AST 105 HW #4 Solution

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1 AST 105 HW # Solution Week of September 1 th, 2015 Note: All Problems are from The Cosmic Perspective (6ed) Chapter 6 Review Problems 2. For purposes of astronomy, what advantages does a camera have over the human eye? What advantages do CCDs have over photographic film? We can easily change the magnification and exposure time of a camera, but not those of the human eye. Also, the camera can collects light for several hours, but the human eyes cannot. Charged-coupled devices, CCDs, are more sensible to light than photographic film.. What is the diffraction limit, and how does it depend on a telescope s size and the wavelength of light being observed? The diffraction limit is a natural, physical limit on the finest resolution a given telescope can achieve at a particular wavelength. As the telescope gets larger, the diffraction limit decreases (leading to the possibility of finer resolution). However, as the wavelength increases, the diffraction limit increases so that longer wavelengths require larger telescopes to achieve the same resolution. 8. What do we mean by spectral resolution? Why is higher spectral resolution more difficult to achieve? Spectral resolution measures how fine the details are that we can see in a spectrum. With better spectral resolution, we can make out features closer together in wavelength in the spectrum. High spectral resolution requires longer exposures (or brighter sources) than we need for images, because the light is spread out when we make a spectrum. 10. Study Figure 6.22 and describe how deeply each portion of the electromagnetic spectrum penetrates Earth s Atmosphere. Based on your answers, why are space telescopes so important to our understanding of the universe? The only wavelengths that make it all the way to the ground are the narrow range of visible light (and a very small amount of the ultraviolet that is nearest in wavelength to visible light) and the radio wavelengths. A few other wavelengths can be detected from high mountains or from aircraft, but most wavelengths require us to put telescopes in space, which is why space-based astronomy is so important. Quick Quiz Choose the best answer to each of the following. Explain your reasoning with one or more complete sentences. 1

2 23. How much greater is the light-collecting area of a 6-meter telescope than a 3-meter telescope? (a) two times (b) four times (c) six times (b) The light-collecting area of a 6-meter telescope: ( 6 2 m)2 π = 9π m 2 The light collection area of a 3-meter telescope: ( 3 2 m)2 π = 9 π m2 So the 6-meter telescope collects four times more light than the 3-meter telescope. 2. Suppose that two stars are separated in the sky by 0.1 arc-second. If you look at them with a telescope that has an angular resolution of 0.5 arc-second, what will you see? (a) two distinct stars (b) one point of light that is the blurred image of both stars (c) nothing at all (a) An angular resolution of the telescope is 0.5 arc-second. With this telescope, you cannot distinguish any two objects that are separated by less than 0.5 arc-second. 28. The twinkling of stars is caused by (a) variations in stellar brightness with time. (b) light pollution. (c) motion of air in our atmosphere. (c) The twinkling of stars is caused by motion of air in our atmosphere. 29. If you wanted a radio telescope to achieve the same angular resolution as a visible-light telescope, it would need to be (a) much larger. (b) slightly larger. (c) in space. (a) The diffraction limit of telescope is proportional to wavelength, but inversely proportional to the diameter of telescope. Radio wave has much longer wavelength than visible-light, so we need a much larger diameter to achieve the same angular resolution. Quantitative Problems Be sure to show all calculations clearly and state your final answers in complete sentences. 2. Light-Collecting Area. a. How much greater is the light-collecting area of one of the 10-meter Keck telescopes than that of the 5- meter Hale telescope? b. Suppose astronomers built a 100-meter telescope. How much greater its light collecting area than that of the 10-meter Keck telescope? a) The light collecting area of a 10-meter Keck telescope = ( 10 2 m)2 π = 25π m 2 2

3 The light collecting area of the 5-meter Hale telescope = ( 5 2 m)2 π = 25 π m2 The light collecting area of a 10-meter Keck telescope is four times larger than that of the 5-meter Hale telescope b) Since the light-collecting area is proportional to the square of the diameter of telescope. The lightcollecting area of a 100-meter telescope is 100 times bigger than that of the 10-meter Keck telescope. Chapter 7 Review Problems 1. What do we mean by comparative planetology? Does it apply only to planets? Comparative planetology is a way of studying the solar system that relies on comparing the objects in the solar system to each other. The objects do not need to be planets; moons, rings, asteroids, and comets are all part of the field, for example. 5. What are the four major features of our solar system that provide clues to how it formed? Describe each one briefly. (1) Planetary motions are mostly orderly: orbits and rotations are in the same direction and with generally small tilts; (2) There are two types of planets, Jovian and terrestrial, with very different properties and locations; (3) There are also two classes of small bodies, comets and asteroids, also with distinction properties and locations; () Despite the neatness of the preceding facts, there are notable exceptions that require explaining. 6. What are the basic difference between the terrestrial and jovian planets? Which Planets fall into each group? Terrestrial planets orbit close to the Sun and are tightly spaced together. They are made mostly of rock and metal and are smaller and denser than Jovian planets. Terrestrial planets tend to have few, if any, moons and none has rings. In contrast, Jovian planets are more distant from the Sun and are separated by much larger distances. They are made mostly of hydrogen, helium, and hydrogen compounds. They are much less dense than terrestrial planets. They are also larger than terrestrial planets. Jovian planets have many moons and have ring systems. The terrestrial planets are Mercury, Venus, Earth, and Mars. The Jovian planets are Jupiter, Saturn, Uranus, and Neptune. Pluto does not fit into either class. 9. What are asteroids? Where do we find most asteroids in our solar system? 3

4 Asteroids are rocky or metallic bodies that orbit the Sun. Most known asteroids are found between the orbits of Mars and Jupiter. Test Your Understanding Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain clearly; not all of these have definitive answers, so your explanation is more important than your chosen answer. 15. Pluto orbits the Sun in the opposite direction of all the other planets. False. Pluto and other Kuiper Belt objects orbit in the same direction as the planets. 16. If Pluto were as large as the planet Mercury, we would classify it as a terrestrial planet. False. Terrestrial planets are the rocky planets from inner solar system. Pluto is an icy Kuiper Belt object. 17. Comets in the Kuiper belt and Oort cloud have long, beautiful tails that we can see when we look through telescopes. False. Tails of comets appear only when those comets come near the Sun. If comets are in the Kuiper belt and Oort cloud, they are too far from the Sun to be observed with tails. 18. Our Moon is about the same size as moons of the other terrestrial planets. False. Only terrestrial planets that have any moon are the Earth and Mars. Mars have two moons that are much smaller than our Moon. 19. The mass of the Sun compared to the mass of all the planets combined is like the mass of an elephant compared to the mass of a cat. True. The Sun contains about 99.8% of the total mass of the solar system. If we assume an elephant weights 5 tons and a cat weight 50 kg, the comparison is valid. 20. On average, Venus is the hottest planet in the solar system even hotter than Mercury. True. The average temperature of Venus is 70 Kelvin. Mercury s temperature is about 700 Kelvin during the day and 100 Kelvin in the night. 21. The weather condition on Mars today are much different than they were in the distant past. True. In the distant past, Mars were warmer and more humid than it is now.

5 22. Moons cannot have atmospheres, active volcanoes, or liquid water. False. Jupiter s moon Io is the most volcanically active in the solar system. Titan have a thick atmosphere and liquid water underneath its surface. 23. Saturn is the only planet in the solar system with rings. False. All the Jovian planets have rings. 2. We could probably learn more about Mars by sending a new spacecraft on a flyby than any other method of studying the planet. False. A flyby spacecraft will spend only short amount of time around Mars. If we want to study Mars in detail, instead of sending a flyby, we should send either a spacecraft that will orbit Mars or a lander that can study the Mars surface. Quick Quiz Choose the best answer to each of the following. Explain your reasoning with one or more complete sentences. 26. Which terrestrial planets have had volcanic activity at some point in their histories? (a) Only Earth (b) Earth and Mars (c) all of them. (c) You can find evidences of volcanic activities in all the terrestrial planets. 33. Are there any exceptions to the rule that planets rotate with small axis tilts and in the same direction that they orbit the Sun? (a) No (b) Venus is the only exception. (c) Venus and Uranus are exceptions. (b) Venus rotates in the opposite direction. Uranus rotate with very large axis titles. Uranus axis tilt is about 90 degree. Short-Answer/Essay Questions 39. Two Classes of Planets. In terms a friend or roommate would understand, write a paragraph explaining why we say that the planets fall into two major categories and what those categories are. Do all planets fit in the two groups? Explain. There are two classes of planets, terrestrial planets and Jovian planets. While Terrestrial planets are small rocky planets from inner solar systems, Jovian planets are large gaseous planets father away from the Sun. Those two types of planets are separated by asteroid belt between Mars and Jupiter. All the planets fall into one of these two groups. (Note that Planets do not include Pluto, which is a KBO.) 5