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| Properties of Stars |
1. The reasons are somewhat different. In the star the colors are influenced by the possible electronic excitations of the atoms and ions, not primarily by the types of atoms and molecules present. In the case of Jupiter and Saturn, we think the temperature more directly influences the types of compounds present (and thus the color) because it controls the rates of chemical reactions producing those compounds. They are not completely different; for example, in cool stars molecules are present that are not there in hotter stars.
3. The essential point is the amount of spectral light emitted in the visible relative to other wavelength regions. This is determined by Planck's law and depends only on the temperature, since this determines the intensity curve. For intermediate temperature stars like the Sun most light is in the visible, so the correction is small. For very hot stars most light is in the UV and for very cool stars most light is in the IR, so the corrections are large in that case.
7. Using Earth as a guideline, evolution of intelligence has taken several billion years. Presumably this would have not been very likely unless the Sun were stable over periods of billions of years, which being on the main sequence ensures. Thus, let us assume that life is most likely to have evolved for stars that can spend at least of order a billion years on the main sequence. This eliminates O and B stars for sure, and probably A stars. Thus, we may expect that spectral classes F-M are a good starting point.
9. There are 60 x 60 = 3600 seconds of arc in a degree. The Moon subtends about 1/2 degree ~ 1800 seconds of arc. Barnard's Star moves by 10.3 seconds of arc per year on the celestical sphere. Thus, it takes about 1800 / 10.3 = 175 years to move the diameter of the Moon on the celestial sphere.
13. In a million years the apparent magnitude will be about -0.6. The radial velocity is about -14 km/s if it must cover 63 light years in about a million years.