Astronomy 110: Stars, Galaxies, & Cosmology - Spring 2004

Solutions to Chapter 18 Problems (Universe, 6th edition, Freedman & Kaufmann)

2. Thermonuclear reactions can only occur at very high temperatures (so that the nuclei are moving fast enough to overcome the electromagnetic repulsion between them). Only in the core of the Sun -- where the pressures are highest and the gases are most compressed -- will the temperatures be high enough for nuclear fusion to take place.

4. An example of hydrostatic equilibrium: In a swimming pool, a parcel of water will not rise or fall, because the downward forces acting on it (the weight of the parcel, and the water pressure just above it) are exactly balanced by the upward forces acting on it (the water pressure just below it). As a consequence of this, the water pressure in a swimming pool increases as you go to lower and lower depths.

A pot of hot water that has been taken off the stove will not remain hot indefinitely, because heat will naturally leave the pot and flow towards its cooler surroundings. However, the water can remain at the same temperature if you put it on a lit stovetop -- as long as the rate at which heat enters the water (from the flame) is exactly equal to the rate at which heat flows out of it. This is an example of thermal equilibrium.

8. Gamma-ray photons produced by nuclear reactions in the Sun's core take something like 100,000 years to get out of the Sun, because they are continually being absorbed and re-emitted along the way. So even if nuclear reactions ceased, the photons that had been generated during the previous 100,000 years would continue to make their slow way out of the Sun. This means that the Sun would continue to shine normally for a further 100,000 years.

10. A neutrino is a neutral particle that can be emitted during certain nuclear reactions, and can carry energy. It was originally thought to be massless and to travel at the speed of light, but recent experiments and observations seem to imply that it has a tiny mass and therefore moves a bit slower than light-speed.

Since our theories of how the Sun generates energy predict that neutrinos are formed as by-products of nuclear fusion, the detection of neutrinos coming from the Sun helps confirm that these theories are correct.

Neutrinos allow us to learn about the interior of the Sun, since they are rarely absorbed on their way out. (On the other hand, we detect no photons emitted from the innermost 99.9% of the Sun, since they are absorbed before reaching us.)


Last edited 19 Feb 04 M. A. Weinstein.