## AST 324: HOMEWORK 2

1. Imagine that you throw a baseball straight up in the air; make a plot of the ball's height above the ground versus time. The details are not important, so just sketch how it would look in such a plot. Now suppose you were such an incredible pitcher than you could throw the ball faster than 11.2 km per second (or 7 miles per second), the escape velocity for the Earth. In this case, the ball will escape the gravity of the Earth and coast into space, gradually slowing down, but never coming to a stop. Sketch the path of this ball in the same plot. Which kind of Universe is each of these paths similar to? What would happen if you threw the ball at a velocity exactly equal to the escape velocity of the Earth? What kind of Universe would this path correspond to?

2. You are piloting the Millenium Falcon toward Alderaan, the planetary base of the rebel forces, when you begin to notice a large field of asteroids expanding from a point where the planet should be. Using your ship's Doppler radar, you establish that the asteroids farthest from the center are moving fastest. You quickly establish that the "Rubble Law" applies and find that the value of the "Rubble Constant" is 3 x 103 km s-1 per light hour. (A light-hour is the distance traveled by light in one hour.) How long ago was the planet destroyed? How is this problem similar to the determination of the age of the Universe from the Hubble constant? How is it different?

3. Zarkon, famous astronomer of the first galactic empire, while working for the Galactic Ma Bell Laboratories, discovered a uniform radio background with a blackbody spectrum. The temperature characterizing this background radiation was 6 K. How much bigger (in the sense of the scale size a) is the Universe now than it was in Zarkon's time? Zarkon then moved on to measuring redshifts of distant galaxies. He soon announced that their velocities were proportional to their distances -- Zarkon's Law. What was the constant of proportionality (Zarkon's Constant?)? From this information can you date the first galactic empire? (In this problem, assume the cosmic background temperature at present to be 3 K.)