Having only one planetary system that we can carefully observe, we try to generalize from our solar system to model the formation of planets. This involves modeling the gravitational collapse of a large diffuse cloud of gas and dust. Given a non-zero angular momentum of the cloud with respect to some axis, there will be an increase in rotational angular velocity associated with the collapse. The formation of a disk perpendicular to the spin axis results, and in the case of our Sun we would call the growing system with its disk the primitive solar nebula. Modeling from the solar planets, it is judged that the protoplanetary disk must contain a minimum of about 2% of the system mass.

In the protoplanetary disc, cooling leads to the condensation of some of the elements and compounds to dust grains, followed by the formation of larger solid bodies. Gravitational forces including tidal forces are involved. de Pater and Lissauer is a good reference for discussion of some of the stages of planet formation.

 

Orbit and rotation

Image showing Uranus, its bands, rings and moons clearly outlining its sideways pose

Uranus's orbit is roughly 84 Earth years long. Its average distance from the Sun is roughly 3 billion km; at that distance, sunlight is barely 1/400 that of Earth.^[17] Its orbit was first calculated in 1792, however, almost immediately discrepancies began to appear between the orbit predicted and the actual orbit as observed. In 1841, John Couch Adams, then an undergraduate at Cambridge, first proposed that the discrepancy might be due to the gravitational tug of an unseen planet beyond it. In 1845, Urbain Le Verrier, working at the Paris Observatory, began his own independent research into Uranus's uncertain orbit. On the 23 September, 1846, German astronomer Johann Gottfried Galle, working from information supplied by Le Verrier, located a new planet, later named Neptune, at nearly the position predicted. Le Verrier gained credit for its discovery.^[18]

Uranus's rotational period, its "day", lasts roughly 17 hours, 14 minutes. Like all gas giant planets, its core spins more slowly than its upper atmosphere. The fastest region of Uranus's atmosphere, around its south pole, makes one rotation in only 14 hours. Windspeeds in that region reach upwards of 720 kilometers per hour.^[19]

Axial tilt

One of the most unusual features of Uranus is its axial tilt of ninety-eight degrees. Effectively, Uranus is lying on its side. Consequently, for part of its orbit one pole faces the Sun continually while the other pole faces away. At the other side of Uranus's orbit the orientation of the poles towards the Sun is reversed. This gives each pole 42 years of continuous sunlight, followed by 42 years of darkness.^[20] Between these two extremes of its orbit, particularly at the equinoxes, the Sun rises and sets around the equator normally. Uranus will reach its next equinox around December 2007, and not again until 2049.^[21

Antimatter

In 1930, Paul Dirac developed the first description of the electron that was consistent with both quantum mechanics and special relativity. One of the remarkable predictions of this theory was that an anti-particle of the electron should exist. This antielectron would be expected to have the same mass as the electron, but opposite electric charge and magnetic moment. In 1932, Carl Anderson, was examining tracks produced by cosmic rays in a cloud chamber. One particle made a track like an electron, but the curvature of its path in the magnetic field showed that it was positively charged. He named this positive electron a positron. We know that the particle Anderson detected was the anti-electron predicted by Dirac. In the 1950's, physicists at the Lawrence Radiation Laboratory used the Bevatron accelerator to produce the anti-proton, that is a particle with the same mass and spin as the proton, but with negative charge and opposite magnetic moment to that of the proton. In order to create the anti-proton, protons were accelerated to very high energy and then smashed into a target containing other protons. Occasionally, the energy brought into the collision would produce a proton-antiproton pair in addition to the original two protons. This result gave credibility to the idea that for every particle there is a corresponding antiparticle.

A particle and its antimatter particle annihilate when they meet: they disappear and their kinetic plus rest-mass energy is converted into other particles (E = mc²). For example, when an electron and a positron annihilate at rest, two gamma rays, each with energy 511 keV, are produced. These gamma rays go off in opposite directions because both energy and momentum must be conserved. The annihilation of positrons and electrons is the basis of Positron Emission Tomography (PET) discussed in the section on Applications (Chapter 14). When a proton and an antiproton annihilate at rest, other particles are usually produced, but the total kinetic plus rest mass energies of these products adds up to twice the rest mass energy of the proton (2 x 938 MeV).

Antimatter is also produced in some radioactive decays. When ¹⁴C decays, a neutron decays to a proton plus an electron and an electron antineutrino, . When ¹⁹Ne decays, a proton decays to a neutron plus a positron, e⁺, and an electron neutrino, .

¹⁴C --> ¹⁴N + e^- +

¹⁹Ne --> ¹⁹F + e⁺ +

The neutrino and electron are leptons while the antineutrino and positron are anti-leptons. Leptons are point-like particles that interact with the electromagnetic, weak and gravitational interaction, but not the strong interaction. An antilepton is an antiparticle. In each reaction, one lepton and one antilepton is produced. These processes show a fundamental law of physics - that for each new lepton that is produced there is a corresponding new antilepton.

Although from a distance matter and antimatter would look essentially identical, there appears to be very little antimatter in our universe. This conclusion is partly based on the low observed abundance of antimatter in the cosmic rays, which are particles that constantly rain down on us from outer space. All of the antimatter present in the cosmic rays can be accounted for by radioactive decays or by nuclear reactions involving ordinary matter like those described above. We also do not see the signatures of electron-positron annihilation, or proton-proton annihilation coming from the edges of galaxies, or from places where two galaxies are near each other. As a result, we believe that essentially all of the objects we see in the universe are made of matter not antimatter.

Elementary particle physicists create massive particles by accelerating lower mass particles close to the speed of light, and then smashing them together. The mass/energy of the colliding particles becomes the mass of the created particles. One method includes taking positrons and electrons, accelerating both of them, and smashing them into each other. Out of this energy, very massive particles such as quarks, tau-particles, and the Z⁰ can be created. Studies of such electron-positron annihilations are carried out at the Stanford Linear Accelerator and at the LEP facility at CERN. A similar technique is used at the Fermi National Accelerator Laboratory except that it involves colliding protons with anti-protons. Collisions of this kind were recently used to produce the sixth type of quark, known as the top. This particle has a rest mass energy of approximately 160,000 MeV, which is nearly the same as the mass of nucleus of a gold atom!

Atoms of anti-hydrogen, which consist of a positron orbiting an antiproton, are believed to have been created in 1995 at the CERN laboratory in Europe. Physicists are now searching for very small differences between the properties of matter atoms and antimatter atoms. This will help confirm or confound our understanding of the symmetry between matter and anti-matter.