Two early thinkers about the formation of the solar system were Immanuel Kant, the German philosopher, and Pierre-Simon de Laplace, the French mathematician and astronomer. Though Kant was primarily a pure philosopher, he made forays into science, and among his most successful was his 1755 publication Allgemeine Naturgeschichte und Theorie Des Himmels (General natural history and theory of the heavens), in which he articulates the hypothesis of the formation of the universe from a spinning nebula.The nebula hypothesis was later developed independently by Laplace. Laplace presented his hypothesis in a 1796 publication titled Exposition du systeme du monde (Exposition of the system of the world), describing the origin of the solar system from a contracting, cooling, slowly rotating cloud of incandescent gas.These early formulations from a philosopher and a mathematician remain the fundamental understanding of the formation of the solar system. Laplace shows his clear understanding of the theoretical basis of these hypotheses, set so far back in time that few direct clues to their functioning remain:
If man were restricted to collecting facts the sciences were only a sterile nomenclature and he would never have known the great laws of nature. It is in comparing the phenomena with each other, in seeking to grasp their relationships, that he is led to discover these laws. . . .
Though many calculations and correlations with planetary data have been made since the 18th century, the fundamental hypotheses of Kant and Laplace remain intact. The planets are thought to have grown from accumulations of matter in this early solar system nebula. Chunks of material collided and stayed together, eventually gathering enough mass to create significant gravity. Growing masses are often referred to as planetesimals, bodies that are too small and evolving too fast to be considered planets yet. These planetesimals continue to collide with each other and grow into a larger body, sweeping up the smaller matter available in the orbit of this growing planet. Some physicists believe that this process may have been completed within a few hundred thousand years.
The early planetesimals were probably irregular. The final planet Earth is round. When and how did that transformation occur? There are three main characteristics of a body that determine whether or not it will become round:
1. The first is its viscosity, that is, its ability to flow. Fluid bodies can be round because of surface tension, no matter their size; self-gravitation does not play a role. The force bonding together the molecules on the outside of a fluid drop pull the surface into the smallest possible area, which is a sphere. Solid material, like rock, can flow slowly if it is hot, so heat is an important aspect of viscosity. When planets are formed it is thought that they start as agglomerations of small bodies, and that more and more small bodies collide or are attracted gravitationally, making the main body larger and larger. The transformation of the original pile of rubble into a spherical planet is helped along significantly by the heat contributed by colliding planetesimals: The loss of their kinetic energy acts to heat up the main body. The hotter the main body, the easier it is for the material to flow into a sphere in response to its growing gravitational field.
2. The second main characteristic is density. Solid round bodies obtain their shape from gravity, which acts equally in all directions and therefore works to make a body a sphere. The same volume of a very dense material will create a stronger gravitational field than a less dense material, and the stronger the gravity of the object, the more likely it is to pull itself into a sphere.
3. The third characteristic is mass, which is really another aspect of density. If the object is made of low-density material, there just has to be a lot more of it to make the gravitational field required to make it round.
Bodies that are too small to heat up enough to allow any flow, or to have a large enough internal gravitational field, may retain irregular outlines. Their shapes are determined by mechanical strength, and response to outside forces such as meteorite impacts, rather than by their own self-gravity. In general, the largest asteroids, including all 100 or so that have diameters greater than 60 miles (100 km), and the larger moons are round from self-gravity. Most asteroids and moons with diameters larger than six miles (10 km) are round, but not all of them. Their ability to become round depends on their composition and the manner of their creation.
There is another stage of planetary evolution after attainment of a spherical shape: internal differentiation. All asteroids and the terrestrial planets probably started out made of primitive materials, such as the enstatite chondrites, which are an asteroidal composition that dates to the beginning of the solar system and seems to be among the least processed of solar system materials.The planets and some of the larger asteroids then became compositionally stratified in their interiors, a process called differentiation. In a differentiated terrestrial body, metals, mainly iron with some nickel and other minor impurities, have sunk to the middle of the body, forming a core. Lighter, silicate materials form a thick layer above the core, normally called the mantle. In some of these bodies, an even lighter crust covers the surface, such as the continents on Earth, and the white, anorthosite highlands on the Moon (anorthosite is a low-density mineral in a group of minerals called feldspars).
Terrestrial planets are therefore made up, in a rough sense, of concentric shells of materials with different compositions. The outermost shell is a crust, made mainly of material that has melted from the interior and risen buoyantly up to the surface. The mantle is made of silicate minerals, and the core is mainly of iron.The gas giant outer planets are similarly made of shells of material, though they are gaseous materials on the outside and rocky or icy in the interior. Planets with systematic shells like these are called differentiated planets. Their concentric spherical layers differ in terms of composition, heat, density, and even motion, and planets that are differentiated are more or less spherical. All the planets in the solar system seem to be thoroughly differentiated internally, with the possible exception of Pluto and Charon. What data there is for these two bodies indicates that they may not be fully differentiated. Some bodies in the solar system, though, are not differentiated; the material they are made of is still in a more primitive state, and the body may not be spherical. Undifferentiated bodies in the asteroid belt have their metal component still mixed through their silicate portions; it has not separated and flowed into the interior to form a core.
Among asteroids, the sizes of bodies that differentiated vary widely. Iron meteorites, thought to be the differentiated cores of rocky bodies that have since been shattered, consist of crystals that grow to different sizes directly depending upon their cooling rate, which in turn depends upon the size of the body that is cooling. Crystal sizes in iron meteorites indicate parent bodies from six to 30 miles (10 to 50 km) or more in diameter.Vesta, an asteroid with a basaltic crust and a diameter of 326 miles (525 km), seems to be the largest surviving differentiated body in the asteroid belt.Though the asteroid Ceres is much larger than Vesta, an unevenly shaped asteroid approximately 577 X 596 miles (930 X 960 km), seems from spectroscopic analyses to be largely undifferentiated. It is thought that the higher percentages of volatiles available at the distance of Ceres' orbit may have helped cool the asteroid faster, and prevent the buildup of heat required for differentiation. Ceres and Vesta are thought to be among the last surviving "protoplanets," and that almost all asteroids of smaller size are the shattered remains of larger bodies.
Where does the heat for differentiation come from? The larger asteroids generated enough internal heat from radioactive decay to melt (at least partially) and differentiate (for more on radioactive decay, see the sidebar "Elements and Isotopes" on page 64). Generally, bodies larger than about 300 miles (500 km) in diameter are needed, in order to be insulated enough to trap the heat from radioactive decay so that melting can occur. If the body is too small, it cools too fast and no differentiation can take place.
A source for heat to create differentiation, and perhaps the main source, is the heat of accretion. When smaller bodies, often called planetesimals, are colliding and sticking together, creating a single larger body (perhaps a planet), they are said to be accreting. Eventually the larger body may even have enough gravity itself to begin altering the paths of passing planetesimals and attracting them to it. In any case, the process of accretion adds tremendous heat to the body, by the transformation of the kinetic energy of the planetesimals into heat in the larger body. To understand kinetic energy, start with momentum, called p, and defined as the product of a body's mass m and its velocity v:
Sir Isaac Newton called momentum "quality of movement." The greater the mass of the object, the greater its momentum is, and likewise, the greater its velocity, the greater its momentum is. A change in momentum creates a force, such as a person feels when something bumps into her.The object that bumps into her experiences a change in momentum because it has suddenly slowed down, and she experiences a force. The reason she feels more force when someone tosses a full soda to her than when they toss an empty soda can to her is that the full can has a greater mass, and therefore momentum, than the empty can, and when it hits her it loses all its momentum, transferring to her a greater force.
How does this relate to heating by accretion? Those incoming plan-etesimals have momentum due to their mass and velocity, and when they crash into the larger body, their momentum is converted into energy, in this case, heat.The energy of the body, created by its mass and velocity, is called its kinetic energy. Kinetic energy is the total effect of changing momentum of a body, in this case, as its velocity slows down to zero. Kinetic energy is expressed in terms of mass m and velocity v:
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