Planetary distances

While dust continuum emission can be used to estimate disk masses, line emission from optically thin molecules (e.g., CO) can be used to map the line-of-sight velocities in disks, using the Doppler shift of the moving gas. Evidence for Keplerian velocity profiles is typically found (e.g., Launhardt and Sargent, 2001), as is to be expected for gas in a stable orbit around a central protostar. These measurements only apply to the gas at considerable distances from the young star, however, typically at several hundred astronomical units or more. The situation inside these disks at planetary distances is not constrained by these observations, and even the outer disk measurements are subject to possible confusion with infalling gas in the envelopes and outflowing gas from stellar winds. 

FIGURE 2.6 Midplane solar nebular temperatures (K) calculated for 0.04 and 0.02 solar masses in the accreting disk, and estimated temperatures from meteorites and comets, plotted against distance from the sun, expressed both as astronomical units (1 AU = Earth-Sun distance) (bottom) and planetary distance (top). The temperatures presented here are indicative only, as they are dependent upon the size of the disc and the thermal model used (after Boss, 1998). 

Note that equations containing t involve only time differences, not their absolute values (e.g., Eqns. 7 and 11). Consequently the fractionations of initial isotopic and elemental ratios generated by hydrodynamic escape do not depend on any specific choice for to, the time in solar evolutionary history when atmospheric escape begins. Permitted values of to are constrained, however, by the solar EUV flux needed to drive an escape episode. For example, as noted in the following section, EUV-driven Xe loss from Earth requires a flux that exceeds the present solar level by a factor of 450, and thus a to no later than -100 Ma if the flux history follows the i = 90 Ma exponential in Figure 10. It is assumed that to, whatever its value, marks the time at which dust and gas in the nebular midplane had cleared to the extent that solar EUV radiation could penetrate to planetary distances, so that EUV-driven atmospheric loss would not have occurred prior to to (Prinn and Fegley 1989). 

Starting with the sequence of numbers 0, 3, 6, 12, 24, 48, 96,. .., in which each new term beyond 3 is obtained by doubling the previous term, adding 4 to each term, and divide by 10, the sequence of planetary distances is reproduced in astronomical units. lAU equals the distance of planet Earth from the sun. Hence ... 

The incident power is the planetary cross section times the solar flux at the planetary distance from the Sun,... 

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... 

Fig. 3.40. Abundances in Galactic stars, H n regions and planetary nebulae, as a function of Galactocentric distance, with the Sun shown for comparison. After Hou, Prantzos and Boissier (2000). The curves show a model calculation by the authors nitrogen is underproduced in the model because only massive stars were considered. 

Upper panels show vertical profiles of manganese in the North Pacific Ocean at (a) an open-ocean station, (b) a coastal station, and (c) the Mn content of surface water with increasing distance from the California coast. Note the tenfold scale difference in concentration between these diagrams. Source From Landing, W. M., and K. W. Bruland (1980). Earth and Planetary Sciences Letters, 49, 45-56. 

Many of the newest areas of scientific research involve objects or places that are not easily accessible, if at all. These objects may be trillions of miles away, such as the newly discovered planetary systems, or they may be as close as inside a person s head the brain, a delicate organ encased and protected by the skull, has frustrated many of the best efforts of biologists until recently. The subject of interest may not be at a vast distance or concealed by a protective covering, but instead it may be removed in terms of time. For example, people need to learn about the evolution of Earth s weather and climate in order to understand the changes taking place today, yet no one can revisit the past. 

Using these ideas, Bohr developed a conceptual model in which an electron moving around the nucleus is restricted to certain distances from the nucleus, with these distances determined by the amount of energy the electron has. Bohr saw this as similar to how the planets are held in orbit around the sun at given distances from the sun. The allowed energy levels for any atom, therefore, could be graphically represented as orbits around the nucleus, as shown in Figure 5.13. Bohr s quantized model of the atom thus became known as the planetary model. 

The angular momentum or an electron moving in an orbit of the type described by Bohr is ail axial vector L = r x p, formed from the radial distance r between electron and nucleus and the linear momentum p of the electron relative lo a fixed nucleus. Figure 2 shows the customary method used to illustrate the axial vector L in terms of the orbital morion of any object, of which the electron of the Bohr atom is only one example. Although Bohr s planetary model needed only circular orbits lo explain the spectral lines observed in the spectrum of a hydrogen atom, subsequent... 

With the modern concept of a hydrogen atom we do not visualize the orbital electron traversing a simple planetary orbit. Rather, we speak of an atomic orbital, in which there is only a probability of finding the electron in a particular volume a given distance and direction from the nucleus. The boundaries of such an orbital are not distinct because there always remains a finite, even if small, probability of finding the electron relatively far from the nucleus. 

In general, the methods are difficult to interpret quantitatively in terms of aerosol properties because of ambiguities in the size distribution-concentration-distance profiles and variations in chemical properties contributing to the index of refraction. Nevertheless, remote sensing continues to be important for the surveillance of aerosol behavior in planetary atmospheres. 

Synthesis of the three observations led to Bohr s proposal of a planetary atom consisting of a heavy small stationary heavy nucleus and a number of orbiting electrons. Each electron, like a planet, had its own stable orbit centred at the atomic nucleus. The simplest atom, that of hydrogen, with atomic number 1 could therefore be described as a single electron orbiting a proton at a fixed, relatively large, distance. The mechanical requirement to stabilize the orbit is a balance between electrostatic and mechanical forces, expressed in simple electrostatic units, and particle momentum p = mv, as ... 

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