Energy Sources Energy Losses and Interior Temperatures

Interior temperatures are an important property of a planetary body. For example, along with composition, they largely determine whether there are any liquids in the interior, and consequently whether a powerful magnetic field is possible. Temperatures in the past can determine whether core formation has occurred, and whether other compositional divisions have become established. Temperatures also determine the dynamics of the interior, such as the rate of any convection. And the thermal history of a planetary body helps to determine the nature of the surface and of any atmosphere, as you will see in later chapters. The temperatures inside a body at any particular moment in its history depend on the accumulated effects of the energy sources and the energy losses at all earlier times.

It is important to distinguish between the internal energy of a body, its temperature, and heat. The internal energy consists of kinetic and potential energy. The kinetic energy is almost entirely in the random energy of motion of the particles (atoms and molecules) that constitute the body (the motion of the body as a whole is excluded). The potential energy is the energy of interaction between the particles, be this gravitational or electrical. It generally increases as the mean separation between the particles increases. The temperature of the body is proportional to the random kinetic energy per particle. Heat is a particular form of energy transfer, i.e. transfer that is random at a microscopic level. For example, when a body at a certain temperature is in contact with a body at a lower temperature there is a net transfer of random energy from the higher to the lower temperature region through the random collisions of the microscopic particles at the interface. 'Heat' is often used interchangeably with 'energy'. This is avoided here unless the language would otherwise sound peculiar. Power is the rate of energy transfer, by heat, or by any other means.

If a region is a net receiver of heat its temperature might rise, and if it is a net loser its temperature might fall. Temperature changes can also be caused without heating, by any other process that causes a rise in the random kinetic energy part of the internal energy. One example is the temperature rise when two bodies collide. However, heat transfer does not always give a temperature change. For example, heat fed into a solid at its melting point does not cause a rise in temperature but a change in phase from solid to liquid. When a liquid solidifies at its melting point it gives out heat with no change in temperature. Heat that produces no temperature change is called latent heat. It is the energy that has to be supplied either to increase the average separation between the particles against their chemical attraction for each other, or (e.g. water) to break chemical bonds between the molecules. In either case there is an increase in the potential energy component of the internal energy.

It is important to stress that the present-day interior temperatures do not depend on the present energy sources and losses, but on their accumulated effect right back to the formation of the body. A familiar example of this dependence on history is the heating of water in an electric kettle. The temperature of the water at any instant does not depend on the flow of electric current and the energy losses at that instant, but on their earlier values. We cannot therefore separate the present from the past when we consider energy sources and losses in a planetary body.

4.5.1 Energy Sources

Energy sources no longer active: primordial energy sources

You saw in Chapter 2 that planetary bodies are thought to have been built up from planetesimals and other bodies in a process called accretion. This led to temperature rises as the kinetic energy of the infalling material was partially converted to internal energy of the surface materials at the point of impact. For the giant planets there was also a significant infall of nebular gas. The kinetic energy of the infall, solid or gas, was derived from gravitational accelerations, and so this accretional energy, as it is called, came from the conversion of gravitational energy to internal energy.

If the rate of accretion was low, much of the internal energy would have been lost by IR radiation from the surface to space, so the interior temperatures would not have risen much. But if the rate of accretion was high, the hot surface would have been buried, leading to raised temperatures in the whole interior. For a given mass of impactor, the energy transfer is greater, the more speed the impactor picks up as it is accelerated by the gravitational field of the body to its point of impact on the surface. This leads to accretional energy per unit mass being roughly proportional to pmR2, where pm and R were the then current mean density and radius respectively of the planetary body. Therefore, in large bodies, rapid accretion will lead to extensive interior melting.

Accretion is a primordial source of energy, in that accretion is not continuing today on an important scale. But the effect of accretional energy lives on, as you will see later. Another primordial source is any magnetic induction during the T Tauri phase of the proto-Sun (Section 3.1.6). This could have given considerable temperature rises in bodies of asteroid dimensions.

The other primordial source of importance was short-lived radioactive isotopes. Of particular importance was26Al, which decays to 26Mg. Studies of isotope ratios in meteorites indicate that this isotope accounted for a significant proportion of the aluminium present in the Solar System at its birth; 26Al has a half-life of only 0.73 Ma, and so there are about 62 half-lives in just the first 1% of Solar System history.

□ By what factor did the initial quantity of26Al decrease during this time? With a halving of the quantity every half-life the decrease in 46 Ma was by a factor of 2-62 of its initial quantity, i.e. 2.2 x 10-19. Thus26Al is long gone. But the shortness of its half-life, and the estimates of a modest initial abundance, indicate that the initial rate of energy release was high. If the isotope was distributed throughout the body, or concentrated at its centre, most of this energy would have been contained, and this radiogenic heating would have given considerable temperature rises in bodies of all but the smallest size. If the isotope was concentrated in the surface, then a greater proportion of its energy would have been lost to space. The loss of a greater proportion of energy when an energy source is concentrated at the surface occurs with other energy sources too.

The source of 26Al, and of other short-lived isotopes, is thought to have been supernovae -massive stars ending their lives in huge explosions that generated the isotopes and implanted them in the interstellar medium from which the Solar System was born.


Primordial sources could have raised the temperatures of the interior of a planetary body to the point where an important process occurred that is itself an energy source, and in some bodies it might still be active today. This is differentiation (Section 3.1.6) - the separation of layers of different density. For differentiation to occur, the chemical forces binding different substances together must be weaker than the gravitational forces that tend to separate the denser substances downwards. For example, if the Earth formed with a homogeneous composition throughout (homogeneous accretion) and subsequently underwent partial or total melting, then most of the iron would drain downwards to form a core, and most of the other materials would float upwards to form a predominantly silicate mantle. This downward separation of denser materials would have converted gravitational energy into internal energy, with a consequent rise in temperature. There would have been no such energy source if the iron core formed first and the silicate mantle was acquired later (heterogeneous accretion).

Differentiation can also result from the cooling of the interior. For example, if two liquids are already mixed and the temperature falls, the liquids can unmix, the denser settling towards the centre of the planetary body.

Meteorites provide observational evidence that differentiation has occurred. For example, irons and achondrites are readily interpreted as fragments of asteroids that differentiated to form iron cores and silicate mantles, irons being fragments of the core and achondrites fragments of the mantle (Section 3.3.4). The Widmanstatten pattern in irons (Section 3.3.2) is just what is expected from differentiation in which a body of iron melted and then formed a core, which then cooled slowly under the insulating mantle of the asteroid. Stony-irons could come from the core-mantle interface. By contrast, the chondrites seem to represent the sort of material that was around in the asteroid belt before any differentiation occurred.

Energy sources that can still be active

Ongoing differentiation is one possible 'live' source of energy in planetary interiors. Another is latent heat released when a liquid solidifies.

A further type of active source is radiogenic heating. Of particular and widespread importance are the four long-lived radioactive isotopes 235U, 238U, 40K, 232Th. Table 4.4 lists their half-lives and an estimate of the power they would have been releasing 4600 Ma ago in a typical rocky material. The same data are also included for 26Al. You can see that, unlike 26Al, their half-lives are comparable with or exceed the 4600 Ma age of the Solar System, and so these isotopes can have provided energy throughout the life of the Solar System, though at a declining rate as they decay. They are distributed non-uniformly in the interiors of many planetary bodies. For example, in the Earth there is a significant concentration into the outer 30 km or so, a result of earlier partial melting at greater depths.

The other 'live' source of importance in some bodies is tidal energy. □ Recall what a tide is, and how a tide is caused.

In Section 1.4.5 you saw that a tide is a distortion produced by differential gravitational forces. Now that you have met the concept of gravitational field (equation (4.5)) it is better to think of this as a differential field, which we can call a tidal field. Figure 4.12 shows the elongation of the whole Earth caused by the tidal field of the Moon. The rotation of the Earth carries the elongation slightly ahead of the line connecting the centres of the Earth and Moon, but of crucial importance to tidal heating is that this rotation also moves material into and out of the elongation, as illustrated by the point P in Figure 4.12, which is fixed on the Earth's surface. From the viewpoint of the Earth's interior, the elongation sweeps like a wave through it -literally, a tidal wave. This flexing increases the interior temperatures in the Earth.

A second, smaller tidal effect is due to the variation in distance between the Earth and the Moon. As the Moon moves around the Earth in its elliptical orbit, the size of the tidal elongation varies, being least when the Moon is nearest to the Earth (at perigee), and greatest when it is furthest (at apogee). This is another way that the Earth's interior is flexed.

The Sun produces similar types of effect, but even though the Sun is far more massive than the Moon it is much further away. Therefore, the solar tidal field across the Earth is about

Table 4.4 Radioactive isotopes that are important energy sources




40 K


232 Th

Half-life/ Ma Power a/10-12Wkg-1

0.73 104

0 0

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