Astro 28T - Principles of the Evolution of the Inner Planets, and California Geology

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 of something moving at velocity v is

E = 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 that job. Add to that, the fact that the present earth has an escape velocity of 11 km/sec, which means that even a rock initial 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, albeit small, 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 etc 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 E 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, diatomic nitrogen and, for earth, oxygen generated by plants.

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 if proportional to the diameter 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 figure is proportional the size squared…

Cooling rate ~ surface area ~ r²

So, if you consider larger and larger planets, r certainly rises faster than r 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 it’s atmosphere is very thin; only 1% of the earths. 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

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 India, on one 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 with 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. 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).

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.

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 Pt. Reyes Peninsula

The boundary between the North America and Pacific plates is actually a rift zone of parallel faults each of which are moving northward against the North America plate but at varying rates. This rift zone is up to about 30 miles wide. Pt. Reyes is fully on the Pacific plate, just above the northern end of what’s called the Salinian Block. The Salinian Block is a long skinny sliver of land which is west of the San Andreas, and east of the San Gregorio faults (and the San Gregorio’s extension north). West of the San Gregorio fault is the Pacific Plate, all the way to Japan. The Salinian Block is sliding north but at a slower (average) rate than the rest of the Pacific Plate. Just below Pt. Reyes, the rift zone converges back to a single fault which focuses all the energy of plate movement. The April 18, 1906 San Francisco earthquake which destroyed the city, actually had its epicenter here at Pt. Reyes, perhaps amplified by the bending and focusing of the fault zone here.

The rocks of the east side of the fault (Tomales Bay northward, including the Russian River where we’re camping) are part of the Franciscan Formation. This is a complex set of metamorphosed marine sedimentary material. It was created during the time that the Mendicino triple junction was much further south, and most of California’s coast was defined by a subduction zone. The subducting Farallon plate had its marine sediments scraped off and piled up on the North America plate boundary. Once you cross Tomales Bay, you’re entering very different material which originated as far south as the equator and has been traveling northward for over 100 million years. During the last 30 million years or so, the subduction zone changed to the current strike/slip San Andreas Fault, and the Pacific plate carried the Pt. Reyes headlands and Mt Vision range (granitics formed deep underground and then raised up by pressure) northward. This region was actually in Monterey Bay 5-15 million years ago, and the formations that define the Santa Cruz area – Santa Cruz mudstone, the Monterey conglomerates in particular – are to be found at Pt. Reyes today. It’s a close parallel to the story of the Pinnacles National Monument. That story had a volcano just north of L.A. split by the fault, carrying half of the volcano north to it’s present Pinnacles location 23 million years later. That same movement over that time has brought the Santa Cruz mudstones and Monterey conglomerates northward as an island glommed onto the local coast here at Pt. Reyes. It’s a very different landscape and bedrock than what you see across the fault! We’ll also see wave-cut platforms in the park, similar to the wave-cut platforms around Santa Cruz; defined by emergence and subsidence due to changing pressure by the underlying earth near the fault zone.

Finally, we’ll note that the conglomerates at Monterey’s Pt. Lobos are identical to and formed in the same location as the congomerates we’ll see at the lighthouse at Pt. Reyes. The rounded cobbles in the conglomerate are stream-rounded ancient volcanic stones eroded off the Andes-like volcanic mountain range that pre-dated the current Sierra Nevada’s. This volcanic mountain range was formed, as most volcanic mountain ranges are, by the subduction and re-melting of crust at a subduction zone such as existed along most of the coast of California over 100 million years ago up to fairly recently.