454 14 Fundamental Aspects of Nucleon Interactions
14.10.3 Earth and Solar System Dating
Another example of the close interconnection between nuclear physics and
astrophysics is the possibility of estimating the age of the Sun and of the time
required for the formation of our planetary system. It is believed that the Solar
System was formed from a cloud of gas and dust (with a diameter of about 100
astronomical units, see Appendix A.5, and a mass about two to three times that of the
Sun). The cloud was hit by a shock wave generated by the explosion of a nearby star
(supernova) with mass at least ten times that of the Sun. The shock wave caused the
compression of the gas and dust cloud that, because of the gravitational attraction,
began to pull inward other material forming the solar nebula. In the process of
contraction, as a result of the gravitational attraction, pressure, magnetic fields and
rotation, the nebula was flattened into a protoplanetary disk with a protostar at its
center. In the protoplanetary disk, various planets were formed.
In the inner region of the planetary system in formation (which includes the zone
where the Earth is now), the temperature was too high to allow condensation of
volatile molecules such as water and methane. Only relatively small rocky bodies
were formed (mainly by compounds with high melting point, such as silicates and
metals) that will evolve later in planets of terrestrial type. Externally, “gas giants”
Jupiter and Saturn developed, while Uranus and Neptune captured less gas and
condensed around nuclei of ice.
At the center of the system, the Sun started to shine when the pressure due to
gravity was high enough to cause the activation of fusion reactions in the protostar.
A strong stellar wind began to remove most of the gas and dust. Thanks to their huge
mass and large distance, the “gas giant” planets kept their atmosphere. The current
atmosphere in terrestrial planets is the result of volcanism and impacts with other
celestial bodies.
The dating of the Earth is possible through measurements of radioactive decay.
Heavy elements in the Solar System were formed in a relatively small time, during
the gravitational collapse of the massive star that triggered the formation of the
Sun. The theory of heavy element nucleosynthesis [14B57] hypothesizes that nuclei
such as the
187
Re;
232
Th;
235
U are synthesized by neutron capture (the r-process)
from the lighter elements expelled by the gravitational collapse. The various models
discussed in [14T98] assume, in the formation, a ratio .
235
U=
238
U/
r
D 1:35˙0:30.
The concentration of heavy elements is now different from the original one
because each isotope has a different half-life. The present ratio between these
elements depends on the time T from their synthesis; it is measured in rocks of
the Earth, of the Moon and in meteorites. We can assume that T D
f
C
SS
,where
f
is the time between the supernova explosion that originated the Solar System
and the birth of the Solar System (and Earth), and
SS
is the age of the Solar System
(and Earth).
The calculation can be specifically performed for the important case of uranium
isotopes. The lifetime of the
238
U isotope is
238
D 6:43 10
9
years, larger than
the lifetime of the
235
U isotope, equal to
235
D 1:01 10
9
. Therefore, the ratio