Origin of the Solar System

Cosmogony is a branch of astronomy which studies the origin of the solar system. The first steps of the planetary formation processes are closely connected to star formation.

The solar system has some very distinct features which have to be explained by any serious cosmogonical theory. These include:

- planetary orbits are almost coplanar and also parallel to the solar equator;

- orbits are almost circular;

- planets orbit the Sun counterclockwise, which is also the direction of solar rotation;

- planets also rotate around their axes counterclockwise (excluding Venus, Uranus and Pluto);

- planetary distances approximately obey the empirical Titius-Bode law, i. e.

where the semimajor axis a is expressed in AU;

- planets have 98% of the angular momentum of the solar system but only 0.15% of the total mass;

- terrestrial and giant planets exhibit physical and chemical differences;

- the structure of planetary satellite systems resembles miniature solar systems.

The first modern cosmogonical theories were introduced in the 18th century. One of the first cosmogonists was Immanuel Kant, who in 1755 presented his nebular hypothesis. According to this theory, the solar system condensed from a large rotating nebula. Kant's nebular hypothesis is surprisingly close to the basic ideas of modern cosmogonical models. In a similar vein, Pierre Simon de Laplace suggested in 1796 that the planets have formed from gas rings ejected from the equator of the collapsing Sun.

The main difficulty of the nebular hypothesis was its inability to explain the distribution of angular momentum in the solar system. Although the planets represent less than 1% of the total mass, they possess 98% of the angular momentum. There appeared to be no way of achieving such an unequal distribution. A second objection to the nebular hypothesis was that it provided no mechanism to form planets from the postulated gas rings.

Already in 1745, Georges Louis Leclerc de Buffon had proposed that the planets were formed from a vast outflow of solar material, ejected upon the impact of a large comet. Various catastrophe theories were popular in the 19th century and in the first decades of the 20th century when the cometary impact was replaced by a close encounter with another star. The theory was developed, e.g. by Forest R. Moulton (1905) and James Jeans (1917).

Strong tidal forces during the closest approach would tear some gas out of the Sun; this material would later accrete into planets. Such a close encounter would be an extremely rare event. Assuming a typical star density of 0.15 stars per cubic parsec and an average relative velocity of 20 km/s, only a few encounters would have taken place in the whole Galaxy during the last 5 x 109 years. The solar system could be a unique specimen.

The main objection to the collision theory is that most of the hot material torn off the Sun would be captured by the passing star, rather than remaining in orbit around the Sun. There also was no obvious way how the material could form a planetary system.

In the face of the dynamical and statistical difficulties of the collision theory, the nebular hypothesis was revised and modified in the 1940's. In particular, it became clear that magnetic forces and gas outflow could efficiently transfer angular momentum from the Sun to the planetary nebula. The main principles of plane

Fig. 7.65. Hubble Space Telescope images of four protoplanetary disks, "pro-plyds", around young stars in the Orion nebula. The disk diameters are two to eight times the diameter of our solar system. There is a T Tauri star in the centre of each disk. (Mark McCaughrean/Max-Planck-Institute for Astronomy, C. Robert O'Dell/Rice University, and NASA)

Fig. 7.65. Hubble Space Telescope images of four protoplanetary disks, "pro-plyds", around young stars in the Orion nebula. The disk diameters are two to eight times the diameter of our solar system. There is a T Tauri star in the centre of each disk. (Mark McCaughrean/Max-Planck-Institute for Astronomy, C. Robert O'Dell/Rice University, and NASA)

tary formation are now thought to be reasonably well understood.

The oldest rocks found on the Earth are about 3.9 x 109 years old; some lunar and meteorite samples are somewhat older. When all the facts are put together, it can be estimated that the Earth and other planets were formed about 4.6 x 109 years ago. On the other hand, the age of the Galaxy is at least twice as high, so the overall conditions have not changed significantly during the lifetime of the solar system. Moreover, there is even direct evidence nowadays, such as other planetary systems and protoplanetary disks, proplyds (Fig. 7.65).

The Sun and practically the whole solar system simultaneously condensed from a rotating collapsing cloud of dust and gas, the density of which was some 10, 000 atoms or molecules per cm3 and the temper ature 10-50 K (Fig. 7.66). The elements heavier than helium were formed in the interiors of stars of preceding generations, as will be explained in Sect. 11.8. The collapse of the cloud was initiated perhaps by a shock wave emanating from a nearby supernova explosion.

The original mass of the cloud must be thousands of Solar masses to exceed the Jeans mass. When the cloud contract the Jeans mass decrease. Cloud fragments and each fragment contract independently as explained in later chapters of star formation. One of the fragments became the Sun.

When the fragment continued its collapse, particles inside the cloud collided with each other. Rotation of the cloud allowed the particles to sink toward the same plane, perpendicular to the rotation axis of the cloud, but prevented them from moving toward the axis.

Fig. 7.66a-g. A schematic plot on the formation of the solar system. (a) A large rotating cloud, the mass of which was 3-4 solar masses, began to condense. (b) The innermost part condensed most rapidly and a disk of gas and dust formed around the proto-sun. (c) Dust particles in the disk collided with each other forming larger particles and sinking rapidly to a single plane. (d) Particles clumped together into planetesimals which were of the size of present asteroids. (e) These clumps drifted together, forming planet-size bodies which began (f) to collect gas and dust from the surrounding cloud. (g) The strong solar wind "blew" away extra gas and dust; the planet formation was finished

Fig. 7.67. Temperature distribution in the solar system during planet formation. The present chemical composition of the planets reflects this temperature distribution. The approximate condensing temperatures of some compounds have been indicated

Table 7.4. True distances of the planets from the Sun and distances according to the Titius-Bode law (7.55)

Fig. 7.67. Temperature distribution in the solar system during planet formation. The present chemical composition of the planets reflects this temperature distribution. The approximate condensing temperatures of some compounds have been indicated

This explains why the planetary orbits are in the same plane.

The mass of the proto-Sun was larger than the mass of the modern Sun. The flat disk in the plane of the ecliptic contained perhaps 1/10 of the total mass. Moreover, far outside, the remnants of the outer edges of the original cloud were still moving toward the centre. The Sun was losing its angular momentum to the surrounding gas by means of the magnetic field. When nuclear reactions were ignited, a strong solar wind carried away more angular momentum from the Sun. The final result was the modern, slowly rotating Sun.

The small particles in the disk were accreting to larger clumps by means of continuous mutual collisions, resulting finally in asteroid-size bodies, planetesimals. The gravitation of the clumps pulled them together, forming ever growing seeds of planets. When these protoplanets were large enough, they started to accrete gas and dust from the surrounding cloud. Some minor clumps were orbiting planets; these became moons. Mutual perturbations may have prevented plan-etesimals in the current asteroid belt from ever being able to become "grown-up" planets. Moreover, resonances could explain the Titius-Bode law: the planets were able to accrete in very limited zones only (Table 7.4).

The temperature distribution of the primordial cloud explains the differences of the chemical composition of the planets (Fig. 7.67). The volatile elements (such as

Table 7.4. True distances of the planets from the Sun and distances according to the Titius-Bode law (7.55)

Planet

n

Calculated

True

distance

distance

[AU]

[AU]

Mercury

—œ

O.4

O.4

Venus

O

O.7

O.7

Earth

l

l.O

1.0

Mars

2

l.6

1.5

Ceres

3

2.8

2.8

Jupiter

4

5.2

5.2

Saturn

5

lO.O

9.2

Uranus

6

19.6

19.2

Neptune

7

38.8

30.1

Pluto

8

77.2

39.5

hydrogen and helium, and ices) are almost totally absent in the innermost planets. The planets from Mercury to Mars are composed of "rocks", relatively heavy material which condenses above 500 K or so. The relative abundance of this material in the primeval nebula was only 0.4%. Thus the masses of terrestrial planets are relatively small. More than 99% of the material was left over.

At the distance of Mercury, the temperature was about 1400 K. At this temperature, iron and nickel compounds begin to condense. The relative abundance of these compounds is greatest on Mercury and smallest on Mars, where the temperature was only 450 K. Thus the amount of iron(II)oxide, FeO, is relatively high on Mars, whereas there is practically no FeO on Mercury.

At the distance of Saturn, the temperature was so low that bodies of ice could form; e. g. some moons of Saturn are almost pure water ice. Because 98.2% of the primordial material was hydrogen and helium, the abundance of hydrogen and helium in Jupiter and Saturn is close to those values. However, the relative importance of ices became more prominent at the distance of Uranus and Neptune. A considerable amount of the mass of these planets can be water.

Meteorite bombardment, contraction and radioactive decay produced a great deal of heat after the planetary formation. This gave rise to the partial melting of some terrestrial planets, resulting in differentiation of material: the heavy elements sank to the centre and the light dross was left to float on the surface.

The left over material wandered among the planets. Planetary perturbations caused bodies in unstable or

bits to collide with planets or to be slung outer edges of the solar system, as happened to the bodies now in the Oort cloud. Asteroids remained in their stable orbits. On the outskirts of the solar system, bodies of ice and dust, such as the Kuiper belt objects, could also survive.

The beginning of the solar nuclear reactions meant the end of planetary formation. The Sun was in the T Tauri phase losing mass to a strong solar wind. The mass loss was as high as 10-7 Me/a. However, this phase was relatively short and the total mass loss did not exceed 0.1 Me. The solar wind "blew" away the interplanetary gas and dust, and the gas accretion to the planets was over.

The solar wind or radiation pressure has no effect on millimetre- and centimetre-sized particles. However, they will drift into the Sun because of the Poynting-Robertson effect, first introduced by John P. Poynting in 1903. Later H.P. Robertson derived the effect by using the theory of relativity. When a small body absorbs and emits radiation, it loses its orbital angular momentum and the body spirals to the Sun. At the distance of the asteroid belt, this process takes only a million years or so.

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