Sun/Jupiter

The planet Jupiter occupies a special position in the solar system. It is the largest and heaviest planet, with a mass of 1/1,047 that of the sun. Jupiter consists almost solely of hydrogen and helium with a ratio similar to that found in the sun itself He H 1 10. Small amounts of some heavier elements are present, such as B, N, P, S, C and Ge. The density of Jupiter has been calculated as 1,300 kg/m3. Its atmosphere can be divided into three zones (starting from the outermost) ... 

Figure 1. A nonrelativistic window of the temperature—composition plane, showing electron density (n) and temperature (T). Normal conditions (on earth) for semiconductors and elemental metals and conditions on the Sun, Jupiter, and the White Dwarf are shown. Experimental methods in A, B, C, and D are Tokamak, glow-discharge, laser fusion, and degenerate strongly coupled plasma, respectively. Wigner—Seitz radii, rs, are also shown (adapted from Redmei4).

Other than the Sun, Jupiter is the largest and brightest object in the solar system. It has a radius of 44,325 miles (71,492 km), 11 times that of the Earth, and an alhedo of 0.51, compared with 0.4 for Earth. Jupiter s mass is about 318 times that of the Earth, and its volume is large enough to hold 1,300 planets the size of Earth. The planet s density, like that of all outer planets, is low. At 1.33, Jupiter s density is less than a quarter of Earth s. 

Abstract These lectures are devoted to the main results of classical perturbation theory. We start by recalling the methods of Hamiltonian dynamics, the problem of small divisors, the series of Lindstedt and the method of normal form. Then we discuss the theorem of Kolmogorov with an application to the Sun-Jupiter-Saturn problem in Celestial Mechanics. Finally we discuss the problem of long-time stability, by discussing the concept of exponential stability as introduced by Moser and Littlewood and fully exploited by Nekhoroshev. The phenomenon of superexponential stability is also recalled. 

Using the classical methods of Celestial Mechanics, we can expand the distance A in the Hamiltonian (19) as a function of the Poincare variables, and we can calculate the so called secular system at order two in the masses (used, for instance, in Laskar 1988 in a model with 8 planets, to study the long term evolution of the solar system). In the secular system the dependency on the angles Ai, A2 (which evolve much faster than the other Poincare variables) is dropped out by simply averaging the Hamiltonian over the angles themselves. Thus, the actions Ai, A2 are first integrals for the secular system, which are replaced with their numerical values corresponding to the data for the real system Sun-Jupiter-Saturn at a fixed initial time. Therefore, we can actually expand the secular Hamiltonian as a power series in the form... 

The procedure above allows us to prove only that there is an invariant torus close to the initial conditions of the Sun-Jupiter-Saturn system, not that the orbit of the system actually lies on a torus. Since we can not exclude the possibility of Arnold s diffusion, this is not enough to prove the perpetual stability of the orbit of the secular system. Therefore, we make a more accurate analysis in order to prove that the orbit is actually confined in a gap between two invariant tori. The procedure is illustrated in Figure 3. 

A large majority of known triple stellar systems have the Hill-type stability, and so is the Sun-Jupiter-Saturn system (99.99% of the mass of the Solar System). The close binary is then the Sun and Jupiter, while Saturn is the third body. 

This group of asteroids are found near the equilibriums points L4 and L5 in the Sun-Jupiter system. 

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. 

Portal page to a series of pages Air, Moon, Jupiter, Fire, Mercury, Saturn, Water, Venus, Sun, Earth, Mars. Also an interesting page "A Christian Mandala - explanation of this mandala and its sources by Robert Ellaby"... 

In the region of the terrestrial planets, there may have been several thousand planetesimals of up to several hundred kilometres in diameter. During about ten million years, these united to form the four planets—Mercury, Venus, Earth and Mars—which are close to the sun. Far outside the orbit of the planet Mars, the heavier planets were formed, in particular Jupiter and Saturn, the huge masses of which attracted all the hydrogen and helium around them. Apart from their cores, these planets have a similar composition to that of the sun. Between the planets Mars and Jupiter, there is a large zone which should really contain another planet. It... 

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). 

Callisto orbits Jupiter at a distance of 1.9 million kilometres its surface probably consists of silicate materials and water ice. There are only a few small craters (diameter less than a kilometre), but large so-called multi-ring basins are also present. In contrast to previous models, new determinations of the moon s magnetic field suggest the presence of an ocean under the moon s surface. It is unclear where the necessary energy comes from neither the sun s radiation nor tidal friction could explain this phenomenon. Ruiz (2001) suggests that the ice layers are much more closely packed and resistant to heat release than has previously been assumed. He considers it possible that the ice viscosities present can minimize heat radiation to outer space. This example shows the complex physical properties of water up to now, twelve different crystallographic structures and two non-crystalline amorphous forms are known Under the extreme conditions present in outer space, frozen water may well exist in modifications with as yet completely unknown properties. 

Short-period comets these display a strong tendency for their farthest point from the sun (aphelia) to coincide with a giant planet s orbital radius, so that we can distinguish so-called comet families . The Jupiter family of comets is the largest and numbers around 70 comets. The shortest orbital period known is that of the short-period comet Encke—about 3.3 years. 

The transit method requires that the central star, the planet and the observer are connected by a line of sight. The dark planet passes across the light source and thus diminishes its light intensity to some extent. Observation is only possible when observer, star and planet are in a favourable position, i.e., the planet lies between the star and the observer. In spite of this requirement, the method permits the discovery of planets of about the size of the Earth information is also available on the size, mass and density of the planet as well as on its orbit. Because of its limits of applicability, this method is not often used. In the case of the star OGLE-TR-56, it was possible to detect an extrasolar planet, the orbit of which is very close to its sun only a twentieth of the distance of Mercury away from it. The temperature of the planet was determined to be around 1,900 K its diameter is about 1.3 times larger than that of Jupiter, its density about 500 kg/m3 (Brown, 2003 Konacki, 2003). 

The formation of the planets around the proto-sun initially started as a simple accretion process, aggregating small particles to form larger particles. This process was common to all planets, even the gas giants Jupiter and Saturn and to a lesser extent Neptune and Uranus. The planetesimals form at different rates and as soon as Jupiter and Saturn had reached a critical mass they were able to trap large amounts of hydrogen and helium from the solar nebula. The centres of Jupiter... 

Snow line The distance from the Sun at which water is stable on the surface of particles leading to comets. The presence of a large planetary mass such as Jupiter can then direct comets onto Earth, providing a source of cometary molecules to a prebiotic Earth... 

The density estimates in Table 7.1 show a distinction between the structures of the planets, with Mercury, Venus, Earth and Mars all having mean densities consistent with a rocky internal structure. The Earth-like nature of their composition, orbital periods and distance from the Sun enable these to be classified as the terrestrial planets. Jupiter, Saturn and Uranus have very low densities and are simple gas giants, perhaps with a very small rocky core. Neptune and Pluto clearly contain more dense materials, perhaps a mixture of gas, rock and ice. 

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