Solutions Manual for Physics for

Solutions Manual for Physics for Scientists & Engineers with Modern Physics, Volume 3, Chapter 36- 44 (5 th Global Edition) By Douglas Giancoli (All Chapters 100% Original Verified, A+ Grade)

All Chapters Arranged Reverse: 44-36

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CHAPTER 44: Astrophysics and Cosmology

Responses to Questions

• Long ago, without telescopes, it was difficult to see the individual stars in the Milky Way. The stars

in this region of the sky were so numerous and so close together and so tiny that they all blended together to form a cloudy or milky stripe across the night sky. Now using more powerful telescopes, we can see the individual stars that make up the Milky Way galaxy.

• If a star generates more energy in its interior than it radiates away, its temperature will increase,

indicating a higher average kinetic energy of the particles. Consequently, there will be greater outward pressure opposing the gravitational force directed inward. To regain equilibrium, the star will expand. If a star generates less energy than it radiates away, then its temperature will decrease, reflecting a lower average kinetic energy of the particles. There will be a smaller outward pressure opposing the gravitational force directed inward, and, in order to regain equilibrium, the star will contract. In both situations a new equilibrium will be reached, which means the star will not produce either a runaway heating and explosion, or a runaway total collapse.

• Red giants are extremely large stars with relatively cool surface temperatures, resulting in their

reddish colors. These stars are very luminous because they are so large. When the Sun becomes a red giant, for instance, its radius will be on the order of the distance from the Earth to the Sun. A red giant has run out of hydrogen in its inner core and is fusing hydrogen to helium in a shell surrounding the core. Red giants have left their main sequence positions on the H–R diagram and moved up (more luminous) and to the right (cooler).

• Although the H-R diagram only directly relates the surface temperature of a star to its absolute

luminosity (and thus doesn’t directly reveal anything about the core), the H-R diagram does provide clues regarding what is happening at the core of a star. Using the current model of stellar evolution and the H-R diagram, we can infer that the stars on the main sequence are fusing hydrogen nuclei to helium nuclei at the core and that stars in the red giant region are fusing helium and beryllium to make heavier nuclei such as carbon and that this red giant process will continue until fusion can no longer occur and the star will collapse.

• The initial mass of a star determines its final destiny. If, after the red giant stage of a star’s life, its

mass is less than 1.4 solar masses, then the star cools as it shrinks and it becomes a white dwarf. If its mass is between 1.4 and 2-3 solar masses, then the star will condense down to a neutron star, which will eventually explode as a supernova and become a white dwarf. If its mass is greater than 2-3 solar masses, then the star will collapse even more than the neutron star and form a black hole.

• When measuring parallaxes from the Moon, there are two cases: (1) If you did the measurements two

weeks apart (one at full moon and one at new moon), you would need to assume that the Earth did not move around the Sun very far, and then the d shown in Fig. 44–11 would be the Earth-Moon distance instead of the Sun-Earth distance. (2) If you did the measurements six months apart and at full moon, then the d shown in Fig. 44–11 would be the Sun-Earth distance plus the Earth-Moon distance instead of just the Sun-Earth distance. From Mars, then the d shown in Fig. 44–11 would be the Sun-Mars distance instead of the Sun-Earth distance. You would also need to know the length of a Mars “year” so you could take your two measurements at the correct times.

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Physics for Scientists & Engineers with Modern Physics, 5e, Global Edition Instructor Solutions Manual

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• Measure the period of the changing luminosity of a Cepheid variable star. Use the known

relationship between period and luminosity to find its absolute luminosity. Compare its absolute luminosity to its apparent brightness (the observed brightness) to determine the distance to the galaxy in which it is located.

• A geodesic is the shortest distance between two points. For instance, on a flat plane the shortest

distance between two points is a straight line, and on the surface of a sphere the shortest distance is an arc of a great circle. According to general relativity, space–time is curved. Determining the nature of a geodesic, for instance, by observing the motion of a body or light near a large mass, will help determine the nature of the curvature of space–time near that large mass.

• If the redshift of spectral lines of galaxies were discovered to be due to something other than

expansion of the universe, then the Big Bang theory and the idea that the universe is expanding would be called into question. However, the evidence of the cosmic background microwave radiation would conflict with this view, unless it too was determined to result from some cause other than expansion.

• No. In an expanding universe, all galaxies are moving away from all other galaxies on a large scale.

(On a small scale, neighboring galaxies may be gravitationally bound to each other.) Therefore, the view from any galaxy would be the same. Our observations do not indicate that we are at the center.(See Fig. 44–22.) Here is an analogy, frim Fig. 44–21. If we were sitting on the surface of a balloon and more air was put into the balloon causing it to expand, every other point on the balloon moves away from you. The points close to you are farther away because of the expansion of the rubber and the points on the other side of the balloon are farther away from you because the radius of the balloon is now larger.

• If you were located in a galaxy near the boundary of our observable universe, galaxies in the

direction of the Milky Way would be receding from you. The outer “edges” of the observable universe are expanding at a faster rate than the points more “interior”. Accordingly, due to a relative velocity argument, the slower galaxies in the direction of the Milky Way would look like they are receding from your faster galaxy near the outer boundary. Also see Fig. 44–22.

• An explosion on Earth blows pieces out into the space around it, but the Big Bang was the start of

the expansion of space itself. In an explosion on Earth, the pieces that are blown outward will slow down due to air resistance, the farther away they are the slower they will be moving, and then they will eventually come to rest. But with the Big Bang, the farther away galaxies are from each other the faster they are moving away from each other. In an explosion on Earth, the pieces with the higher initial speeds end up farther away from the explosion before coming to rest, but the Big Bang appears to be relatively uniform where the farthest galaxies are moving fastest and the nearest galaxies are moving the slowest. An explosion on Earth would correspond to a closed universe, since the pieces would eventually stop, but we would not see a “big crunch” due to gravity as we would with an actual closed universe.

• To “see” a black hole in space we need indirect evidence. If a large visible star or galaxy was

rotating quickly around a non-visible gravitational companion, the non-visible companion could be a massive black hole. Also, as matter begins to accelerate toward a black hole, it will emit characteristic X-rays, which we could detect on Earth. Another way we could “see” a black hole is if it caused gravitational lensing of objects behind it. Then we would see stars and galaxies in the “wrong” place as their light is bent as it passes past the black hole on its way to Earth.

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Chapter 44 Astrophysics and Cosmology

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• Both the formation of the Earth and the time during which people have lived on Earth are on the far

right edge of Fig. 44–29, in the era of dark energy.

• Atoms were unable to exist until hundreds of thousands of years after the Big Bang because the

temperature of the universe was still too high. At those very high temperatures, the free electrons and nuclei were moving so fast and had so much kinetic energy, and they had so many high energy photons colliding with them, that they could never combine together to form stable atoms. Once the universe cooled below 3000 K, this coupling could take place, and atoms were formed.

• (a) Type Ia supernovae are expected to all be of nearly the same luminosity. Thus they are a type of

“standard candle” for measuring very large distances.(b) The distance to a supernova can be determined by comparing the apparent brightness to the intrinsic luminosity, and then using Eq. 44–1 to find the distance.

• If the average mass density of the universe is above the critical density, then the universe will

eventually stop its expansion and contract, collapsing on itself and ending finally in a “big crunch.” This scenario corresponds to a closed universe, or one with positive curvature.

• (a) Gravity between galaxies should be pulling the galaxies back together, slowing the expansion of

the universe.(b) Astronomers could measure the redshift of light from distant supernovae and deduce the recession velocities of the galaxies in which they lie. By obtaining data from a large number of supernovae, they could establish a history of the recessional velocity of the universe, and perhaps tell whether the expansion of the universe is slowing down.

• Many methods are available.

• For nearby stars (from about 100 ly to as much as 1000 ly away) we can use parallax. In this method we measure the angular distance that a star moves relative to the background of stars as the Earth travels around the Sun. Half of the angular displacement is then equal to the ratio of Earth-Sun distance and the distance between the Earth and that star. See Fig. 44–11.• Apparent brightness of the brightest stars in galaxies, combined with the inverse square law, can be used to estimate distances to galaxies, assuming they have the same intrinsic luminosity.• The H-R diagram can be used for distant stars. Determine the surface temperature using its blackbody radiation spectrum and Wien’s law, and then estimate its luminosity from the H-R diagram. Using its apparent brightness with Eq. 44–1 will give its distance.• Variable stars, like Cepheid variables, can be used by relating the period to its luminosity. The luminosity and apparent brightness can be used to find the distance.• The largest distances are measured by measuring the apparent brightness of Type Ia supernovae. All supernovae are thought to have nearly the same luminosity, so the apparent brightness can be used to find the distance.• The redshift in the spectral lines of very distant galaxies can be used to estimate distances that are further than 10 7 to 10 8 ly.The Cepheid variable method gives the most accurate distances for far-away stars. For the most distant galaxies, redshifts give the best measurements.

• (a) All distant objects in the universe are moving away from each other, as indicated by the galactic

redshift, indicating that the universe is expanding. If the universe has always expanded, it must have started as a point. The 25% abundance of He supports the Standard Big Bang Model. The Big Bang Theory predicted the presence of background radiation, which has since been observed.

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