more money to spend on agriculture and air pollution control. For all we know, the main feedback loops involve dust and smog in the air. Perhaps, the earth is getting warmer because we’ve got no reflective cloud of dust as in the dust-bowl days, and our cities are no longer covered by a layer of thick, black (reflective) smog. If so, we should be happy to have the extra warmth.

The martian sky: why is it yellow?

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In a previous post, I detailed my calculations concerning the color of the sky and sun. Basically the sun gives off light mostly in the yellow to green range, with fairly little red or purple. A lot of the blue and green wavelengths scatter leaving the sun  looking yellow because yellow looks yellow and the red plus blue also looks yellow because of additive color.

If you look at the sky through a spectroscope, it’s pretty blue with some green. Sky blue involves a bit of an eye trick of additive color so that we see the scattered blue + green as sky blue and not aqua. At sundown, the sun becomes reddish and the majority of the sky becomes greenish-grey as more green and yellow light gets scattered. The sky near the sun is orange as the atmosphere is thick enough to scatter orange, while the blue and green scatters out.

Now, to talk about the color of the sky on Mars, both at noon and at sunset. Except for the effect of the red color of the dust on Mars I would expect the sky to be blue on Mars, just like on earth but a lighter shade of blue as the atmosphere is thinner. When you add some red from the dust, one would expect the sky to be grey. That is, I would expect to find a simple combination of a base of sky blue (blue plus green), plus some extra red-orange light scattered from the Martian dust. In additive colors, the combination of blue-green and red-orange is grey, so that’s the color I’d expect the Martian sky to be normally. Some photos of the Martian sky match this expectation; see below. My guess is this is on a day when there was not much dust in the air, though NASA provides no details here.

martian sky; looks grey

On some days (high dust days, I assume), the Martian sky is turns a shade of yellow-green. I’d guess that’s because the red-dust absorbs the blue and some of the green spectrum, but does not actually add red. We are thus involved with subtractive color and, in subtractive color orange plus blue-green = butterscotch, not grey or pink.

Martian sky color

I now present a photo of the Martian sky at sunset. This is something really peculiar that I would not have expected ahead of time, but think I can explain now that I see it. The sky looks yellow in general, like in the photo above, but blue around the sun. I could explain this picture by saying that the blue and green of the Martian sky is being scattered by the Martian air (CO2, mostly), just like our atmosphere scatters these colors on earth; the sky near the sun looks blue, not red-orange because the Martian atmosphere is thinner (at noon there is less air to scatter light, but at sun-down the atmosphere is the same thickness as ours, more or less). The red of the dust does not show up in the sky color near the sun since the red-color is back scattered near the sun, and not front scattered. The Martian sky is yellow elsewhere where there is some front scatter of the reddish light reflecting off of the dust. This sounds plausible to me; tell me what you think.

Martian sky at sunset

Martian sky at sunset

As an aside, while I have long understood there was an experimental difference between subtractive and additive color, I have never quite understood why this should be so. Why is it that subtractive color combinations are different, and uniformly different from additive color combinations. I’d have thought you’d get more-or-less the same color if you remove red from one part of a piece of paper and remove blue from another as if you add red, purple, and yellow. A mental model I have (perhaps wrong) is that subtractive color looks like it does because of the details of the spectral absorption of the particular pigment chemicals that are typically used. Based on this model, I expect to find someday some new red and green pigments where the combination looks yellow when mixed on a page. I’ve not found it yet, but that’s my expectation — perhaps you know of a really good explanation for why additive color is so different from subtractive color.