PHYSICS 1040 - ELEMENTARY ASTRONOMY - HOMEWORK #14
1. A quasar (quasi-stellar object) is a star-like object that emits huge amounts of energy from a very small region of space. Observations with the Hubble Space Telescope have shown that a quasar is the extremely active nucleus of a very distant galaxy. The typical lookback time for these objects is about 10 billion years, so these energetic galactic nuclei must be very old/young (circle one). The are probably powered by a supermassive black hole at their center.
2. Olbers' paradox asks, "Why is the sky dark at night?" If the universe is infinite in extent and has existed forever, then you should see a star in any direction you look in the sky. This means that the night sky should be bright instead of dark! The solution to Olbers' paradox is that the universe has not existed forever; it was created about 13.7 billion years ago in the Big Bang. The light from any object more than 13.7 billion light years away has not had time to reach us, and so the sky looks dark at night!
3. The scale below shows the distance from the Earth (E) to two galaxies G
1 and G2. On the second scale, draw where the two galaxies will be by the time the universe has expanded to twice its present size.
During this expansion, galaxy G1 has moved a distance of 100 Mpc and galaxy G2 has moved 200 Mpc. This means that galaxy G2, which is twice as far away from the Earth as galaxy G1, is moving away twice as fast as galaxy G1.
4. The Big Bang was not an explosion of matter into empty space, like the explosion of a bomb. Instead, the Big Bang was an explosion of both space and time, and the resulting expansion of the universe is still going on today. Imagine baking a loaf of raisin bread. As the bread rises in the oven, all of the raisins move away from each other, just as all of the galaxies in the universe are moving away from each other. But the raisins are not moving through the dough; the dough is expanding with the raisins. In the same way, galaxies are not moving through space. Instead, they are being carried along with the expanding space in a motion called the Hubble flow. The actual motion of a galaxy through space is a departure from the Hubble flow, called the galaxy=s peculiar motion.
5. The cosmological constant describes the effect of dark energy on the universe. Dark energy fills all of space, causing a repulsive force between any two points in space. For two points that are close together, the effect is too small to notice. However, if the two points are twice as far apart, the repulsive force between them is twice as great. In this way dark energy is causing the expansion of the universe to accelerate. In fact, within 1015 years, even the nearest galaxies will disappear from view as the accelerating expansion of the universe carries all galaxies away from us faster than the light from those galaxies can approach us!
6. There are three possibilities for the overall geometry of space. Suppose two laser beams start out moving parallel to each other.
a. In a universe where space has zero curvature, the laser beams will always remain parallel to each other. This is called a flat universe.
b. In a universe where space has positive curvature, the laser beams will gradually move toward each other until the beams cross. This is called a closed universe.
c. In a universe where space has negative curvature, the laser beams will gradually move away from each other. This is called an open universe.
7. The critical density is the value of the average density of the universe that is required for the geometry of the universe to be flat. If H0 = 71 km/sec/Mpc (million parsecs), then this value is about 9.4 x 10-30 g/cm3 (equivalent to roughly six hydrogen atoms for every cubic meter of space). This value of the critical density_ is compared with the sum of three measured densities to determine the overall geometry of the universe:
a. the average density of atoms in the universe;
b. the average density of dark matter in the universe; and
c. the average density of dark energy (divided by c2) in the universe.
The sum of these three densities is the average density of the universe. The average density divided by the critical density is represented by the Greek letter Aomega@ (Ω):
There are three possibilities for the value of Ω.
Ω = 1: the average density of the universe is equal to the critical density, and the universe is flatd.
e.
Ω > 1: the average density of the universe is greater than the critical density, and the universe is closedf.
Ω < 1: the average density of the universe is less than the critical density, and the universe is open
8. The cosmic microwave background (CMB) is blackbody radiation that is a remnant of the Big Bang, the fiery explosion of space at the beginning of time that gave birth to a hot, dense universe about 13.7 billion years ago. The universe has been expanding and cooling off ever since, and is now at a temperature of 2.7 K. According to Wien's Law (see Question #4 on Homework #3), any object of this temperature emits most of its energy in the microwave part of the electromagnetic spectrum.
9. The overall geometry of the universe can be determined by observing the characteristic size of hot and cold spots in the cosmic microwave background. If our universe is flat, then the images of the cosmic microwave background will be dominated by hot and cold spots of around 1 degree in size (above center). If, on the other hand, the universe is closed or open, then the bending of light by the curvature of space will distort the images. If the universe is closed so parallel lines converge, then the images will be magnified by this curvature, and hot and cold spots will appear larger than 1 degree on the sky (above left). Conversely, if the universe is open so parallel lines diverge, then hot and cold spots will appear smaller than 1 degree on the sky (above right). A comparison of these computer simulations with the actual observation of the cosmic microwave background (top) indicates that space is very nearly flat, so
Ω = 1.
10. In February 2003 the results of a new high-resolution survey of the cosmic microwave background were announced. The results from the Wilkinson Microwave Anisotropy Probe (WMAP) showed that:
a. the universe is 13.7 billion years old (accurate to 1 percent), and that the universe is composed of
b. 72 percent dark energy,
c. 23 percent dark matter,
d. and only 4.6 percent atoms.
The WMAP value of the Hubble constant is
e. 71 km/sec/Mpc (accurate to 5 percent).
These values indicate that the universe will expand forever.