ARRHENIUS, WORLDS IN THE MAKING

thelivyjr
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Re: ARRHENIUS, WORLDS IN THE MAKING

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VII - THE NEBULAR AND THE SOLAR STATES, continued ...

About the bodies which have drifted into nebulae, and about the remnants of new stars which lie inside the nebulae, the gases will thus collect which had formerly been scattered through the outer portions of the nebula.

These gases originate from the explosive compounds which had been stored in the interior of the new stars.

Hydrogen and helium are, most likely, the most important of these; for they are the most difficult to be condensed, and can exist in notable quantities at extremely low temperatures, such as must prevail in the outermost portions of the nebulae, in which gases of other substances would be liquefied.

Even if the nebulae had an absolute temperature of 50 (-223 C.), the vapor of the most volatile of all the metals, mercury, would even in the saturated state be present in such a small quantity that a single gramme would occupy the space of a cube whose side would correspond to about two thousand light-years that is to say, to 450 times the distance of the earth from the nearest fixed star.

One gramme of sodium, likewise a very volatile metal, and of a comparatively high importance in the constitution of the fixed stars, would fill the side of a cube that would be a thousand million times as large.

Still more inconceivable numbers result for magnesium and iron, which are very frequent constituents of fixed stars, and which are less volatile than the just-mentioned metals.

We thus recognize the strongly selective action of the low temperatures upon all the substances which are less difficult to condense than helium and hydrogen.

As we now know that there is another substance in the nebulae, which has been designated nebulium, and which is characterized by two spectral lines not found in any terrestrial substance, we must conclude that this otherwise unknown element nebulium must be almost as difficult to condense as hydrogen and helium.

Its boiling-point will probably lie below 50 absolute, like that of those gases.

TO BE CONTINUED ...
thelivyjr
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Re: ARRHENIUS, WORLDS IN THE MAKING

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VII - THE NEBULAR AND THE SOLAR STATES, continued ...

That hydrogen and helium, together with nebulium, alone seem to occur in the vastly extended nebulae is probably to be ascribed to their low boiling-points.

We need not look for any other explanation.

The supposition of Lockyer that all the other elements would be transformed into hydrogen and helium at extreme rarefaction is quite unsupported.

In somewhat lower strata of the nebula, where its shape resembles a disk, other not easily condensable substances, such as nitrogen, hydro-carbons of simple composition, carbon monoxide, further, at deeper levels, cyanogen and carbon dioxide, and, near the centre, sodium, magnesium, and even iron may occur in the gaseous state.

These less volatile constituents may exist as dust in the outermost strata.

This dust would not be revealed to us by the spectroscope.

In the strongly developed spiral nebulae, however, the extreme layers, which seem to hide the central body, appear to be so attenuated that the dust floating in them is not able to obscure the spectrum of the metallic gases.

The spectrum of the nebula then resembles a star spectrum, because the deepest strata contain incandescent layers of dust clouds, whose light is sifted by the surrounding masses of gases.

It has been observed that the lines of the different elements are not uniformly distributed in the nebula.

Thus Campbell observed, for instance, when investigating a small planetary nebula in the neighborhood of the great Orion nebula, that the nebulium had not the same distribution as the hydrogen.

The nebulium, which was concentrated in the centre of the nebula, probably has a higher boiling-point than hydrogen, therefore, and occurs in noticeable quantities in the inner, hotter parts of the nebula.

Systematic investigations of this kind may help us to a more perfect knowledge of the temperature relations in these peculiar celestial objects.

Ritter and Lane have made some interesting calculations on the equilibrium in a gaseous celestial body of so low a density that the law of gases may be applied to it.

That is only permissive for gases or for mixtures of gases whose density does not exceed one-tenth of that of water or one-fourteenth of the actual density of the sun.

The pressure in the central portions of such a mass of gas would, of course, be greater than the pressure in the outer portions, just as the pressure rises as we penetrate from above downward into our terrestrial atmosphere.

If we imagine a mass of the air of our atmosphere transferred one thousand metres higher up, its volume will increase and its temperature will fall by 9.8 C. (18 F.).

If there were extremely violent vertical convection currents in the air, its temperature would diminish in this manner with increasing altitude; but internal radiation tends to equalize these temperature differences.

The following calculation by Schuster concerning the conditions of a mass of gas of the size of the sun is based on Ritter's investigation.

It has been made under the hypothesis that the thermal properties of this mass of gas are influenced only by the movements in it, and not by radiation.

TO BE CONTINUED ...
thelivyjr
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Re: ARRHENIUS, WORLDS IN THE MAKING

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VII - THE NEBULAR AND THE SOLAR STATES, continued ...

The calculation is applied to a star which has the same mass as the sun (1.9x10 grammes, or 324,000 times the mass of the earth), and a radius of about ten times that of the sun (10 x 690,000 km.), whose mean density would thus be 1000 times smaller than that of the sun, or 0.0014 times the density of water at 4 C.

In the following table the first column gives the distance of a point from the centre of the star as a fraction of its radius; the density (second column) is expressed in the usual scale, water being the unit; pressures are stated in thousands of atmospheres, temperatures in thousands of degrees Centigrade.

The temperature will vary proportionately to the molecular weight of the gas of which the star consists; the temperatures, in the fourth column of the table, concern a gas of molecular weight 1 that is to say, hydrogen gas dissociated into atoms, as it will be undoubtedly on the sun and on the star.

If the star should consist of iron, we should have to multiply these latter numbers by 56, the molecular weight of iron; the corresponding figures will be found in the fifth column.

Schuster's calculation was really made for the sun, that is to say, for a celestial body whose diameter is ten times smaller, and whose specific gravity is therefore a thousand times greater than the above-assumed values.

According to the laws of gravitation and of gases, the pressure must there be 10,000 times greater, and the temperature ten times higher, than those in our table.

The density of the interior portions would, however, become far too large to admit of the application of the gas laws.

I have therefore modified the calculations so as to render them applicable to a celestial body of ten times the radius of the sun or of 1080 times the radius of the earth; the radius would then represent one-twenty-second of the distance from the centre of the sun to the earth's orbit, and the respective celestial body would have very small dimensions indeed if compared to a nebula.

TO BE CONTINUED ...
thelivyjr
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Re: ARRHENIUS, WORLDS IN THE MAKING

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VII - THE NEBULAR AND THE SOLAR STATES, continued ...

The extraordinarily high pressure in the interior portions of the celestial body is striking; this is due to the great mass and to the small distances.

In the centre of the sun the pressure would amount to 8520 million atmospheres, since the pressure increases inversely as the fourth power of the radius.

The pressure near the centre of the sun is, indeed, almost of that order.

If the sun were to expand to a spherical planetary nebula of a thousand times its actual linear dimensions (when it would almost fill the orbit of Jupiter), the specific gravity at its centre would be diminished to one-millionth of the above-mentioned value that is to say, matter in this nebula would not, even at the point of greatest concentration, be any denser than in the highly rarefied vacuum tubes which we can prepare at ordinary temperatures.

The pressure would likewise be greatly diminished namely, to about six millimetres only, near the centre of the gaseous mass.

The temperature, however, would be rather high near the centre namely, 24,600 C., if the nebula should consist of atomatic hydrogen, and fifty-six times as high again if consisting of iron gas.

Such a nebula would restrain gases with 1.63 times the force which the earth exerts.

Molecules of gases moving outward with a velocity of about 18 km. (11 miles) per second would forever depart from this atmosphere.

The estimation of the temperature in such masses of gases is certainly somewhat unreliable.

We have to presume that neither radiation nor conduction exert any considerable influence.

That might be permitted for conduction; but we are hardly justified in neglecting radiation.

The temperatures within the interior of the nebula will, therefore, be lower than our calculated values.

It is, however, difficult to make any definite allowance for this factor.

If the mass of the celestial body should not be as presumed for instance, twice as large we should only have to alter the pressure and the density of each layer in the same proportion, and thus to double the above values.

The temperature would remain unchanged.

We are hence in a position to picture to ourselves the state of a nebula of whatever dimensions and mass.

TO BE CONTINUED ...
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Re: ARRHENIUS, WORLDS IN THE MAKING

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VII - THE NEBULAR AND THE SOLAR STATES, continued ...

Lane has proved, what the above calculations also indicate, that the temperature of such nebula will rise when it contracts in consequence of its losing heat.

If heat were introduced from outside, the nebula would expand under cooling.

A nebula of this kind presumably loses heat and gradually raises its own temperature until it has changed into a star, which will at first have an atmosphere of helium and of hydrogen like that of the youngest stars (with white light).

By-and-by, under a further rise of temperature, the extremely energetic chemical compounds will be formed which characterize the interior of the sun, because helium and hydrogen which were liberated when the nebula was reformed and which dashed out into space will diffuse back into the interior of the star, where they will be bound under the formation of the compounds mentioned.

The atmosphere of hydrogen and of helium will disappear (helium first), the star will contract more and more, and the pressure and the convection currents in the gases will become enormous.

There will be a strong formation of clouds in the atmosphere of the star, which will gradually become endowed with the properties which characterize our sun.

The sun behaves very differently from the gaseous nebulae for which the calculations of Lane, Ritter, and Schuster hold.

For when the contraction of a gas shall have proceeded to a certain limit, the pressure will increase in the ratio 1 : 16, while the volume will decrease in the ratio 8:1, provided there be no change in the temperature.

When the gas has reached this point and is still further compressed, the temperature will remain in steady equilibrium.

At still higher pressures, however, the temperature must fall if equilibrium is to be maintained.

According to Amagat, this will occur at 17 C. (290 absolute) in gases like hydrogen and nitrogen, which at this temperature are far above their critical points, and at a pressure of 300 or 250 atmospheres.

When the temperature is twice as high on the absolute scale, or at 307 C., twice the pressure will be required.

TO BE CONTINUED ...
thelivyjr
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Re: ARRHENIUS, WORLDS IN THE MAKING

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VII - THE NEBULAR AND THE SOLAR STATES, continued ...

We can now calculate when our nebula will pass through this critical stage, to which a lowering of the temperature must succeed.

Accepting the above figures, we find that half the mass of the nebula will fill a sphere of a radius 0.53 of that of the nebula.

If the mass were everywhere of the same density, half of it would fill a sphere of 0.84 of this radius.

When will the interior mass cross the boundary of the above stage, while the exterior portions still remain below this stage?

That will be at about the time when the nebula in its totality will pass through its maximum temperature.

We will now base our calculations on the temperatures which apply to iron in the gaseous state; for in the interior of the nebula the mean molecular weight will at least be 56 (that of iron).

We shall find that the pressure at the distance 0.53 will be about 177,000 atmospheres, and the temperature approximately 71 million degrees i.e., 245,000 times higher than the absolute temperature in the experiments of Amagat.

The specified stage will then be reached when the pressure will be 245,000 times as large as 250 atmospheres viz., 61 million atmospheres.

As, now, the pressure is only 177,000 atmospheres, our nebula will yet be far removed from that stage at which cooling will set in.

We can easily calculate that this will take place when the nebula has contracted to a volume about three times that of our sun.

The assertion which is so often made that the sun might possibly attain higher temperatures in the future is unwarranted.

This celestial body has long since passed through the culminating-point of its thermal evolution, and is now cooling.


As the temperatures which Schuster deduced were no doubt much too high, the cooling must, indeed, have set in already in an earlier stage.

But stars like Sirius, whose density is probably not more than one per cent, of the solar density, are probably still in a rising-temperature stage.

Their condition approximates that of the mass of gas of our example.

TO BE CONTINUED ...
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Re: ARRHENIUS, WORLDS IN THE MAKING

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VII - THE NEBULAR AND THE SOLAR STATES, continued ...

The planetary nebulae are vastly more voluminous.

The immense space which these celestial bodies may occupy will be understood from the fact that the largest among them, No. 5 in Herschel's catalogue, situated near the star B in the Great Bear, has a diameter of 2.67 seconds of arc.

If it were as near to us as our nearest star neighbor, its diameter would yet be more than three times that of the orbit of Neptune; doubtless it is many hundreds of times larger.

This consideration furnishes us with an idea of the infinite attenuation in such structures.

In their very densest portions the density cannot be more than one-billionth of the density of the air.

In the outer portions of such nebulae the temperature must also be exceedingly low; else the particles of the nebula could not be kept together, and only hydrogen and helium can occur in them in the gaseous state.

Yet we may regard the density and temperature of such celestial bodies as gigantic by comparison with those of the gases in the spirals of the nebulae.

There never is equilibrium in these spirals, and it is only because the forces in action are so extraordinarily small that these structures can retain their shapes for long periods without noticeable changes.

It is, probably, chiefly in those parts in which the cosmical dust is stopped in its motion that meteorites and comets are produced.

The dust particles wander into the more central portions of the nebulae, into which they penetrate deeply, owing to their relatively large mass, to form the nuclei for the growth of planets and moons.


By their collisions with the masses of gases which they encounter, they gradually assume a circular movement about the axis of rotation of the nebula.

In this rotation they condense portions of the gases on their surface, and hence acquire a high temperature which they soon lose again, however, owing to the comparatively rapid radiation.

TO BE CONTINUED ...
thelivyjr
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Re: ARRHENIUS, WORLDS IN THE MAKING

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VII - THE NEBULAR AND THE SOLAR STATES, continued ...

So far as we know, spiral nebulae are characterized by continuous spectra.

The splendor of the stars within them completely outshines the feeble luminosity of the nebula.

The stars in them are condensation products and undoubtedly in an early stage of their existence; they may therefore be likened to the white stars, like the new star in Perseus and the central star in the ring nebula of the Lyre.

Nevertheless, it has been ascertained that the spectrum of the Andromeda nebula has about the same length as that of the yellow stars.

That may be due to the fact that the light of the stars in this nebula, which we only seem to see from the side, is partly extinguished by dust particles in its outer portion, as was the case with the light of the new star in Perseus during the period of its variability.

Our considerations lead to the conclusion that there is rotating about the central body of the nebula an immense mass of gas, and that outside this mass there are other centres of condensation moving about the central body together with the masses of gas concentrated about them.

Owing to the friction between the immigrated masses and the original mass of gas which circulated in the equatorial plane of the central body, all these masses will keep near the equatorial plane, which will therefore deviate little from the ecliptic.

We thus obtain a proper planetary system, in which the planets are surrounded by colossal spheres of gas like the stars in the Pleiades (Fig. 52).

If, now, the planets have very small mass by comparison with the central body as in our solar system they will be cooled at an infinitely faster rate than the sun.

The gaseous masses will soon shrink, and the periods of rotation will be shortened; but for those planets, at least, which are situated near the centre, these periods will originally differ little from the rotation of the central body.

The dimensions of the central body will always be very large, and the planets circulating about it will produce very strong tidal effects in its mass.

Its period of rotation will be shortened, while the orbital rotation of the planets will tend to become lengthened.

Thus the equilibrium is disturbed; it is re-established again, because the planet is, so to say, lifted away from the sun, as G. H. Darwin has so ingeniously shown with regard to the moon and the earth.

Similar relations will prevail in the neighborhood of those planets which will thus become provided with moons.

Hence we understand the peculiar fact that all the planets move almost in the same plane, the so-called ecliptic, and in approximately circular orbits; that they all move in the same direction, and that they have the same direction of rotation in common with their moons and with the central body, the sun.

It is only the outermost planets, like Uranus and Neptune, in whose cases the tidal effects were not of much consequence, that form exceptions to this rule.

TO BE CONTINUED ...
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Re: ARRHENIUS, WORLDS IN THE MAKING

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VII - THE NEBULAR AND THE SOLAR STATES, continued ...

In explanation of these phenomena various philosophers and astronomers have advanced a theory which is known as the Kant-Laplace theory, after its most eminent advocates.

Suggestions pointing in the same direction we find in Swedenborg (1734).

Swedenborg assumed that our planetary system had been evolved under the formation of vortices from a kind of "chaos solare," which had acquired a more and more energetic circulating motion about the sun under the influence of internal forces, possibly akin to magnetic forces.

Finally a ring had been thrown off from the equator, and had separated into fragments, out of which the planets had been formed.

Buffon introduced gravitation as the conservational principle.

In an ingenious essay, "Formation des Planetes" (1745), he suggests that the planets may have been formed from a "stream" of matter which was ejected by the sun when a comet rushed into it.

Kant started from an original chaos of stationary dust, which under the influence of gravitation arranged itself as a central body, with rings of dust turning around it; the rings, later on, formed themselves into planets.

The laws of mechanics teach, however, that no rotation can be set up in a central body, which is originally stationary, by the influence of a central force like gravitation.

Laplace, therefore, assumed with Swedenborg that the primeval nebula from which our solar system was evolved had been rotating about the central axis.


According to Laplace, rings like those of Saturn would split off, as such a system contracted, and planets and their moons and rings would afterwards be formed out of those rings.

It is generally believed at present, however, that only meteorites and small planets, but not the larger planets, could have originated in this way.

We have, indeed, such rings of dust rotating about Saturn, the innermost more rapidly, the outer rings more slowly, just as they would if they were crowds of little moons.

TO BE CONTINUED ...
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Re: ARRHENIUS, WORLDS IN THE MAKING

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VII - THE NEBULAR AND THE SOLAR STATES, continued ...

Many further objections have later been raised against the hypothesis of Laplace, first by Babinet, later especially by Moulton and Chamberlin.

In its original shape this hypothesis would certainly not appear to be tenable.


I have therefore replaced it by the evolution thesis outlined above.

It is rather striking that the moons of the outermost planets, Neptune and Uranus, do not move in the plane of the ecliptic, and that their moons further describe a "retrograde" movement that is to say, they move in the direction opposite to that conforming to the theory of Laplace.

The same seems to hold for the moon of Saturn, which was discovered in 1898 by Pickering.

All these facts were, of course, unknown to Laplace in 1776; and if he had known them he would scarcely have advanced his thesis in the garb in which he offered it.

The explanation of these facts does not cause any difficulty.

We may assume that the matter in the outer portions of the primeval nebula was so strongly attenuated that the immigrating planet did not attain a sufficient volume to have the large common rotation in the equatorial plane of the sun impressed upon it by the tidal effects.

Charged only with the small mass of matter which they met on their road, the planet and its moon, on the contrary, remained victorious in the limited districts in which they were rotating.

Only the slow orbital movement about the central body was influenced, and that adapted itself to the common direction and the circular orbit.

It is not inconceivable that there may be, farther out in space, planets of our solar system, unknown to us, moving in irregular paths like the comets.

The comets, Laplace assumed, probably immigrated at a later period into our solar system when the condensation had already advanced so far that the chief mass of the nebular matter had disappeared from interplanetary space.

TO BE CONTINUED ...
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