The Sun-Earth system

The motion of the Earth around the Sun is an example of a two-body system that can be treated by classical mechanics. The interaction between the two particles is the gravitational force. 

The dynamical equation is Newton s second law, which in differential form can be written as in eq. (1.29). 

The first step is to introduce a centre of mass system, and the internal motion becomes motion of a particle with a reduced mass given by eq. (1.30). 

Since the mass of the Sun is 3 x 10 times larger than that of the Earth, the reduced mass is essentially identical to the Earth s mass = 0.999997mEarth). To a very good approximation, the system can therefore be described as the Earth moving around the Sun, which remains stationary. 

The motion of the Earth around the Sun occurs in a plane, and a suitable coordinate system is a polar coordinate system (two-dimensional) consisting of r and 6. 

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Fig. 5.29 Geometry of the sun-earth system (not to scale) and schematic representation of the irradiation of a surface element dA at a distance Des from the centre of the sun, Rs radius of sun...

A quantum analogue of the Sun-Earth system is a nucleus and one electron, i.e. a hydrogen-like atom. The force holding the nucleus and electron together is the Coulomb interaction. 

The potential energy again only depends on the distance between the two particles, but in contrast to the Sun-Earth system, the motion occurs in three dimensions, and it is therefore advantageous to transform the Schrddinger equation into a spherical polar set of coordinates. 

The radiation from the sun that reaches the Earth is mainly in the visible and the near infrared from 0.2 to 4 pm. Taking into account the inclination of the sun s rays and that half of the Earth is not irradiated, a power of 175 petawatt or 342 W/m is calculated to be received by the atmosphere-Earth system. These 342 W/m can be divided into 4 parts ... 

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. 

There are many systems in nature that for practical purposes are perpetual. The rotation of the Earth does not change perceptibly in any person s lifetime. Very careful measurements can detect such changes, and they arc predictable based on the tidal interaction with the sun and the moon. At the current rate of decrease, the Earth s rotation relative to the Sun would stop in 5.4 billion years. Systems that are unchanging lor practical purposes, but which are running down ever so slowly, do not count as perpetual motion. 

Our solar system consists of the Sun, the planets and their moon satellites, asteroids (small planets), comets, and meteorites. The planets are generally divided into two categories Earth-like (terrestrial) planets—Mercury, Venus, Earth, and Mars and Giant planets—Jupiter, Saturn, Uranus, and Neptune. Little is known about Pluto, the most remote planet from Earth. 

In order to understand the impact of pollution on Earth, we must realize that the planet itself is not stagnant, but continually moving material around the system naturally. Any human (anthropogenic) redistribution in the elements is superimposed on these continuous natural events. Energy from the sun and radioactive decay from the Earth s interior drive these processes, which are often cyclic in nature. As a result, almost all of the rocks composing the continents have been processed at least once through a chemical and physical cycle involving... 

The constant transport of material within and through the geospheres is powered by the sun and by the heat of the Earth s interior. A simple diagram of these geospheric concepts and the energy that moves material within them is presented in Fig. 1-1. The result of the interactions shown in Plate 1 and Fig. 1-1 is an Earth system that is complex, coupled, and evolving. 

In fludd s system, the hrst emanation of God, the Word, lived in the middle heaven in the sphere of equality and balance. His name was Metatron ( Mitattron ) the angel who descended to earth to become the Messiah Christ. The sun was his instrument for... 

Two types of theory have been put forward to explain the formation and development of our solar system catastrophe and evolution. The former assumes a collision or coming together of two stars. As early as 1745, the French scientist Count Buf-fon postulated that the Earth had been torn out of the sun by a passing comet. He estimated the age of the Earth to be 70,000 years, while theology proclaimed that the Earth was less than 6,000 years old. 

Binzel et al. (1991) give an account of the origin and the development of the asteroids, while Gehrels (1996) discusses the possibility that they may pose a threat to the Earth. The giant planets, and in particular Jupiter, caused a great proportion of the asteroids to be catapulted out of the solar system these can be found in a region well outside the solar system, which is named the Oort cloud after its discoverer, Jan Hendrik Oort (1900-1992). Hie diameter of the cloud has been estimated as around 100,000 AU (astronomic units one AU equals the distance between the Earth and the sun, i.e., 150 million kilometres), and it contains up to 1012 comets. Their total mass has been estimated to be around 50 times that of the Earth (Unsold and Baschek, 2001). 

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