CEN 511: Recent Discoveries in Astronomy

1. A conventional rocket using H+O fuel could reach a velocity of 10 km/s. Coupled with the gravity-assist procedure within our Solar System, a velocity of 100 km/s could be achieved. This is equivalent to about 0.0003 c, where c is the speed of light. How long would it take it to travel to the nearest star, alpha-Centauri, which is about 4.25 light-years away?
2. A nuclear-propulsed rocket could achieve much higher velocities. However, what are two severe problems with the use of nuclear fuel (or any other fuel that the rocket carries, for that matter), if high velocities are to be achieved in a reasonable length of time?
3. According to the idea of time dilation, if you are in a spaceship which was accelerated to a velocity of 99.99% of light speed (i.e., v/c=0.9999), how many times faster would time elapse on the Earth compared to your spaceship's clock? (Hint, in class and in the web notes we did the problem in which v/c=0.99, and got the time dilation factor 7.1).
4. What are two other possibilities for spaceship designs that could avoid some of the problems associated with conventional rockets (i.e., rockets that carry all their own fuel)?
5. The speed of light is 3 x 10^(10) cm/s.
   1. How fast do X-rays, with a wavelength of 10^(-6) cm, travel in space?
   2. What is the frequency of these X-rays?
   3. How fast do radio waves travel in space, if they have a wavelength of 100 cm?
   4. What is the frequency of these radio waves?
6. The star Capella is 14 pc away. The star Dubhe, the brightest star in the Big Dipper, is 160 pc away. Both stars have approximately equal luminosities (i.e., intrinsic power outputs). Which star appears brighter to us, and by what factor?
7. Suppose there exists a star that has exactly the same radius as the Sun, but at the same time has twice the surface temperature. How many times more luminous than the Sun would this star be?
8. Suppose you are comparing two stars, A and B, that have the same surface temperature. Star A is 100 times as luminous as star B. What could cause this difference in luminosities, in other words, what is different between star A and B?