Principles of the Evolution of the Inner Planets and Moons

Formation

The inner planets formed from the gravitational instabilities in the inner solar nebula disk. We know this happened about 4.6 billion years ago from radioactive age-dating of meteorites. We don't know how many inner planets originally formed, but it was likely more than we see today. 4.6 billion years is also about 4.6 billion orbits around the sun for these planets, and the gravitational tugs of one planet on another can resonate and change orbits until they intersect. Then it's only a matter of time and chance before there's a nasty collision. Collisions will likely result in a merging of the colliding planets, which in any case are going to start out being basically balls of lava. Why? Consider that the average speed of orbiting material in the inner solar system is of order 30 km/sec. The kinetic energy (KE) of something of mass m moving at velocity v is

 

KE = (1/2)m v2

 

A collision converts most of that energy into heat - the most random (highest entropy) form of energy. If you equate the energy with that needed to melt rock, you'll find it's plenty enough to do the job. Add to that the fact that the present Earth has an escape velocity of 11 km/sec, which means that even a rock initially at rest will speed up to 11 km/sec by the time it hits our planet.

 

The early inner planets also had a certain amount of radioactive elements (radioactive elements are elements with nuclei which are too large to be completely stable against the tendency of the protons to repel each other inside a nucleus. So, after a time, they tend to spit out a piece of themselves and become a different chemical element, generating a lot of heat in the process). The radioactive decay of e.g. uranium and thorium will help keep the inside of a planet warm. Both early accretion and radioactivity are important in understanding why our interior is still molten.

 

Chemical Composition

The inner solar system is too warmed by the sun for the light elements hydrogen and helium to stay bound to the planets. Energy equilibrium is enforced by the collisions of atoms and molecules against one another in an atmosphere. By the kinetic energy formula above, you'll see that if the average energy is the same for all particles (atoms or molecules) in an atmosphere, that the heavy atoms must move slower and the lighter ones move faster. This means that the light ones will preferentially evaporate, as the highest velocity particles in the upper atmosphere are above the escape velocity necessary to overcome gravity. But note that hydrogen and helium - the lightest particles - are also ~97% of all the material from which the solar nebula and planets formed. This means that the inner planets will find themselves to be just the heavy elements left over after most of the stuff escapes into space and is carried to the outer solar system by the solar wind and radiation pressure from the sun. Hence, we get an inner solar system of small, rocky planets, and an outer solar system made of mostly hydrogen and helium, with small rocky cores buried deep underneath the lighter gases.

 

Outgasing from volcanoes and also the collision of comets then helps add an atmosphere of relatively heavy elements like carbon dioxide, water, diatomic nitrogen and, for Earth, oxygen generated by plants. About 1% of the Earth's atmosphere is the noble gas argon.

 

Cooling and Evolution of the Inner Planets

Collisions from gravity made the young inner planets very hot - well over a thousand degrees. The inner solar system relatively quickly cleaned itself up by having most of the floating debris fall onto planets. This period - the so-called early bombardment period lasted a few hundred million years or so and collisions since then have been rare enough that the planets were able to begin cooling. What governs how fast a planet loses heat? All the inner planets are made of roughly the same stuff - lots of iron and iron-related elements, and mantles and crusts of aluminum, silicates, calcium, potassium, phosphorus, and magnesium. Let's just call it "rock". Consider a molten planet trying to cool off. The amount of heat energy it has is proportional to the mass it has. But the mass it has is proportional to the volume if you assume that the density of all the inner planets is roughly the same (because they're all made of "rock"). And, the volume is proportional to the radius r cubed. For a planet with N atoms, the following relation holds approximately... (where k is just Boltzmann's constant)

 

3NkT ~ M ~ volume ~

 

Heat content ~ Volume ~

 

So the heat content goes as the cube of the size of the planet. However, the rate at which the planet can cool is proportional to the surface area from which it can radiate away that heat to outer space, and surface area for any object is proportional the radius squared...

 

Cooling rate ~ surface area ~ r2

 

So, if you consider larger and larger planets, r3certainly rises faster than r2 and therefore larger planets will cool slower. The Earth is the largest inner planet, and we would then expect that the Earth would be cooling the slowest and have retained the largest fraction of its initial heat.

 

Now, as a planet cools, its surface will go from being molten to forming a crust. Because smaller planets cool quicker, You would expect that smaller planets will have thicker crusts, and this is what we find (near as we can tell! We don't have seismometers there to get precise measurements.). There are a lot of factors which come into play in deciding how thick a crust a planet will have. Here's a few variables which would come into play...

1. An overlying thick atmosphere, especially one with complex molecules which absorb infrared light, will act as more of an insulating blanket, slowing heat loss.

2. Being closer to the sun will make a hotter surface which will cool more slowly.

3. Being closer to the asteroid belt may make for more frequent collisions even into the present time, adding collision heat and leading to a thinner crust.

4. Rotating faster will cause more internal convection in the mantle, recirculating heat from the core to the surface and making for a thinner crust.

 

Mercury: is the densest planet. It has the largest fraction of its mass in the form of a dense iron core. It's also closest to the sun. Both factors would argue for a thinner crust. But, it's also the smallest planet, only 40% the diameter of the earth. Also, it rotates very slowly - one day is 59 2/3 of our days. These last two effects seem to dominate, since we see no evidence of a thin crust on Mercury today. However, both the Mariner Mission in the early '70's, and also the new Messenger Mission to Mercury in 2014 showed compression cracks in many places on the surface, and the evidence suggests that Mercury shrunk in circumference by up to several miles, most likely by the loss of volatiles. We also see ancient volcanic cones there. Most craters on Mercury are due to impacts, but there are some volcanic craters that are long inactive.

 

Venus: is the same size as Earth, has a dense atmosphere of carbon dioxide 100 times the density of the Earth's atmosphere. The "greenhouse effect" (incoming visible light is scattered through the atmosphere to the ground, but outgoing infrared from the surface is absorbed and trapped by carbon dioxide, raising the temperature) makes for a very hot 800K surface. Both of these argue for a thin crust, perhaps thinner than Earth's. However, Venus also rotates very slowly; a Venus day is over 243 of our days. We see some evidence of a thin crust on Venus, because there are estimated to be ~100,000 volcanoes of all sizes, but the very high temperatures make for a plastic kind of rock and it's not clear we would expect to see the same evidence as we see on Earth.

 

Mars: rotates with the same period as Earth; 24 hours. But its atmosphere is very thin; only 1% of the Earth's. And, it's only half the diameter of the Earth. These last two effects argue for a thicker crust to Mars. However, it's also close to the asteroid belt, and perhaps has been heated more often by asteroid impacts. We see volcanoes on Mars - a few very large ones. These are evidence for a thin crust. There is some recent Mars Orbiter evidence that volcanic activity has happened in the relatively recent past, only a few million years. However, we do not see the same mountainous and fault-laced

Martian gullies - springs from ancient subsurface water? Or sand flowing from sublimating CO2?

landscape on Mars as we see on Earth. Probably, crustal dynamics is much weaker here. There is evidence of recent water flow on Mars which is controversial. The wall of a large crater seems to show fairly fresh evidence of flow. Could it be water underground which is melting, flowing before it vaporizes in the thin Martian atmosphere? But the thermal properties of ground mean that a few meters beneath the surface, there is no temperature change at all and hence no ability for what's there to melt. One would think that whatever frozen water might have been able to melt, would have done so eons ago. Could it be a powdery substance flowing "like water"? The favored theory now is that the gullies are caused by flowing sand, which is able to flow despite being too shallow for the "angle of repose", because frozen CO2 sublimates, and turns the sand into a fluid.

 

The Processes of the Earth's Surface

An important determiner of these processes is the dramatic collision which resulted in the formation of the moon. A Mars-sized planet is believed to have collided with the Earth soon after formation. This made the Earth about 12% more massive, likely raised its rotation speed and both of these set the stage for plate tectonics. The evidence for this collision is (1) the moon orbits within 6 degrees of being in the plane of the other planets, not the earth's equator as you would expect if the moon formed as a part of the spinning Earth. (2) The moon has an unusually small iron core, consistent with it being the collision material ejected from the mantle of the earth, after it had chemically differentiated. (3) tidal friction shows that the moon was originally much much closer to the Earth, and that the Earth rotated much faster.

 

The Earth still has a rapid rotation compared to Mercury and Venus, and strong convective motion in its mantle, and is the largest inner planet. This means that even now, 4.6 billion years after it formed, it still has a thin enough crust for tectonic activity to be strong and on-going. The friction of the sticky silica-rich mantle against the thin (~50 miles or less) crust has broken the Earth's crust into "tectonic plates". Nearly a hundred years ago, Wegner looked at the world map and was struck by how neatly the Americas fit into Europe and Africa , and proposed the theory of plate tectonics. It was a pretty bold idea for the times, but is now widely accepted as the evidence is overwhelming that the Earth's plates do indeed move around. Plates boundaries can show the following types of motion:

  1. Collision. This action buckles the plates and makes for high, folded mountain ranges. The classic example is the Himalayas in Asia, where Indian plate is moving north and colliding with the Eurasian plate. The Himalaya are a young mountain range and still growing faster than erosion can take it back down. Still, the collision speed is only twice the rate at which your fingernails grow!
  2. Subduction. If one plate is significantly heavier than another, or perhaps for other reasons, one plate can meet another in a collision but be deflected underneath, where it re-melts. The remelted material carries a lot of volatiles from e.g. limestone and deep sea detritus, and the lighter remelt can convect back upward and create volcanic mountain ranges. Best example today is the Andes, which form the western edge of South America. The entire western South America coast is a deep sea trench formed by a subduction zone. Nearby, the Cascades are another example.
  3. Strike-slip. One plate can move parallel to the boundary with another plate, in which case there is little mountain building, but frequent and usually moderate earthquakes result.
  4. Spreading. Near a mantle upwelling zone, the mantle material will mushroom in opposite directions, carrying the crustal plates apart and allowing fresh mantle to rise and solidify. The most spectacular example is the mid-atlantic ridge, which spread the Americas away from Europe/Africa. Another example is the Great Rift Valley of East Africa, dotted by the great lakes of Africa.

The Processes on the Asteroids and Comets

Mysterious bright spots on Ceres

We now have close-up images of several asteroids, especially Ceres, and Comet GS, as well as smaller asteroids such as Eros and Gaspra. The

Spin-diameter plot for asteroids, demonstrating that most asteroid smaller than 300m are solid rock, most that are larger, are loose congregations

surface of Ceres is covered with craters, which was expected, since it lives in the main belt of the asteroids. Asteroids are very small, and there should be no hot molten material on or interior to these - they should have cooled long ago and hence have ancient surfaces which will show the accumulated scars of many crater impacts. Ceres also has a 20,000 ft mountain, and an amazing set of brilliant spots along the bottom of one of the larger craters. Many months now after discovery, we still are puzzling over what causes their brilliant shine. A plot of all known asteroids spin rate vs. size shows a fascinating break at 300m diameter. Asteroids larger than this cannot spin faster than about 10 times per Earth day, which corresponds to where the centrifugal force of the spinning would cause the asteroid to fly apart. Asteroids larger than 300m in diameter are clearly made of loosely held together smaller materials, and the weak self-gravity won't permit faster spin. There are many asteroid smaller than 300m, however, which spin faster than this, and these must be solid rocks held together by solid-state forces and not gravity.

  Processes on the Outer Moons of the Solar System

There are also active faults on Europa, Jupiter's 2nd Galilean moon. These are due to the motion of a liquid water interior against a thin water ice crust. Europa is heated by tidal friction within the body of the moon, caused by the close proximity to mighty Jupiter, and the elliptical orbit of Europa, which makes for varying tidal stress throughout the orbit. So the materials are different than on Earth, but the result is the same: large-scale faults between plates. There is also a different form of volcanism on some outer moons. Titan is the large moon of Saturn, and it shows evidence of "cryovolcanoes", where the working fluid is not liquid mantle rock like on Earth, but instead a water/ammonia mixture which has a very low freezing point, and is a sticky thick liquid at the frigid temperatures of the outer solar system. Cryovolcanoes are also seen on Pluto, in the New Horizons images, although it will take some time before we have a better understanding of mountain formation on Pluto..

At right, a strike-slip fault on the icy crust of Europa, which is not much thinner than the crust of the Earth - at left the San Andreas Fault of California