AST 248: The Search for Life in the Universe

Fall 2009

HOMEWORK # 1 SOLUTIONS

  1. Define the two main premises on which the ancients based their belief in extraterrestrial intelligent life. Plurality -- there are lots of possible sites for life, and Design -- there is an intelligent being responsible for the universe who designed everything.
  2. In one hour, how many kilowatt-hours (kwh) of energy does the Sun radiate? Energy is Power X Time. The solar luminosity is 1023 kw, so in one hour the Sun radiates 1023 kwh.
    1. This amount of energy is equivalent to how many megatons of TNT? 1 megaton TNT=3 x 108 kwh, so 1023 kwh = 3.3 x 1014 megatons TNT
    2. This amount of energy is equivalent to how many times the world's energy consumption in one hour? World's power consumption is 32 billion kw, in one hour this is 32 billion kwh of energy. The ratio is 1023kwh/32 billion kwh = 3.2 x 1012 or 32 trillion.
  3. Suppose a star is 8 pc away.
    1. How many light-years is that? 8 x 3.26 = 26.1
    2. How many miles is that? 1 pc = 1.9 x 1013 miles, so 8 pc is 1.5 x 1014 miles
    3. What parallax angle, in seconds of arc, does this star have? D=1/angle, so angle=1/D=1/8 seconds of arc.
    4. How long does it take light (or, equivalently, a radio message) to travel from the Earth to the star? It takes light 1 year to travel 1 light-year, so it takes 26.1 years for light to travel to the star.
  4. How many times more massive is the Sun compared to the Earth? The ratio of the Sun's mass to the Earth's mass is 2 x 1033/6 x 1027 = 3.3 x 105
  5. How many times farther is 1 light-year than 1 AU (astronomical unit)? The ratio of 1 light-year to 1 AU is 9.5 x 1017/1.5 x 1013 = 6.3 x 104.
  6. How long does it take light to travel from the Sun to the Earth? Time = Distance/Velocity, so the light-travel time from the Sun to the Earth is 1AU/c = 1.5 x 1013 cm/3 x 10 cm/s = 500 s = about 8 minutes.