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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.
2. A primary reason is that O stars are hot and bright, and so don't live very long. So one is much less likely to see O stars in a given population.
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.
6. d(pc) = 10(m - M + 5) / 5, so d = 103 = 1000 pc
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.
8. Since both are important ways used to determine distance, the further they can be seen the more useful they are as distance indicators. From the magnitude formula, 14 magnitudes corresponds to a factor in brightness of
The square root of this is about 630. Since the brightness goes as the square of the distance, a Type Ia supernova 630 times further away than a Cepheid will have the same apparent brightness at peak as the Cepheid. The order of magnitude of 630 is 1000, so we commonly say that a type 1A supernova can be used at distance about 1000 times larger than a Cepheid variable to determine distance.
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.
10. The solution is provided by the star velocity calculator.
12. Light travels 3 x 105 km in a second, so this is the length of a light second. There are about 150,000,000 kilometers in an AU, so 1 light second = (300,000 km)/(150,000,000 km) = 0.002 AU.
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.
14. If stars have no proper motion, they either have zero space velocity, or they are moving directly toward us or directly away from us. Since most stars have a finite space velocity, the latter possibility is more likely. This can be confirmed by measuring the radial velocity using Doppler methods. If a star observed to have a certain space velocity is (unknown to us) actually a member of a binary, part of its motion is not space velocity of the center of mass but orbital motion of the binary. These two contributions must be separated before we can determine the true space velocity of the center of mass and thus project whether the system will pass close to Earth.