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Geology 130F

Lecture Seven

Heat Loss

(pp 30-36 Christiansen & Hamblin)

Thermal History

Many of the properties of a planet are controlled by the amount of heat trapped in the interior, and by the rate at which this heat leaks out. For example, the surface of the Earth is relatively young---typical rocks have an age of about 1 billion years. Moon rocks are typically three billion years old or older. The difference arises because the Earth's mantle is still hot and therefor plastic, so that the surface is constantly being destroyed and rebuilt by tectonic processes. Similarly, Neptune is currently losing more heat than Uranus, indicating that the interior of Neptune is hotter than that of Uranus. The warm core of Neptune is believed to be responsible for Neptune's rather strong magnetic field.

Heat Loss Mechanisms

  1. Conduction. Heat is the random motion of atoms. Collisions between atoms will transport this random motion. This is the least efficient of the major heat loss mechanisms, but in opaque rigid matter is the operative one.
  2. Convection. Most fluids (air, water under most conditions, magma) become less dense when they are heated, since the more vigorous atomic motion means that each atom occupies more space. In a gravitational field, lighter fluids surrounded by heavier fluids are buoyant. Since planets tend to be hot in the center and cool at the surface, it can happen that hot, less dense fluids lie below cool, more dense fluids. In that case, the hot fluids will rise toward the surface of the planet, carrying heat with them. This motion is called convection.
  3. Radiation (Light). Photons escaping from the visible surface of a planet remove energy from the planet. The rate at which energy is lost by this mechanism is proportional to the temperature of the surface to the fourth power (T4). The result is that the surfaces of hot bodies cool very efficiently.

Heat Reservoirs

The amount of heat or energy in a body is proportional to the body's temperature, and to the total mass of the body (since more stuff means more stuff in motion). The total mass of a spherical body is proportional to the radius cubed (R3). The rate of heat loss of the same body is proportional to the surface area, or R3. The cooling time tcool is the ratio of the amount of heat to the rate of heat loss, so tcool~ R3/R2~ R. Large bodies take longer to cool off. If you cook, you are familiar with the inverse result---cooking a large roast takes longer than cooking a small roast.\hfill\break The efficient loss of heat from the surface of terrestrial planets ensures that a crust forms rapidly. In larger bodies like Earth and Venus, the large reservoir of heat ensures that the crust is pushed around by convective flows for billions of years. In smaller bodies like the moon, the crust rapidly thickens, and after a billion years or so all tectonic activity ceases.

Results of Solar System Formation

At the end of the formation period, which lasted about 100,000,000 years,
  1. The sun burning H into He to produce heat.
  2. Terrestrial planets formed in the hot near solar region, devoid of volatiles. The terrestrial planets were hot enough (due to accretion heating) that they could differentiate (with denser material moving to the center and less dense material moving to the surface). Surface temperatures are estimated to be
    Initial Surface Temperatures
    Mercury 4,000K
    Venus 25,000K
    Earth 30,000K
    Mars 6,000K
    Moon 1,300K
  3. Gas giant planets with rock/ice cores surrounded by H and He.
  4. Large number of planetesimals---asteroids, comets, Pluto and etc.

Physically Differentiated Zones

Planets have different physical properties at different radii:

  1. Core. Metallic, either solid (in small bodies) or molten (in larger bodies)
  2. Asthenosphere. Plastic or ductile material. Convection can occur in this region.
  3. Lithosphere. Rigid material (``solid Earth'').
  4. Biosphere. Where life is.
  5. Hydrosphere. Fluid regions. The atmosphere of Earth, and the bulk of Jupiter are two examples.
  6. Photosphere. The region from which photons can escape to space. This is what we see from the outside of the planet.
  7. Magnetosphere. The region outside the photosphere where the magnetic field of the planet dominates the physics of the interplanetary plasma.

Chemically Differentiated Zones

Planets also have different chemical properties at different radii; the different chemical zones do not necessarily correspond to the physically determined zones described above.

  1. The core. Siderophile metals
  2. The mantle. Siderophile and Chalcophile elements, silicates rich in Fe and Mg (``mafic'').
  3. The crust. Lithophile elements.

Chemical Jargon

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