AST 248: The Search for Life in the Universe

1. The speed of light is 3 x 10¹⁰ cm/s.
   1. How fast do X-rays with a wavelength of 10^-6 cm travel in space? All electromagnetic waves travel at the speed of light in space, 3 x 10¹⁰ cm/s. The wavelength is not needed to determine this.
   2. What is the frequency of these X-rays? wavelength x frequency = c = speed of light, so frequency = 3 x 10¹⁰ cm/sec /10^-6 cm = 3 x 10¹⁶ per second.
2. The star Capella is 12 pc away. The star Regulus is 24 pc away. It is known that both stars are very similar and have approximately equal luminosities. Which star appears brighter to us, and by what factor? Capella appears brighter because it is closer. It will appear (24/12)² = 4 times brighter.
3. Vega is a main sequence star, as is the Sun, but Vega has a luminosity about 40 times that of the Sun and a mass about 3 times that of the Sun. Which star will live longer, and by what factor? The less massive star lives longer in general, but the lifetime is quantitatively proportional to mass/luminosity. So (M_sun/L_sun)/(M_Vega/L_Vega) = (1/1)/(3/40) = 40/3 = 13.3 is the factor by which the Sun outlives Vega. You could also estimate the lifetime using the approximate relation L proportional M³ so the lifetime ratio Sun:Vega is approximately [M(Vega)/M(Sun)]² = 9.
4. Which star, Vega or the Sun, has a larger habitable zone, i.e., region in which an Earth-like planet could retain liquid water? One would expect the habitable zone size to be larger for the more luminous star, in this case Vega.
5. Of all the spectral types, which type is the most abundant in our Galaxy? The least luminous stars are most abundant, so this would be M-type stars.
6. What spectral type is the Sun? The Sun is a G-type star.
7. Why do collapsing, rotating, gas clouds flatten into pancake-like shapes? Conservation of angular momentum dictates that collapsing clouds will spin up. The faster the spin, the larger the strength of centrifugal forces that resist gravity along the equator. Thus matter falls into the center near the poles but into a disc from locations farther out.
8. What is the reason that elements like Fe are more abundant in solid materials in the inner solar system than in the outer solar system? Iron is a refactory material; it condenses at a higher temperature than volatile materials like ices. In the inner solar system where the temperatures are higher, ices can't condense but iron can. So solid materials contain much more iron there.
9. Where are most asteroids in the solar system located? The asteroid belt.