# hw5

```Homework 5 Solutions
p. 458 RQ # 6 Why do we think that liquid water is necessary for the origin of life?
All life on earth is made of the same organic materials and comprised mostly of water.
The basic building blocks of living matter are theorized to have come together in the
oceans. Most importantly, the Miller experiment showed that in the early periods of
earth's history hydrogen gas, methane, and water in the presence of electricity could
combine to form basic amino acids and building blocks of DNA present in life on Earth.
At a time when the Earth’s atmosphere lacked ozone’s protection from ultraviolet light,
the oceans provided a safe region that UV can’t penetrate.
p. 458 RQ# 9 How does intelligence make a creature more likely to survive?
A creature’s likelyhood of surviving changes in their environment over time depends on
how quickly they can adapt to those changes. An intelligent creature can adapt very
quickly to changes through use of tools and rational behavior.
p. 370 RQ# 3 How can astronomers use variable stars to find distance?
Astronomers have discovered that there is a direct relation between the period of a
variable star and its luminosity. By simply observing the changes in brightness over time,
astronomers can determine the period. Then by applying the period/luminosity relation,
the luminosity is estimated. The luminosity is converted into an absolute magnitude (M).
We can then use the difference between the observed apparent magnitude of the star (m)
and the absolute magnitude (the distance modulus) to find the distance, using the
equation m-M = 5 log d - 5 .
p. 370 RQ# 8 How can astronomers find the mass of the Galaxy?
Astronomers find the mass of the galaxy by studying the orbital motions of stars in the
galaxy. We use the Doppler shift of stars to find their radial motions. We use the
distance to and proper motion of stars to find their perpendicular velocity. For example,
we know that the sun is ~ 8.5 kpc from the center of the galaxy and it has an orbital
period around the galaxy of ~ 240 x 106 years. We can use Kepler's law to estimate the
mass of the galaxy interior to the sun, M (mass of the sun) = a3 (AU) / p2 (years).
Problem: If the fastest plane can travel at 1600 km / hour, how long will it take to get to
the Sun? Alpha Centauri? The Center of the Galaxy?
First find the distance the plane can travel in a year.
Distance plane travels/yr = 1600 km/hr x 24 hr/day x 365.25 d/yr
= 1.4 x 107 km/yr
For the Sun, the distance is 1 AU = 1.4 x 108 km. (p. 128—data file on Earth)
So time =distance/velocity
time to reach Sun = 1.4 x 108 km / 1.4 x 107 km/yr
=1 x 108-7 = 1 x 101 = 10 years
For Alpha Centauri, which is the nearest star:
p. 249 gives the parallax of Alpha Centauri as 0.76 seconds of arc, d = 1/p, d=1/0.76=1.3
parsecs
1 parsec =3.08 x 1016 m = 3.08 x 1013 km (p.465 Appendix),
so 1.3 parsecs x 3.08 x 1013 km/pc = 4 x 1013 km = distance to Alpha Centauri
(also Alpha Centauri appears in Table A-7 Nearest Stars, p. 466, distance given as 4.37
LY; 1 LY = 9.5 x 1012 km, p. 465)
So time = distance/ velocity
= 4 x 1013 km / 1.4 x 107 km/yr
= 2.9 x 1013-7 yr
= 2.9 x 106 yr
29 million years!
To the Center of the Galaxy
Distance = 8.5 kpc (p. 353)
kpc = 1 kiloparsec = 1000 parsecs and 1 parsec = 3.08 x 1013 km (above)
Distance to galactic center = 8.5 x 103 pc x 3.08 x 1013 km/pc
= 26 x 103+13 km = 2.6 x 1017 km
time = distance / velocity
So time = 2.6 x 1017 km / 1.4 x 107 km/yr
= 1.9 x 1017-7 yr
= 1.9 x 1010 yr
19 billion years!
```