Fundamental Astronomy

the centrifugal force equal to the gravitational force:
GMm
R2 mv2
= , (7.10)
R
where m is a small test mass on the surface at a distance
of R from the center of the body. Substituting the
rotation period P,
P = 2πR
v ,
we get
GM
R2 = 4π2 R
P2 ,
or
R3 3
P = 2π = 2π
GM 4πGρ =
3π
. (7.11)
Gρ
If we substitute the density ρ with the mean density
of terrestrial rocks, i.e. 2700 kg m−3 , we get for the
minimum rotation period P ≈ 2 hours.
The structure of the terrestrial planets (Fig. 7.8) can
also be studied with seismic waves. The waves formed in
an earthquake are reflected and refracted inside a planet
like any other wave at the boundary of two different
layers. The waves are longitudinal or transversal (P and
S waves, respectively). Both can propagate in solid materials
such as rock. However, only the longitudinal
Fig. 7.8. Internal structure and relative sizes of the terrestrial
planets. The percentage shows the volume of the core relative
to the total volume of the planet. In the case of the Earth, the
percentage includes both the outer and the inner core
7.5 The Structure and Surfaces of Planets
wave can penetrate liquids. One can determine whether
a part of the interior material is in the liquid state and
where the boundaries of the layers are by studying the
recordings of seismometers placed on the surface of
a planet. Naturally the Earth is the best-known body,
but quakes of the Moon, Venus, and Mars have also
been observed.
The terrestrial planets have an iron-nickel core.Mercury
has the relatively largest core; Mars the smallest.
The core of the Earth can be divided into an inner and
an outer core. The outer core (2900–5150 km) is liquid
but the inner core (from 5150 km to the centre) is
solid.
Around the Fe–Ni core is a mantle, composed of
silicates (compounds of silicon). The density of the outermost
layers is about 3000 kg m −3 . The mean density
of the terrestrial planets is 3500–5500 kg m −3 .
The internal structure of the giant planets (Fig. 7.9)
cannot be observed with seismic waves since the planets
do not have a solid surface. An alternative is to study the
shape of the gravitational field by observing the orbit of
a spacecraft when it passes (or orbits) the planet. This
will give some information on the internal structure, but
the details depend on the mathematical and physical
models used for interpretation.
Fig. 7.9. Internal structure and relative sizes of the giant planets.
Differences in size and distance from the Sun cause
differences in the chemical composition and internal structure.
Due to smaller size, Uranus and Neptune do not have
any layer of metallic hydrogen. The Earth is shown in
scale
141