Surface gravity

It is tempting to take a tour of the solar system, stopping off at each planet to look at the chemistry from the origin of the red colour in Jupiter s great red spot to the volcanic activity of Io, but this would be another book for each planet. Instead, we will generalise the study to the formation of Earth-like planets in order to focus on the possibilities for life. 

The mass of a planet determines its surface gravity and hence the potential of the planet to capture and retain an atmosphere. Surface gravity also has implications for 

The mass of the Earth is 5.977 x 1024 kg. Assuming that the Earth is a sphere of radius / /, the mean density of the Earth can be calculated using  

Using the numbers quoted above and the derived mass of the Earth gives pc = 5.52 gem-3, which, by comparison with the density of other materials measured in the laboratory, means that the Earth must be made of rock, and heavy rock at that. The mass of the other planets can be determined from their orbital periods and their radii can be measured, for example, from rates of transit in front of the Sun, and so the density of the other planets within the solar system can then be determined (Table 7.1). 

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Although the spiral concentrator is mechanically a veiy simple piece of equipment, the separating ac tion taking place is complex. It involves centrifugal force, rric tion against the spiral surface, gravity, and the drag of the water. 

Our most important insight into the connection between thermodynamics and black holes comes from a celebrated result obtained by Bardeen, Carter and Hawking [bard73], that the four laws of black hole physics can be obtained by replacing, in the first and second laws of thermodynamics, the entropy and temperature of a thermodynamical system by the black hole event horizon (or boundary of the black hole) and surface gravity (which measures the strength of the gravitational field at the black hole s surface). 

Method 1 The effective temperature was derived from the excitation equilibrium of the Fel lines and the surface gravity from the ionization equilibrium of the iron lines. 

Radial velocities were measured by cross-correlation, using a synthetic spectrum as template. Individual spectra were shifted to rest wavelength and coadded. Effective temperatures were derived from the (V — I)o colours by means of the Alonso calibration [8], We assumed log g = 2.0 for all stars (estimated from isochrones) and with these parameters we fed the spectra to our automatic procedure for the determination of abundances [9], We found that the S/N ratio was too low to be able to determine reliably the microturbulent velocities, the weak Fe I lines could not be measured on many spectra. This resulted in a marked dependence of derived abundances on microturbulent velocities. It is well known that microturbulence is not a truly independent parameter but correlates with surface gravity and, more mildly also with effective temperature. By considering the large sample of stars studied by [10] one can be convinced that for all stars with 1.5 < logg < 3.0 (20 stars) there is no marked dependence from either Tefi or log g, and the mean value of the microturbulent velocity is 1.6 kms 1. For this reason we fixed the microturbulent velocity at 1.6 kms-1. 

The surface gravity, g0, is a measure of the weight of a person on the planet determined by the mass of the planet and the gravitational constant G (Figure 7.2) according to ... 

Calculation of surface gravity as a marker for internal planetary structure... 

A planet has a mass and radius the same as that of Earth but has a much lower surface gravity. 

The volatile-trapping mechanism has a further problem associated with the temperature. Very volatile molecules such as N2, CO and CH4 are not easily trapped in laboratory ice simulation experiments unless the ice temperature is 75 K, which is somewhat lower than the estimated Saturnian subnebula temperature. This has led to the suggestion that the primary source of nitrogen within the Titan surface ices was NH3, which became rapidly photolysed to produce H2 and N2 upon release from the ice. The surface gravity is insufficient to trap the H2 formed and this would be lost to space. However, the origin of methane on Titan is an interesting question. Methane is a minor component of comets, with a CH4/CO ratio of clCT1 compared with the present atmospheric ratio of > 102. The D/H ratio is also intermediate between that of comets and the solar nebula, so there must be an alternative source of methane that maintains the carbon isotope ratio and the D/H isotope ratio and explains the abundance on Titan. 

The surface gravity for Titan has been measured as 1.35 m s 2. Given that the radius is 2575 km, estimate the mass of Titan. 

Surface gravity The measure of the acceleration due to gravity at the surface of a planet on Earth this is 9.8 ms 2. 

The quantities determined directly by the spectroscopic analysis as performed for hot stars are effective temperature Tef f surface gravity g and element abundances. Of course, this is not sufficient to place a star in the HR diagram. This is possible only with further knowledge of either luminosity, radius, mass or distance of the star. However, uncertainties in these quantities (which are usually much larger than the uncertainties in Te and g) directly translate into the HR diagram. On the other hand, theoretical evolutionary tracks can be easily expressed in terms of Teff and g without loss of precision. It is therefore good practice to discuss the results of spectroscopic analyses directly in a (log Te -log g) diagram as we shall do in this paper. 

Figure 1 summarizes the results of all available fine analyses of hot evolved stars. It is important to note that most of these stars are not known to be members of binary systems. We find that all sdB and sdOB stars are drastically depleted in helium. A well-defined border line at Te = 4200OK separates these stars from the classical or "compact sdOs which cluster at Teff 50000K, have surface gravities log g > 5 and are systematically enriched in helium (y = NHe/(Njj+Njje)... 

Figure 1. Sodium overabundance versus surface gravity of P-, G- and early K-supergiants...

Figure 2. Non-LTE sodium overabundance for P-type supergiants ot-UMi, ot Gar, vCyg and pCas plotted against0 surface gravity and mass.

Everyone has practical experience with fluids, i.e., liquids and gases, and knows how a fluid will behave under normal" circumstances. Steam rises from llic surface of a hot spring or a boiling poL and water spilled on a tabletop runs over, then off. the surface. Gravity drives much of die fluid behavior we are accustomed to on Earth. 

Precht, E., and Huettel, M. (2003) Advective porewater exchange driven by surface gravity waves and its ecological implications. Lirnnol. Oceanogr. 48, 1674—1684. 

At some point, the Sun becomes so extended that the surface gravity is too weak to hold the atmospheric gas dust, and this mixture blows out of the star as a stellar wind. The Sun in this state is called a planetary nebula, with a hot central blue-violet star surrounded by rings of yellow and red. The rings are made of material from the Sun that has been blown into space. The core becomes a white dwarf (figure 7.8). 

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