11.6 The Big Bang

The light of a galaxy that moves away from us is “redshifted.” What occurs to the light of a galaxy that moves toward us?

What is meant by cosmological expansion? Express your answer in terms of a Hubble graph and the red shift of distant starlight.

Distances to local galaxies are determined by measuring the brightness of stars, called Cepheid variables, that can be observed individually and that have absolute brightnesses at a standard distance that are well known. Explain how the measured brightness would vary with distance, as compared with the absolute brightness.

If the speed of a distant galaxy is 0.99c, what is the distance of the galaxy from an Earth-bound observer?

If a galaxy is 153 Mpc away from us, how fast do we expect it to be moving and in what direction?

Our solar system orbits the center of the Milky Way Galaxy. Assuming a circular orbit 30,000 ly in radius and an orbital speed of 250 km/s, how many years does it take for one revolution? Note that this is approximate, assuming constant speed and circular orbit, but it is representative of the time for our system and local stars to make one revolution around the galaxy.

(a) Calculate the approximate age of the universe from the average value of the Hubble constant, $H_{0} = 20 \text{km}/\text{s} \cdot \text{Mly}$. To do this, calculate the time it would take to travel 0.307 Mpc at a constant expansion rate of 20 km/s. (b) If somehow acceleration occurs, would the actual age of the universe be greater or less than that found here? Explain.

Show that the velocity of a star orbiting its galaxy in a circular orbit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.