Astro 28T - Principles of the
Evolution of the Inner Planets, and
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
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.
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.
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…
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
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
The north is
dominated by the subduction of the Juan de Fuca plate
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,
is dominated by the
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
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
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
The rocks of the
east side of the fault (Tomales Bay northward,
note that the conglomerates at