The Solar System

The first indication of a regular numerical pattern, which summarizes the mean planetary orbital radii in astronomical units (lau= 1.496 x 10 km) by the formula 

The fractional radii are obtained by defining the mean orbital radius of Nep-truie at unit distance from the Sun. 

The fractions that describe the orbits of the four inner (rocky) planets are an order of magnitude (i) smaller than those of the outer gas giants. On 

The many moons of Saturn are readily shown to orbit the planet at commensurable distances, exactly analogous to those of the planets orbiting the sun. Assuming the moon Hyperion to reside at a relative orbital distance of 5/6, which means N = 5, the other major moons, likewise assume integer A-values. 

By the same reasoning the orbits of the major moons that orbit all other planets are seen to obey the same rules, as shown in Table 5.4. 

It has been known since 1772 that the planets orbit the sun at non-random distances, specified, in astronomical units1, by the Titius-Bode law  

This division corresponds to the division into rocky planets of the inner solar system and gaseous planets of the outer solar system, separated by the minor planets. By analogy, a larger sequence of solar satellites (planetoids, comets), of which the Pluto/Charon system is the first, is predicted to continue the regular progression beyond Neptune. 

The orbits from Venus to Ceres are represented by the unimodular series 4. In the outer system the Ford circles of only Uranus and Neptune are tangent, but the likeness to Farey sequences in atomic systems is sufficient to support the self-similarity conjecture. 

A formal refinement can be done by taking the average interaction between the planets into account, i.e. a Hartree-Fock type approximation. In this model, the orbit of one planet (e.g. the Earth) is determined by taking the average interaction with all the other planets into account. The average effect corresponds to spreading the mass of the other planets evenly along their orbits. 

The Flartree-Fock model represents only a very minute improvement over the independent orbit model for the solar system, since the planetary orbits do not cross. The effect of a planet inside the Earth s orbit corresponds to adding its mass to the Sun, while the effect of the spread-out mass of a planet outside the Earth s orbit is zero. The Flartree-Fock model for the Earth thus consists of increasing the Sun s effective mass with that of Mercury and Venus, i.e. a change of only 0.0003%. For the solar system there is thus very little difference between totally neglecting the planetary interactions and taking the average effect into account. 

The real system, of course, includes all interactions, where each pair interaction depends on the actual distance between the planets. The resulting planetary motions 

Since the perturbations due to the other planets are significantly smaller than the interaction with the Sun, the wiggles are small compared with the overall orbital motion, and a description of the solar system as planets orbiting the Sun in elliptical orbits is a very good approximation to the true dynamics of the system. 

The question of the origin and evolution of the solar system is one of the most fundamental in astronomy. It bears directly on such related issues as stellar evolution, the formation of planetary systems, and on the existence of life itself. Gamma-ray observations from spacecraft, either via remote sensing from orbit or through in situ measurements 

The gamma-ray observations relevant to planetary studies are spectroscopic in nature, aimed at identifying specific key elements present in planetary surfaces via their characteristic emission energies. The abundances of elements with different condensation temperatures and geochemical behavior relate directly to the origin and evolution of planetary bodies. For example, the K/U ratio provides a measure of the remelting of primordial condensates, while the K/Th ratio indicates the relative abundance of volatile to refractory elements. 

Since the 1960s measurements of X-rays, gamma rays, alpha particles, and neutrons from the Moon, Mars, and Venus have been undertaken successfully with a variety of instruments aboard both U.S. and Russian spacecraft. The two U.S. Viking landers on Mars, for example, carried out X-ray fluorescence measurements of the Martian surface, while the Russian Venera 8, 9, and 10 spacecraft measured the natural radioactivities of potassium, uranium, and thorium at three landing sites on Venus. 

Until very recently the most detailed and extensive remote-sensing observations of a planetary body were carried out during the Apollo 15 and 16 flights to the Moon (1971, 1972) when instruments aboard the orbiting command modules mapped approximately 20% of the lunar surface in X-rays, gamma rays, and alpha particles. The Apollo missions were also unique in that a detailed comparison could be made between the results of the remote mapping and follow-up compositional analysis of actual returned samples of lunar material. 

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In fact, even in the solar system, despite the relative strengths of planetary attraction, there are constituents, the asteroids, with very irregular, chaotic behaviour. The issue of chaotic motion in molecules is an issue that will appear later with great salience.)... 

Earth to space (sateUite) to earth communication links are relatively insensitive to ionospheric disturbances. Communications between earth and manned space vehicles are barely affected by plasmas when the spaceships are well away from the atmosphere, eg, in orbit or in a translunar trajectory. However, during reentry of a spaceship, a low temperature plasma forms around the vehicle and intermpts the communication links to it (183). Plasmas are incidental to the performance of modem rockets used to explore the solar system. 

Most schemes that have been proposed to propel starships involve plasmas. Schemes differ both in the selection of matter for propulsion and the way it is energi2ed for ejection. Some proposals involve onboard storage of mass to be ejected, as in modem rockets, and others consider acquisition of matter from space or the picking up of pellets, and their momentum, which are accelerated from within the solar system (184,185). Energy acquisition from earth-based lasers also has been considered, but most interstellar propulsion ideas involve nuclear fusion energy both magnetic, ie, mirror and toroidal, and inertial, ie, laser and ion-beam, fusion schemes have been considered (186—190). 

Th ese manufactured light sources are, perhaps ironically, largely dependent on the Sun. The radiant energy from the Sun has been stored in the fossilized remains of billions of creatures over millions of years and is used to power the electric light sources created by modern humans. The power generated by hydroelectric sources also is a result of solar evaporation and subsequent rainfall. Only nuclear reactors provide power independent of the Sun, which is, of course, the largest nuclear reactor in the solar system. 

Book II investigates the dynamical conditions of fluid motion. Book III displays the law of gi avitatioii at work in the solar system. It is demonstrated from the revolutions of the six known planets, including Earth, and their satellites, though Newton could never quite perfect the difficult theory of the Moon s motion. It is also demonstrated from the motions of comets. The gravitational forces of the heavenly bodies are used to calculate their relative masses. The tidal ebb and flow and the precession of the equinoxes is explained m terms of the forces exerted by the Sun and Moon. These demonstrations are carried out with precise calculations. 

The solid plates that resulted from the cooling process at the surface of the eanli were able to float on the remaining molten inner portion of the earth. Because of the rotational motion of the earth about its own axis and the earth s motion in the solar system, inertial and gravitational forces have produced great interactive forces between the plates. It is speculated that these interactive forces have led to plate contact and situations where one plate has slid over another. The great forces created by plate tectonics are likely responsible for the forces that have resulted in the folding and faulting of the earth s crust [30j. 

We might as well attempt to introduce a new planet into the solar system, or to annihilate one already in existence, as to create or destroy a particle of hydrogen. All the changes we can produce consist in separating particles that are in a state of combination, and joining... 

Progress in aeronautics and astronautics within the past decades has been remarkable because people have learned to master the difficult feat of hypervelocity flight. A variety of manned and unmanned aircraft have been developed for faster transportation from one point on earth to another. Similarly, aerospace vehicles have been constructed for further exploration of the vast depths of space and the neighboring planets in the solar system. 

These isotopes are sometimes used as tracers of natural terrestrial processes and cycles. Long-lived isotopes, such as Rb and Sm are used for precise dating of geological samples. When the solar system formed it also contained several short-lived isotopes that have since decayed and are now extinct in natural systems. These include Al, Fe, Pu, Pd, and Al with a half-life of less than a million years is particularly important because it is a potentially powerful heat source for planetary bodies and because its existence in the early solar system places tight constraints on the early solar system chronology. 

Fig. 2-4 The sequence of condensation of solids from a solar composition gas at a nebular pressure of 10 Pa (ca. 10 atm). (Modified with permission from J. A. Wood, "The Solar System," p. 162, Copyright C 1979, Prentice-Hall, Englewood Cliffs, NJ.)...

A collision with a Mars-sized object may have resulted in the formation of the Earth s moon. Our moon is by no means the largest satellite in the solar system, but it is unusual in that it and the moon of Pluto are the largest moons relative the mass of the planets they orbit. Geochemical studies of returned lunar samples have shown that close similarities exist between the bulk composition of the moon and the Earth s mantle. In particular, the abimdances of sidero-... 

As can be seen in Fig. 2-1 (abundance of elements), hydrogen and oxygen (along with carbon, magnesium, silicon, sulfur, and iron) are particularly abundant in the solar system, probably because the common isotopic forms of the latter six elements have nuclear masses that are multiples of the helium (He) nucleus. Oxygen is present in the Earth s crust in an abundance that exceeds the amount required to form oxides of silicon, sulfur, and iron in the crust the excess oxygen occurs mostly as the volatiles CO2 and H2O. The CO2 now resides primarily in carbonate rocks whereas the H2O is almost all in the oceans. 

The capacity to solve novel problems by constructing analogies to already-used visualisations. (Gilbert, 2008). For example, using Kepler s model of the Solar System to explain the electronic structure of an atom, in the manner of Bohr, and hence being able to predict, very approximately, the absorption spectram that it will produce. 

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