Principles of the Evolution of the Inner Planets

 

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 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 moving at velocity v is

 

KE = ½mv²

 

Where m is the mass of the colliding object. 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 acquire a speed of 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. However, the main reason the inner planets are molten inside is the kinetic energy of collisions which formed them.

 

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.

     Outgassing 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.

 

(3/2)kT  ~ M ~ volume ~ r³

 

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, r3 certainly 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!). 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 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, 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 it’s mass in the form of an 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 of our days. These last two effects seem to dominate, since we see no evidence of a thin crust on Mercury.

 

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, 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 – 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. Perhaps Mars is still geologically active in some sense. However, we do not see the same mountainous and fault-laced landscape on Mars as we see on earth. Probably, crustal dynamics is much weaker here.

 

The Geology of the Earth

     An important determiner of the geology of the earth 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 roughly 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 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 has a rapid rotation 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 geologic 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 theory for the times, but is now widely accepted as the evidence is now 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 remelt can “belch” 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.
  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 Geology of California

     North America and all the way to the mid-Atlantic Ridge lies on a single plate, with the exception of a narrow band along the California coast. California is almost unique among regions of the earth. It lies along the boundaries of the three tectonic plates which intereact to produce 3 of the 4 boundary types shown above. This has led to some of the most spectacular, complex, and interesting geology in the world.  I’ll outline it briefly.

     The north is dominated by the subduction of the Juan de Fuca plate beneath the North America plate. The Juan de Fuca plate is the last remnant of a once larger plate which has been disappearing under the North America plate. This subduction is occurring along the coast of California above Cape Mendicino, all the way up to near Vancouver, BC. The subduction re-melt occurs inland, and has produced the Cascade Mountain Range, extending from southern B.C. all the way to Mt. Lassen in Northern California. This is an active zone, and these volcanoes are all still active: Mt. St. Helens, Mt. Rainer, Mt. Lassen, Mt. Baker…

   Central California is dominated by the San Andreas Fault, a strike-slip fault as the Pacific Plate slides northward by about 3cm/year relative to the North America Plate. Little mountain building is associated with this fault today, although there is some, for example the Big Sur Range. The most dramatic geology of the San Andreas Fault is at Carrizo Plain, California’s newest national monument (and a place still undiscovered by tourists). If you look at a world geologic map

   Southern California is dominated by the San Andreas Fault where it transitions into a spreading zone. The Gulf of California all the way up to Palm Springs is a deep valley formed from the spreading of these two plates.

 

Google map of the San Andreas Fault.

 

Slide Show of Northern California Subduction Geology

 

Earthquakes

     The motion of the plates is sticky. The motion doesn’t happen smoothly at a constant rate, as if there were oil at the interface. Instead, forces build up until the rock gives way and the motion happens all at once. Rub a slightly sweaty hand across a table to see what that’s like. The strongest earthquakes happen at subduction zones, where the force of friction is aided by gravity of one plate on top of another, holding the plates fixed while forces build to a very high level – until the rock gives in one great heave. Earthquakes of magnitude 9 can happen here, as they did in 1964 in Alaska, and in 2004 in Indonesia. Earthquakes along strike slip faults are less, but can still reach magnitude 8. Earthquakes along spreading zones are usually milder, but sometimes can be large. Earthquakes can even happen not at plate boundaries, such as the great quake of 1812 in Missouri.

 

The Sierras

     The Sierras have a complicated history. What I’ll write is a bit oversimplified, but you can read more from the links below, and from your own web explorations. Roughly 100 million years ago, the Juan de Fuca plate was much larger and the subduction zone which today ends at Mt. Lassen, extended down most of California. This subduction made for a high, Andes-type volcanic mountain range. This mountain range likely had 20,000 foot peaks, higher than the current Sierras. As the subduction boundary migrated north, volcanic activity quited and the volcanic mountains quickly eroded away, making the great deposits now filling the Central Valley. Then, only about 20 million years ago, the stretching of the crust leading to the Basin and Range province began. The stretching is most violent along the eastern and western margins. This ruptured the crust making a fault, and rising silicon-rich material (which is lighter than the volcanic rocks made from deeper material) was buoyed up and pushed the crust up, forming the Sierras. The Sierras are still rising, and in the last 2 million years, the overlying sediments have been significantly eroded away and exposing the underlying silicon-rich rock – granite. Granites are mostly silicon-oxygen and cool to rock very slowly deep underground. The slow cooling allows large crystals to grow and give granites their distinctive look. The fault tilted and the Sierras have a very steep eastern edge and gently sloping foothills to the west.

 

The Basin and Range Province.

   California on the east side is within the Basin and Range Province. It extends from Idaho and Utah to California and northern Mexico. Here, beginning about 20 million years ago, the crust all through the western U.S. experiences stretching forces, perhaps due to convective upwelling in the underlying mantle. The stretching has created breaks in the surface – faults. Along these faults, the blocks have tilted and thus created mountain ranges with one side steep and the otherside shallow. The Sierras mark the western-most edge of the Basin-and-Range geology. The Sierras tilt with the steep side facing east. At the eastern edge of the province, the tilt is opposite, and the mountain range at Salt Lake City has it’s steep face towards the city, facing west. The stretching is the strongest at the margins, which are now at eastern California and central Utah. Hence, we have strong mountain building here – the Sierra, and the Wasatch in Utah – both young mountain ranges. Nearly as impressive are the great valleys. The dramatic elevation changes in California are the most extreme in the entire province – The 14,000 ft Sierras, cut by Owens Valley, then  the 14,000 foot White and Inyo Mountains, then Panamint Valley, the 12,000 ft Funeral Range, and then the lowest spot in the Western Hemisphere -  Death Valley.

    

The California High Desert

     The Mojave Desert is in the Basin and Range province. It is in a contorted triangular region bounded by the Sierras pushing up, the Basin and Ranges pulling away, and the compressional transverse range of the San Gabriels near Los Angeles where the San Andreas fault takes a sharp westward turn. Some of this transverse-generated stress has propagated farther north than the San Gabriels, and has led to complex faulting of the Mojave Desert.  The desert is very young, only a few million years old. The desert owes its dryness to being in the rain shadow of the Sierras, which take out the moisture of the storms blowing in from the west off the ocean. This has lead to steep jagged mountains both due to being young, and due to little erosion from rain. The basins are dominated by sediments, and the mountains are usually dominated by granites which formed deep underground and were pushed up by the thinning of the crust caused by Basin and Range stretching. However, some ranges have a mixture, such as the Red Rock Canyon State Park area, which has colorful sedimentary layers and areas of granite, together with mineral-rich partially volcanic and complex mountains – the El Paso Mountains.

 

Here are some web resources, found by just google’ing some relevant phrases. You can find many more on your own.

 

http://www2.nature.nps.gov/geology/usgsnps/province/basinrange.html

http://wrgis.wr.usgs.gov/docs/parks/deva/devatime.html