# Planet Earth/2e. Other Sources of Energy: Gravity, Tides, and the Geothermal Gradient.

A schematic view of the geothermal gradient of increasing temperature with depth inside the Earth.

The sun may appear to be Earth’s only source of energy, but there are other much deeper sources of energy hidden inside Earth. In the pursuit of natural resources such as coal, iron, gold and silver during the heights of the industrial revolution, mining engineers and geologists took notice of a unique phenomenon as they dug deeper and deeper into the interior of the Earth. The deeper you travel down into an underground mine, the warmer the temperature becomes. Caves and shallow mines near the surface, take on a yearly average temperature making hot summer days feel cool in a cave and cold winter days feel warm, but as one descends deeper and deeper underground, ambient temperatures begin to increase. Of course, the amount of increase in temperature varies depending on the proximity you are to an active volcano or upwelling magma, but in most regions on land, a descend of 1,000 meters underground will increase temperatures between 25 to 30° Celsius. One of the deepest mines in the world is the TauTona Mine in South Africa, which descends to depths of 3,900 meters with ambient temperatures rising between 55 °C (131 °F) and 60 °C (140 °F), rivaling or topping the hottest temperatures ever recorded on Earth’s surface. Scientists pondered where this energy, this heat within the Earth comes from.

Scientists of the 1850s viewed the Earth like a giant iron ball heated to glowing hot temperatures in the blacksmith-like furnace of the sun and slowly cooling down ever since its formation. Such view of a hot Earth, bore its origins to the rise of industrial iron furnaces that dot the cityscapes of the 1850s, suggested that Earth, like poured molten iron was once molten and over its long history has cooled. Suggesting that the observed heat experienced deep underground in mines was the cooling remnant of Earth’s original heat from a time in its ancient past when it was forged from the sun. Scientists term this original interior heat within Earth left over from its formation, Accretionary heat.

## Lord Kelvin and the First Scientific Estimate for the Age of Earth

As a teenager, William Thomson pondered the possibility of using this geothermal gradient of heat in Earth’s interior as a method to determine the age of the Earth. He imagined the Earth to have cooled into its current solid rock from an original liquid molten state, and that the temperatures on the surface of the Earth had not changed significantly over the course of its history. The temperature gradient was directly related to how long the Earth had been cooling. Before changing his name from William Thomson to Lord Kelvin, he acquired an accurate set of measurements of the Earth’s geothermal gradient from reports of miners in 1862, and returned to the question of the age of the Earth.

Lord Kelvin assumed three initial criteria, first was that Earth was once a molten hot liquid, with a uniform hot temperature, and second that this initial temperature was about 3,900 °C, hot enough to melt all types of rocks. Lord Kelvin also assumed that the temperature on Earth’s surface would be the same throughout its history near 0 °C. Like a hot potato thrown into an icy freezer, the center of the Earth would retain its heat at its core, while the outer edges of the Earth would cool with time. He devised a simple formula:

${\displaystyle {{\text{Age of Earth}}={\frac {(T/G)^{2}}{\pi k}}}}$

Where T is equal to the initial temperature, 3,900 °C. G is the geothermal gradient he estimated to about 36 °C/km from those measurements in mines, and k was the thermal diffusivity, or the rate that a material cools down measured in meters per second. While Lord Kelvin had established estimates for T, G, and used the constant π, he still had to determine k the thermal diffusivity. In his lab, he experimented with various materials, heating them up and measuring how quickly heat was conducted through the material, and found a good value to use for the Earth of 0.0000012 meters squared per second. During these experiments of heating various materials and measuring how quickly they cooled down, Lord Kelvin was aided by his assistant a young student named John Perry. It must have been exciting when Lord Kelvin calculated an age of the Earth to around 93 million years, although he gave a broad range in his 1863 paper between 22 to 400 million years. Lord Kelvin’s estimate gave hope to Charles Darwin’s budding theory of evolution, which required a long history for various lifeforms to evolve, but ran counter to a notion that Earth had always existed.

John Perry who idolized his professor, graduated and moved on to a prestigious teaching position in Tokyo, Japan. It was there in 1894 he was struck by a foolish assumption that they had made in trying to estimate the age of the Earth, and it may have occurred to him after eating some hot soup on the streets of Tokyo. In a boiling pot of soup, heat is not dispersed through conduction the transfer of heat energy by simple direct contact, but dispersed through convection, that is the transfer of energy with the motion of matter, and in the case of the Earth, the interior of the planet may have acted like a pot of boiling soup, the liquid bubbling and churning bringing up not only heat to the surface, but also matter. John Perry realized if the heat transfer of the interior of the Earth was like boiling soup, rather than an iron ball, the geothermal gradient would be prolonged far longer near the surface due to the upwelling of fresh liquid magma from below. In a pot of boiling soup, the upper levels will retain higher temperatures because the liquid is mixing and moving as it is heated on the stove.

Convection of heat transfer (boiling water), versus Conduction of heat transfer (the hot handle of pot).

In 1894, John Perry published a paper in Nature, indicating the error in Lord Kelvin’s previous estimate for the age of the Earth. Today, we know from radiometric dating that the Earth is 4.6 billion years old, 50 times longer than Lord Kelvin’s estimate. John Perry explained the discrepancy, but it was another idea that captured Lord Kelvin’s attention. The existence of an interior source of energy within the Earth, thermonuclear energy, that could also claim to keep the Earth’s interior hot.

## Earth’s Interior Thermonuclear Energy

Marie Skłodowska Curie, the great scientist.

Unlike the sun, Earth lacks enough mass and gravity to trigger nuclear fusion at its core. However, throughout its interior, the Earth contains a significant number of large atoms (larger than iron) that formed during the initial giant supernova explosion that formed the solar system. Some of these large atoms, such as thorium-232 and uranium-238 are radioactive. These elements have been slowly decaying ever since their creation around the time of the initial formation of the sun, solar system and Earth. The decay of these large atoms into smaller atoms is called nuclear fission. During the decay, these larger atoms are broken into smaller atoms, some of which can also decay into even smaller atoms, like the gas radon which decays into lead. The decay of larger atoms into smaller atoms produces radioactivity, a term coined by Marie Skłodowska-Curie. In 1898, she was able to detect electromagnetic radiation emitted from both thorium and uranium, and later she and her husband demonstrated that radioactive substances produce heat. This discovery was confirmed by another female scientist named Fanny Gates, who demonstrated the effects of heat on radioactive materials, while the equally brilliant female scientist discovered that radioactive solid substances produced from the decay of thorium and uranium, further decay to a radioactive gas, called radon.

The New Zealand scientist Ernest Rutherford, who wrote the classic book on radioactivity.

These scientists worked and corresponded closely with a New Zealander, named Ernest Rutherford, who in 1905 published a definitive book on “Radio-activity.” This collection of knowledge begun to tear down the assumptions made by Lord Kelvin. It also introduced a major quandary in Earth sciences. How much of Earth’s interior heat is a product of accretionary heat and how much is a product of thermonuclear heat from the decay of thorium and uranium?

A century of technology has resulted in breakthroughs in measuring nuclear decay within the interior of the Earth. Nuclear fusion in the sun causes beta plus (β+) decay, in which a proton is converted to a neutron, and generates a positron and neutrino, as well as electromagnetic radiation. In nuclear fission, in which atoms break apart, beta minus (β−) decay occurs. Beta minus (β−) decay causes a neutron to convert to a proton, and generates an electron and antineutrino as well as electromagnetic radiation. If a positron comes in contact with an electron the two sub-atomic particles annihilate each other. If a neutrino comes in contact with an antineutrino the two sub-atomic particles annihilate each other. Most positrons are annihilated in the upper regions of the sun, which are enriched in electrons, while neutrinos are free to blast across space, zipping unseen through the Earth, and are only annihilated if they come in contact with antineutrinos produced by radioactive beta minus (β−) decay from nuclear fission on Earth.

Any time of day, trillions of neutrinos are zipping through your body, followed by a few antineutrinos produced by background radiation. Neither of these subatomic particles cause any health concerns, as they cannot break atomic bonds. However, if they strike a proton, they can emit a tiny amount of energy, in the form of a nearly instantaneous flash of electromagnetic radiation.

The Kamioka Liquid-scintillator Anti-Neutrino Detector in Japan is a complex experiment designed to detect anti-neutrinos emitted during radioactive beta minus (β−) decay caused by both nuclear reactors in energy generating power plants, as well as natural background radiation from thorium-232 and uranium-238 inside the Earth.

The detector is buried deep in an old mine, and consists of a steel sphere filled with a balloon filled liquid scintillator, and buffered by a layer of mineral oil. Light within the steel sphere is detected by highly sensitive phototubes mounted on the inside surface of the steel sphere. Inside the pitch-black sphere any tiny flash of electromagnetic radiation can be detected by the thousands of phototubes that line the surface of the sphere. These phototubes record tiny electrical pulses, which result from the collision of antineutrinos striking protons. Depending on the source of the antineutrinos, they will produce differing amounts of energy in the electrical pulses. Antineutrinos produced by nearby nuclear reactors can be detected, as well as natural antineutrinos caused by the fission of thorium-232 and uranium-238. A census of background electrical pulses indicates that Earth’s interior thermonuclear energy accounts for about 25% of the total interior energy of the Earth (2011 Nature Geoscience 4:647–651, but see 2013 calculations at https://arxiv.org/abs/1303.4667) the other 75% is the accretionary heat, left over from the initial formation of the Earth. Thorium-232 is more abundant near the core of the Earth, while uranium-238 is found closer to the surface. Both elements contribute to enhancing the geothermal gradient observed in Earth’s interior, and extending Earth’s interior energy beyond that predicated for a model involving a cooling Earth with only heat left over from its formation. A few other radioactive elements contribute to Earth’s interior heat, such as potassium-40, but the majority of Earth’s interior energy is a result of residual heat from its formation.

Comparing the total amount of Earth’s interior energy sources with the amount Earth receives via the Sun, reveals an order of magnitude of difference. The entire interior energy from Earth accounts for only about 0.03% of Earth’s total energy. The other 99.97% comes from the sun’s energy, as measured above the atmosphere. It is important to note that it is estimated that current human populations utilize about 30 Tetrawatts or about 0.02% of Earth’s total energy. Hence, the interior energy of Earth and the resulting geothermal gradient could support much of the energy demands of large populations of humans, despite the fact that it accounts for a small amount of Earth’s total energy budget.

## Gravity, Tides and Energy from Earth’s Inertia

While the vast amount of Earth’s energy comes from the Sun, and a small amount comes from the interior of the Earth, a complete census of Earth’s energy should also discuss a tiny component of Earth’s energy that is derived from its motion and the oscillations of its gravitational pull with both the Moon and the Sun.

Animation of tides as the Moon goes round the Earth with the Sun on the right.

Ocean and Earth tides are caused by the joint gravitational pull of the Moon and Sun. They daily cycle between high and low tides over a longer two-week period. Twice a lunar month, around the new moon and full moon, when a straight line can be draw through the center of the Sun, Moon and Earth, a configuration known as a syzygy, the tidal force of the Moon is reinforced by the gravitational force of the Sun, resulting in a higher than usual tides called a spring tide. When a line drawn through the center of the Sun to the Earth, and Moon to the Earth forms a 90° angle, or is perpendicular, the gravitational force of the Sun partially cancels the gravitational force of the moon, resulting in a weakened tide, called a neap tide. These occur when the Moon is at first quarter or third quarter in the night sky.

Gravitational pull of the Moon generates a tide-generating force, effecting both liquid water, as well as the solid interior of Earth.

Daily tides are a result of Earth’s rotation relative to the position of the Moon. Tides can affect both the solid interior of the Earth (Earth tides), as well as the liquid ocean waters (Ocean tides), which are more noticeable, as ocean waters rise and fall along coastlines. Long records of sea level are averaged to indicate the average sea level along the coastline. The highest astronomical tide and lowest astronomical tide are also recorded, with the lowest record of the tide equivalent on navigational charts as the datum. Metrological conditions (such as hurricanes), as well as tsunamis (caused by earthquakes) can dramatically rise or lower sea level alongs coasts, well beyond the highest and lowest astronomical tides. It is estimated that tides contribute only 3.7 Tetrawatts of energy (Global Climate and Energy Project, Hermann, 2006 Energy), or about 0.002% of Earth’s total energy.

In this census of Earth’s energy, we did not include wind and fossil fuels such as coal, oil and natural gas, as these sources of energy are ultimately a result of input of solar irradiation. Wind is a result of thermal and pressure gradients in the atmosphere, that you will learn more of later when you read about the atmosphere, while fossil fuels are stored biological energy, due to sequestration of organic matter produced by photosynthesis, in the form of hydrocarbons, that you will learn more of as you read about life in a later chapter.