Dating the Solar System Through Radioactive Decay

Some of the isotopes trapped in interplanetary grains at the time of their condensation are unstable. These isotopes, or 'parent nuclei', have decayed into 'daughter nuclei' since the date at which they were incorporated into the grains. The excess abundance of the latter isotopes may be measured, which allows the formation of the grains to be dated, once the radioactive decay-rate constant has been determined. This is the inverse of the time Te, the time after which the number of parent isotopes has been divided by e. To measure the age of the Solar System use is made of long-period 'clocks', in particular the (40K, 40Ar), (87Rb, 87Sr), and (238U, 238Pb) pairs, which have constants less than 10~10/year. Measurements made of these elements in meteorite samples have shown that the age of the Solar System is 4.55 x 1010 years. In addition, measurements made on plutonium-244 and iodine-129 (with shorter radioactive half-lives), show that 108 years at most passed between the separation of the protosolar material from the interstellar medium and the formation of the planets. These results show that the Sun and the material in the protosolar disk have the same origin.

4.3 The Emergence of a 'Standard Model'

The observers of the 17th century were well aware that the Solar System's planets all orbited the Sun in the same direction, and on quasi-circular orbits, close to the plane of the ecliptic. These fundamental properties prompted the concept of a primitive nebula, first proposed by Immanuel Kant and the by Pierre-Simon Laplace. According to this idea, which is the basis of the model accepted today, a primitive, rotating nebula collapsed into a disk, within which the planets and the small bodies subsequently formed. Other models for the formation of the Solar System have been proposed, however, both before and after the nebular model.

4.3.1 The Nebular Theory

The model of a primitive nebula in rapid rotation that collapses into a disk, first proposed by Kant and Laplace in the 17th century, has the merit of explaining simply the essential orbital properties of the objects in the Solar System. These formed through condensation within the disk itself. The principal objection to this theory was put forward at the end of the 19th century, and concerned the conservation of angular momentum in the system. In fact, almost all of the angular momentum is located in the giant planets, whereas the Sun represents 99.8 per cent of the overall mass. If it had retained most of its original angular momentum, it would rotate extremely rapidly (in about half a day), which is obviously not the case: its rotation period is 26 days at the equator. How could the Sun have transferred its angular momentum to the planets? For a long time the question remained without an answer, which encouraged the development of alternative theories, such as tidal theories. Nowadays we know the answer to this question: The Sun formed from material that transferred its angular momentum to material that remained in the protoplanetary disk. In addition, the solar magnetic field acted to slow the Sun's rotation (see also Sect. 6.1.4) If the particles are transported out to a distance of 10 solar radii, a mass-loss of just 0.003 M. is sufficient to explain the Sun's current rate of rotation, and such mass-losses are actually measured for young, rapidly rotating stars with strong magnetic fields.

With the principal objection to the nebular model having been discounted, the model has slowly been accepted and refined over recent decades. We see the emergence of two main classes of model:

• the massive nebula model, developed by A.G.W. Cameron in particular, in which the mass of the disk is about one solar mass. The planets form directly within it through gravitational instabilities. The remnants of the disk are either accreted by the Sun, or ejected from the system by the solar wind. As we shall see, this model cannot account for the formation of the planets (both terrestrial and giant) in the Solar System, but it may apply to other planetary systems; • the low-mass nebular model, notably as suggested by V. Safronov, in which the mass of the disk is about one-hundredth of that a solar mass. The disk forms through gravitational collapse, and cools. The solid material gathers together into planetesimals and then into planetoids through the action of multiple collisions. The latter have the effect of regularizing the orbits, which tend to lose their eccentricity and their inclination to the plane of the disk. During a phase of intense solar activity, the gas is ejected from the system, carrying dust with it, and leaving only objects with diameters larger than about one kilometre. This model is currently the basis for our understanding of the formation of the Solar System. It is still subject to many further developments, which aim to take better account of all the phenomena that are observed.

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