Physics 110: Homework #12 Solutions

12.1

The decoupling epoch is that time in the evolution of the early Universe when electromagnetic radiation (e.g., light) stopped interacting with matter and began to stream freely through space. That is to say, matter and radiation became ``decoupled'' from each other at this epoch. The main reason why this became possible was because electrons were finally able to remain combined with protons as atoms. (Prior to this the radiation was too hot to allow atoms to survive.) Astronomers also refer to this as the recombination epoch. The radiation that decoupled from the matter at this epoch is what we see now as the cosmic microwave background radiation.

12.2

The curvature of an expanding universe becomes more pronounced as time passes. In order for the present universe to be as close to flat as it is, the early universe must have been almost precisely flat. Inflation has been proposed to solve this as well as other problems. During inflation the curvature of the universe was rapidly driven toward flatness.

12.3

The properties of water that are crucial to life include (1) excellent solvent, (2) large heat capacity, (3) liquid over a large temperature range, (4) high heat of vaporization. Ammonia has a smaller temperature range over which it is liquid and has a lower heat of vaporization. Compared to water, methyl alcohol has a lower heat capacity and heat of vaporization.

12.4

Since 1995 a number of planets have been discovered around nearby solar-type stars by astronomers using high resolution visible-band spectra taken repeatedly over the course of many years. The goal of these observations is to detect the reflex motion of the star caused by a planet orbiting it. The spectral observations are designed to detect motions of 10 m/s or more by the Doppler effect caused by the star's motion in reaction to its planetary companion. The discovery of more than 10 stars with planetary systems has made it clear that planetary systems are common in the Galaxy.

12.5

The speeds of current spacecraft vary quite a bit. The space shuttle orbits the Earth at an altitude of roughly 500 km in about 90 minutes. This corresponds to a speed of 8.0 km/s. The Apollo astronauts took about 2.5 days to cover the distance between the Earth and the Moon (384,000 km). Their average speed was only 1.8 km/s. The fastest moving spacecraft are four interplanetary probes (Pioneers 10 and 11, and Voyagers 1 and 2) sent by NASA to study the outer planets. They are moving fast enough, roughly 20 km/s, to escape from the solar system. (They acquired these high speeds by passing close to the giant planets and using the planet's gravity as a kind of gravitational slingshot.) Even at this high speed - 0.000067 times the speed of light - it will take them about 64,000 yrs to travel a distance of 1.3 parsec, which is the distance to the nearest star. However, the trajectories of these spacecraft are such that they will not pass close to any nearby stars.

• About this document ...