| MadSci Network: Astronomy |
Dear Matt,
Your question is in fact several questions, which I shall try to answer
one by one. As we know more about the Earth than about other terrestrial
planets, much of what I say below is based on direct knowledge of the
Earth supplemented by observations and deductions about other planets.
Is a terrestrial planet's lifetime determined by its mass? I understand that by "lifetime" you mean the length of time that it takes for a planet to cool down, with a good definition of "cool" being the point at which a planet ceases to be volcanically active. The short answer is that it is size, not mass, that determines the rate of cooling of a planet. The rate of cooling is proportional to the ratio of surface area to volume. A small body has a greater ratio of surface area to volume than a large one and will more rapidly dissipate heat to space.
The picture is complicated by the fact that a terrestrial planet like the Earth doesn't just cool down in a simple, linear fashion. Instead we can identify four sources of heat which operate at different rates at different times during a planet's history. These are:
Planets are thought to form by a process of accretion from the nebula surrounding a proto-star. Gases, dust grains, rocky fragments and larger planetesimals clump together under gravity, and as the size of the parent body increases the force of its gravity increases, to the point where runaway growth takes place. Gravitational energy is released by accretion, and this energy is thought to be sufficient to melt a young planet totally, creating what is called a magma ocean. Heat will also be added later by further impacts as the planet sweeps up the remaining debris in its orbit.
Terrestrial planets are composed of a combination of metals (iron and nickel especially) and silicate minerals. During the magma ocean phase the denser materials will sink to the centre under gravity to form the core. Differentiation into layers is the result, with a metallic core surrounded by a silicate mantle. The process of core formation converts gravitational energy into heat.
The matter composing a terrestrial planet will contain a complement of radioactive elements, the decay of which releases heat. These elements will be concentrated in the mantle after core formation. In the Earth the principal radiogenic elements during most of geological time have been isotopes of potassium (40K), thorium (232Th), and uranium (235U and 238U). As time passes radiogenic heat will overtake primordial heat as the principal heat source. Today primordial heat is thought to contribute 20% to 50% of the Earth's heat flow, with the remainder being largely radiogenic heat (so for the sake of argument let's say that 20% of the Earth's heat flow today is primordial heat, and 80% is radiogenic heat).
The gravitational pull on a planet or moon from other bodies in the solar system will generate heat in its interior. The most spectacular example of tidal heating in the solar system is Io, one of the four largest moons of Jupiter. Tidal heating of the Earth today contributes between one and two orders of magnitude less heat than radiogenic heating, so I will not consider it further as a significant heat source.
So, the cooling history of a planet is one in which primordial heat declines in relative importance compared to radiogenic heat, which continues for billions of years to heat the interior. But even primordial heat will continue to be significant in a planet the size of the Earth or Venus for billions of years. A planet cools as its primordial heat is dissipated to space, and as its complement of radiogenic elements decays. Four billion years ago the Earth’s interior is thought to have been about five times hotter than it is today, but the Earth's heat flow is still sufficient to drive convection in the mantle, plate tectonics and volcanism. The Earth is still hot enough to be very much an active planet.
Mars is a little more than half as large as the Earth. Its primordial heat will have been dissipated more rapidly than the Earth's. Its radiogenic heat kept it active for billions of years, however, and Mars is known to have had a very active history. By counting impact craters on the giant volcano Olympus Mons, it has been determined that this volcano was active as recently as 10 to 30 million years ago. This is very recent, and raises the possibility that Mars may not be completely extinct even now. If there is some residual volcanic activity on Mars, however, this does not invalidate the general observation that Mars has cooled much more quickly than the Earth and is almost, if not actually, dead.
"Planets are geologically active because the energy produced from the pressure of its mass on its core melts the surrounding rock..." This is not correct. This type of heating is known as adiabatic heating. It is certainly real and contributes to the internal heat of a planet. However, it is not sufficient to keep a planet active when the major heat sources are exhausted. The Moon's core and mantle, for example, are heated adiabatically today, but the Moon is geologically completely inactive. Most of the heat that drives convection in the mantle, plate tectonics and volcanism comes from the decay of radiogenic elements in the mantle and crust, not from the core.
Loss of atmosphere. A planet's gravity, which does depend directly on its mass, is responsible for its ability to hold an atmosphere. Mars may have had a denser atmosphere in the distant geological past than it has today, but its gravity was not strong enough to prevent molecules in its upper atmosphere from being accelerated to escape velocity by incoming solar radiation and escaping to space. Volcanic outgassing is a major source of atmospheric gases, and even Mars could have maintained a thick atmosphere as long as volcanism was sufficient to replenish the losses to space. When Martian volcanic activity declined, however, the density of its atmosphere would also have declined.
The Earth and Venus are large enough to retain their atmospheres. Volcanic outgassing continues on both planets, but even without outgassing the losses to space are very small, and the Earth would still have a dense atmosphere today. The Earth’s magnetic field also protects the atmosphere by shielding it from the solar wind.
Biological contribution to the atmosphere. The Earth is unique in the solar system in having life, as far as we know. On Earth the biosphere has acted over geological time to change the composition of the atmosphere. Especially, oxygen and methane would not be present in the Earth's atmosphere witout life. But an atmosphere would still exist if there was no life. The early atmosphere formed by outgassing four billion years ago and more is thought to have consisted mainly of nitrogen and carbon dioxide, and if life had not existed this would probably still be the case today. Life has acted to replace carbon dioxide with oxygen, to the point where oxygen now makes up 21% of the atmosphere by volume, and carbon dioxide is a trace gas.
Mars' atmosphere is largely carbon dioxide. We do not know if life ever existed on Mars. All we can say is that the atmosphere of Mars still looks today like a primitive atmosphere, even though thinner than it used to be.
"How long would it take for Earth to cool down?" This is a difficult question to answer. The Earth faces several possible fates, and science cannot at present choose between them. It is certain, however, that eventually the output of radiogenic heat in the Earth will decline to the point where the Earth will cease to be active (mantle convection and plate tectonic processes will halt and volcanism will cease), but it is difficult to calculate when this will happen. The Earth's complement of radiogenic elements in the mantle and crust is still very large. The Earth will probably continue to be active far into the geological future (probably for a billion years and perhaps for much longer).
It is possible that the Earth’s core may cool and solidify before the output of heat in the mantle and crust declines to the point where plate tectonics and volcanism cease. If this were to happen the Earth would probably lose its atmosphere because convection in the core generates the Earth’s magnetic field, which protects the atmosphere from the solar wind. The Earth could face a scenario in which its atmosphere is stripped away by the solar wind while the planet remains volcanically active.
Simon Lamb & David Sington Earth Story: The Shaping of Our World, (BBC Books, 1998). This book was published to accompany the BBC television series Earth Story. The book is an excellent introduction to many aspects of Earth history.
David McNab & James Younger The Planets (London: BBC Worldwide, 1999). This book was published to accompany the BBC television series The Planets.
"The Planets", unit 2 of the Open University course S281, Astronomy and Planetary Science (The Open University, 1994).
"Origins of Earth and Life", unit 1 of the Open University course S269, Earth and Life (The Open University, 1997).
I live in Britain, which is why my references are to sources published in Britain. The two books, however, should be available in any good university library, and may be available in book stores. The two Open University course units may be available in university libraries; if you can get hold of them they are packed with information.
David Scarboro
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