Interiors of the Giant Planets 411
5. Planetary Interior Models
5.1 General Overview
Even early “cosmographers” recognized that the giant plan-
ets of the solar system were distinct from the inner terres-
trial planets. The terrestrial planets have mean densities of
4000–5000 kg m−^3 , intermediate between the density of
rocks and iron, whereas the giant planets have mean densi-
ties closer to that of water (1000 kg m−^3 ), between 700 and
1700 kg m−^3. From this single piece of information, it is
clear that the bulk composition of the giant planets must be
substantially different from that of the terrestrial planets.
It has been known since the 1940s that if the interiors
of Jupiter and Saturn are “cold,” the primary component
of these planets must be hydrogen. In this context, “cold”
means that the densities throughout the interior must not
deviate significantly from the values they would assume at
the same pressures if the temperature was 0 K. The ap-
proximation is relevant because the behavior of substances
at 0 K and high pressure can be calculated analytically.
Hydrogen is then a likely dominant constituent because,
at the high pressures prevalent in the interiors of Jupiter
and Saturn, it would be a metallic fluid with a density of
about 1000 kg m−^3 , not the more familiar molecular gas.
Because the density of “cold” metallic hydrogen is close to
the bulk densities of Jupiter and Saturn, it was recognized
as a plausible major constituent of these planets.
Mass–radius calculations provide a more compelling
demonstration of the dominance of hydrogen in the interi-
ors of Jupiter and Saturn. For a given composition, there is
a unique relation between the radius of a spherical body in
hydrostatic equilibrium and its mass. These relations can be
calculated analytically for all elements at high pressure and
zero temperature. Although the interiors of jovian planets
are not at zero temperature, they are cool when measured
on an atomic temperature scale. This is adequate for a qual-
itative calculation, but zero-temperature equations of state
are insufficiently accurate for the calculation of detailed in-
terior models.
Mass-radius curves for several likely planetary con-
stituents are shown in Fig. 6. For low masses, the interior
pressures are small compared to intermolecular forces and
the volume of an object is just proportional to its mass,
thusR∝M^1 /^3. This is a realm with which we are famil-
iar in daily life. At much larger masses, the greater interior
pressures ionize the material, liberating many electrons. In
this regime,R∝M−^1 /^3 ; when mass is added to an object,
it shrinks. For intermediate masses where the curves meet,
there is a region where the radius is not highly sensitive to
the mass. At sufficiently high masses, the hydrogen in the
core of the object will undergo fusion, the temperature will
rise, and the zero-temperature relations shown in Fig. 6
are no longer applicable. However, for planets and white
FIGURE 6 Mass–radius curves for objects of various
compositions at zero temperature. Curve labeledx=0.25 is for
an approximately solar mixture of hydrogen and helium. Points J,
S, U, and N represent Jupiter, Saturn, Uranus, and Neptune,
respectively. Radius is in units of hundredths of a solar radius
and mass is in units of solar masses (1R⊙=6.96× 105 km and 1
M⊙= 1. 99 × 1033 g). Jupiter and Saturn are clearly composed
predominantly of hydrogen and helium; Uranus and Neptune
must have a large complement of heavier elements.dwarf stars, Fig. 6 is applicable. An important consequence
of these considerations is that for any given composition,
there is a maximum radius that a planet can have. For solar
composition, the maximum radius is about 80,000 km for a
planet with about four times Jupiter’s mass.
The total mass and radius of each Jovian planet are plot-
ted on Fig. 6 as well. This figure immediately proves that
Jupiter must be composed primarily of hydrogen and he-
lium. The maximum radii of planets composed of heavier,
cosmically abundant elements are all much smaller. For ex-
ample, only if Jupiter were very hot and very thermally
expanded could carbon be a dominant constituent. But
Jupiter’s observed heat flux rules out a very hot (> 107 K)
internal state. Thus, Jupiter must primarily consist of a mix-
ture of hydrogen and helium. Saturn’s position on the graph
implies a greater abundance of elements heavier than hy-
drogen, but it is still a primarily hydrogen bulk composi-
tion. Uranus and Neptune lie well below the mass–radius