Chapter Questions
A single human cell encloses about $1.5 \mathrm{m}$ of DNA containing 4.5 billion base pairs. What is the spacing between these base pairs in nanometers? That is, how far apart are the rungs on the DNA ladder?
If you represent the history of the Earth by a line $1 \mathrm{m}$ long, how long a segment would represent the 400 million years since life moved onto the land? How long a segment would represent the 3-million-year history of human life?
If a human generation, the time from birth to childbearing, is 20 years, how many generations have passed in the last million years?
If a star must remain on the main sequence for at least 5 billion years for life to evolve to intelligence, how massive could a star be and still harbor intelligent life on one of its planets? (Hint: See Reasoning with Numbers $9-1 . .$
If there are about $1.4 \times 10^{-4}$ stars like the sun per cubic light-year, how many lie within 100 light-years of Earth? (Hint: The volume of a sphere is $\frac{4}{3} \pi r^{3}$.)
Mathematician Karl Gauss suggested planting forests and fields in a gigantic geometric proof to signal to possible Martians that intelligent life exists on Earth. If Martians had telescopes that could resolve details no smaller than 1 second of arc, how large would the smallest element of Gauss's proof have to be? (Hint: Use the small-angle formula.)
If you detected radio signals with an average wavelength of $20 \mathrm{cm}$ and suspected that they came from a civilization on a distant planet, roughly how much of a change in wavelength should you expect to see because of the orbital motion of the distant planet? (Hint: Use the Doppler shift.)
Calculate the number of communicative civilizations per galaxy from your own estimates of the factors in Table $26-1$