AST 248: The Search for Life in the Universe

Fall 2009

HOMEWORK # 4 SOLUTIONS

YOU MUST TYPE YOUR ANSWERS.

  1. What is the difference between Dark Matter and Dark Energy? Dark matter is matter that is not made of neutrons, protons or electrons but exerts a gravitational attraction for ordinary matter nonetheless. Its presence can be inferred, for example, from the rotation of galaxies which suggests that much of their mass is invisible. Dark energy isn't made out of matter at all, but it exerts a force on matter also. However, the force it exerts seems to be opposite to gravity, and is producing an acceleration of the expansion of the universe.
  2. What are two kinds of astronomical observations that indicate that the vast majority of the universe is made up of dark matter and/or dark energy, i.e., most matter/energy is not visible or observable as ordinary matter such as gas, stars or galaxies? Evidence for dark matter include observations of the rotation of galaxies. Additional evidence for both dark matter and dark energy include observations of distant supernova of Type I, and observations of small fluctuations in the cosmic background radiation.
  3. Suppose a rock formed 4.47 billion years ago and it contained 40K and 238U nuclei in equal proportions.
    1. Today, which nucleus is more abundant in the rock? The halflife of 40 K is 1.25 Gyr. The halflife of 238U is 4.47 Gyr. Since the halflife of 40K is shorter, less of it will be left.
    2. Originally, the abundance ratio of these two nuclei was 1. Today, the ratio is about (choose one answer and show work) 1.2, 3.4, 5.9, 7.8 or 9.2. About 4.47/1.25 = 3.576 40K halflives have passed, and 1 238U halflife has passed. So the ratio today will be 23.576/21 = 22.576 = 6.0.
  4. Pretend that the Geologic Time Chart was made into a 24-hour clock. If the Earth was formed at 00:00, the Earth's atmosphere became oxidizing 2.5 billion years later, or at approximately 13:11 on the 24-hour clock.
    1. What time on the clock corresponds to the age of the oldest evidence (from carbon isotopes) for life? 3.85 Gyr corresponds to (4.55-3.85)/4.55 = 0.154 day or 3.69 hours or 3 hours and 42 minutes; therefore 03:42.
    2. What time on the clock did dinosaurs become extinct? 65 million years corresponds to .065/4.55 = 0.0143 day or 0.343 hour or 21 minutes; therefore 23:39.