EXAMPLE QUIZ QUESTIONS - ASTRONOMY 1010 – FALL 2021– CHAPTERS 2 & S1 CHAPTERS 2 & S1 – EXAMPLE QUIZ QUESTIONS Review Questions: 1. Why does the “local sky” look like a dome? Define “horizon”, “zenith”, and “meridian”. How do we describe the location of an object in the local sky? The local sky looks like a dome because we only see half of the celestial sphere at any given time. (The other half is blocked from our view by the ground.) The horizon is the boundary between the Earth and the sky. The zenith is the point directly overhead. The meridian is an (imaginary) half circle which extends from the horizon due north, through the zenith point overhead, to the horizon due south. When an object is “on the meridian” it is at its highest point in the sky. When we describe the location of an object in the local sky we usually use its altitude (how high it is above the horizon in degrees) and its azimuth (its direction along the horizon). 2. What are “circumpolar stars”? Are more stars circumpolar at the North Pole or in the United States? Explain. Circumpolar stars are stars that never set below the horizon at a given latitude. More stars are circumpolar near the North Pole than in the United States because the North Celestial Pole (NCP), around which the stars appear to rotate as we see them from Earth, is directly overhead at the North Pole. This means that more stars can complete full circuits of the sky without crossing the horizon at the North Pole than in the United States, where the NCP appears closer to the horizon. 3. What are “latitude” and “longitude”? Does the sky vary with latitude? Does it vary with longitude? Explain. Latitude measures north-south position on the Earth. An object along the equator has a latitude of 0°, while one at the north pole has a latitude of 90°N, and one at the south pole has a latitude of 90°S. All latitudes on Earth are between 90°N and 90°S. Longitude measures east-west position, and is specified relative to the prime meridian (in Greenwich, England). Longitude is measured from 180°W through 180°E, depending on whether one is east or west of the prime meridian. What we see in the sky DOES vary with latitude because our latitude affects the location of our (local) horizon and zenith relative to the stars on the celestial sphere. The sky does NOT vary with longitude – people at the same latitude and differing longitudes will all see the same sky. The longitude only affects when the Sun and stars will rise/set relative to a centralized clock for the world (e.g., one in England). 4. What is the “zodiac”, and why do we see different parts of it at different times of the year? The zodiac is the collection of 12 constellations that lie along the ecliptic (the projection of the Earth’s orbital plane around the Sun). We see different parts of it at different times of the year because as we orbit around the Sun, the Sun blocks out the constellations that we see directly behind it. These constellations that the Sun passes directly in front of are the zodiacal constellations. These constellations still rise and set in our sky every day, but we do not always see them because of the bright sunlight. Since there are 12 zodiacal constellations (plus Ophiuchus) the Sun appears to move through one constellation per month. 5. Suppose Earth’s axis had no tilt. Would we still have seasons? Why or why not? No. If the Earth’s axis did not tilt, then all locations on Earth would receive the same amount of sunlight every day of the year. Seasons result from the tilt, which alternately causes the Northern and Southern hemisphere to point toward or away from the Sun. The more direct sunlight which a location receives, the warmer it will be. For instance, during summer in the Northern Hemisphere, the tilt of the Earth’s axis causes the Northern Hemisphere to point toward the Sun, and thus receive more light and heat. 6. Briefly describe key facts about the solstices and equinoxes. The summer solstice is the moment when the Northern Hemisphere is pointed most directly toward the Sun; on this date the Northern Hemisphere receives the greatest amount of annual sunlight (the Sun reaches its highest point above the horizon when crossing the meridian and the Sun is visible for the largest fraction of the day). The winter solstice is the moment when the Northern Hemisphere is pointed most directly away from the Sun; on this date the Northern Hemisphere receives the least amount of sunlight (the Sun is at its lowest meridian crossing, and is visible for the shortest fraction of the day). The spring and fall equinoxes are the transition points as the Northern Hemisphere shifts toward receiving more direct sunlight (spring equinox) or less direct sunlight (fall equinox). On these dates the two hemispheres receive equal amounts of light. EXAMPLE QUIZ QUESTIONS - ASTRONOMY 1010 – FALL 2021– CHAPTERS 2 & S1 7. What is “precession”, and how does it affect what we see in our sky? Precession is a gradual wobble that changes the orientation of the Earth’s rotation axis in space. It is present because the Earth is not a perfect sphere and is acted on by gravitational forces from the Sun and Moon. Precession causes the Earth’s axis to change the direction in which it points with a period of about 26,000 years. The most direct effect of this precession is that Polaris is not always the North Pole Star. Precession also affects which constellations are associated with solstices and equinoxes. Note that precession does NOT change the size (23.5°) of the axis tilt. 8. Briefly explain the Moon’s cycle of “phases”. Can you ever see a full moon at noon? Explain. The Moon takes approximately 29.5 days to complete a cycle of phases. The phases are determined by the intersection between the half of the Moon which is illuminated by the Sun and the half of the Moon which is visible from Earth. The full moon occurs when the Sun is opposite the Moon, and so the face of the Moon that we see is completely illuminated. The new moon occurs when the Moon is between the Earth and the Sun, so the illuminated portion of the Moon faces away from Earth. Halfway between the new moon and the full moon are the quarter moons, in which we see half of the Moon face illuminated and half in the dark. Between the quarter moon phases and the new moon phase are the crescent moons, during which less than half of the face is illuminated, and between the quarter moon phases and the full moon phase are the gibbous moon phases, during which more than half of the Moon face is illuminated. As the percentage of the illuminated moon is increasing we say the moon is waxing (waxing crescent, waxing gibbous), and as it is decreasing we say the moon is waning (waning crescent, waning gibbous). We say that the quarter moon that occurs during the waxing half of the month is a first quarter moon, while that occurring during the waning half of the month is the third quarter moon. We can never see a full moon at noon, since by definition the full moon occurs when the Sun and Moon are on opposite sides of the Earth, allowing the Moon to be fully illuminated. Thus, as the full Moon rises, the Sun sets, and as the full Moon sets, the Sun rises. At noon, the full moon is below the horizon, just as at noon the new moon is always above the horizon. 9. Why don’t we see an “eclipse” at every new and full moon? Describe the conditions needed for a “solar” or “lunar eclipse”. We do not see an eclipse every full/new moon because in addition to the alignment between the Sun-Earth-Moon, an eclipse requires the alignment to occur at an intersection between the plane in which the Earth orbits the Sun and the plane in which the Moon orbits the Earth. These two planes are inclined at about 5° relative to one another. In order to have a lunar eclipse, the Moon needs to be passing through the intersection between the Earth’s orbital plane and the Moon’s orbital plane AND the Earth needs to lie directly between the Sun and the Moon. For a solar eclipse, the Moon needs to be passing through the intersection between the Earth’s orbital plane and the Moon’s orbital plane AND the Moon needs to lie directly between the Sun and the Earth. 10. Distinguish among “apparent solar time”, “mean solar time”, “standard time”, “daylight savings time”, and “universal time”. Apparent solar time is the time based on the Sun’s actual position in the sky. Noon is the precise moment when the Sun is on the meridian. Mean solar time is based on the average length of the day (since the length of the day varies a little over the course of the year), and provides the time at a fixed location on Earth. Noon is the average time that the Sun crosses the meridian. Standard time divides the Earth into time zones – of which there are 4 in the continental US. All people within a given time zone set their clocks to the same time (even though at noon the Sun may not quite be on the meridian yet, or may have just passed through the meridian). Daylight savings time shifts the standard time zones by one hour – so when the Sun is near the meridian the clocks read 1 PM instead of noon. (The reasons for this are socio-political and have to do with saving energy by more closely matching the hours we are awake/working with the hours of daylight.) Lastly, universal time is a single time for the entire world. This single time is set equal to the mean solar time in Greenwich, England (the location of the prime meridian used in longitude). This time is often used in astronomy and in navigation since it avoids confusion about where a person is located and in what time zone a person is located -there is only a single time. EXAMPLE QUIZ QUESTIONS - ASTRONOMY 1010 – FALL 2021– CHAPTERS 2 & S1 11. What are “declination” and “right ascension”? How are these celestial coordinates similar to latitude and longitude on Earth? How are they different? Declination and right ascension are coordinates on the celestial sphere which are similar to latitude and longitude on the Earth. Declination measures how far an object is above or below the celestial equator. Declinations can range from +90° (north celestial pole) to 0° (celestial equator) to -90° (south celestial pole). Right ascension (like longitude) measures how far around the celestial sphere an object is located. The zero-point in right ascension is picked to be the point where the ecliptic crosses the celestial equator at the spring/vernal equinox. Right ascensions are then measured in hours around the celestial sphere eastward from this point, ranging from 0 hours to 24 hours. Declination is similar to latitude – it is how far above/below the equator something is located, while right ascension is similar to longitude – it is how far around the sphere one has travelled. The differences are that latitude and longitude are terrestrial, while right ascension and declination refer to celestial coordinates. Furthermore, latitude is specified as being above or below the equator with a N or a S, respectively, while declination uses + or -, respectively. Longitude is measured in degrees east or west of the reference point (prime meridian) while right ascension is in hours eastward of the reference point (the vernal equinox). 12. How and why do the Sun’s celestial coordinates change over the course of each year? The Sun’s celestial coordinates vary over the course of the year as it moves along the ecliptic on the celestial sphere. This is unlike the stars – which have a fixed right ascension and declination. The declination of the Sun varies from 0° (on the equinoxes) to +23.5° (on the summer solstice) to -23.5° (on the winter solstice). The right ascension of the Sun also varies - from 0 hours on the vernal/spring equinox through 6 hours (on the summer solstice) through 12 hours (on the autumnal equinox) through 18 hours (on the winter solstice) and then back around to 0 hours. 13. What is special about the tropics of Cancer and Capricorn? Describe the Sun’s path on the solstices at these latitudes. Do the same for the Arctic and Antarctic Circles. The tropics of Cancer and Capricorn have latitudes of 23.5°N and 23.5°S, respectively. At locations along the tropics of Cancer and Capricorn the sun is directly overhead (at the zenith) on one day each year. It is directly overhead on the summer solstice along the tropic of Cancer and it is directly overhead on the winter solstice along the tropic of Capricorn. At latitudes between 23.5°N and 23.5°S (a region known as the tropics) the Sun is at the zenith on two calendar days throughout the year. The Arctic and Antarctic Circles are at 66.5°N and 66.5°S, respectively. At these two latitudes there is one day during the year when the Sun is continuously above the horizon, and there is one day during the year when the Sun is continuously below the horizon. The Sun is continuously above the horizon on the summer solstice along the Arctic Circle (and it never rises along the Antarctic Circle). On the winter solstice the Sun is continuously above the horizon along the Antarctic Circle (and it never rises along the Arctic Circle). At locations north of the Artic Circle and south of the Antarctic Circle there are more than one days during the year where the Sun never rises, and more than one days during the year where the Sun never sets. 14. Briefly describe how you can use the Sun or stars to determine your latitude and longitude. You can determine your latitude in three different ways. First, if you can find Polaris, then the altitude of Polaris above the horizon is equal to your latitude (N). If you are in the southern hemisphere you can do the same thing using the location of the South Celestial Pole, as determined using the Southern Cross. A second way you can find your latitude is using the altitude of the Sun as it crosses the meridian, assuming that you know the declination of the Sun on that date. Lastly, you can find your latitude using the altitude of a star as it crosses the meridian, assuming that you know the star’s declination. (For example, you can use the relationship that the altitude of the celestial equator is 90°-your latitude, and that the declination of the Sun or star tells you how far above or below the celestial equator the object is located.) You can find your longitude by comparing your local time with the time at a known location (such as Greenwich, England). You can determine your local time by using a sundial during the daytime. At nighttime you can instead use the stars, and compare the time when a star crosses your meridian with the time that star crosses the meridian at a location where you know the time. For instance if a star is on your meridian now, but in Greenwich, England that star was on the meridian 6 hours ago, then you know you are 6 hours (or 90°) west of Greenwich. EXAMPLE QUIZ QUESTIONS - ASTRONOMY 1010 – FALL 2021– CHAPTERS 2 & S1 Does It Make Sense? 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. I live in the United States, and during my first trip to Argentina I saw many constellations that I’d never seen before. True. Since Argentina is in the southern hemisphere, you would be able to see stars close to the south celestial pole which are always below the horizon at latitudes in the northern hemisphere. 16. Although all of the known stars appear to rise in the east and set in the west, we might someday discover a star that will appear to rise in the west and set in the east. False, the Earth’s rotation from west to east causes the stars to appear to rise in the east and set in the west. The motions of the stars themselves do NOT cause the stars to rise and set in the night sky. Since the Earth rotates as a solid body, i.e. every point on the Earth is rotating in the same direction at the same time, at every point on the Earth all of the stars will rise in the east and set in the west. 17. If Earth’s orbit were a perfect circle, we would not have seasons. False, the distance from the Sun has no impact on the seasons. The seasons are produced by the amount of sunlight that we receive, which is a function of the tilt of the Earth’s axis and of the Earth’s orbit around the Sun. 18. Los Angeles is west of New York by about 3 hours of right ascension. False, right ascension is a measure of position on the celestial sphere (or for celestial object). It is not a terrestrial measurement. Los Angeles is west of New York by about 3 hours of time, or by about 3 hours of longitude (45°). Quick Quiz: Choose the best answer to each of the following. Explain your reasoning with one or more complete sentences. 19. The north celestial pole is 35° above your northern horizon. This tells you that a. you are at latitude 35°N. b. you are at longitude 35°E. c. you are at latitude 35°S. The North Celestial Pole is the same number of degrees above the horizon as your latitude. Since it is 35° above the horizon, you are at a latitude of 35°. Since you are looking at the NORTH Celestial Pole, above the Northern horizon, you are at a northern latitude. 20. In winter, the Earth’s axis points toward the star Polaris. In spring, a. the axis also points toward Polaris. b. the axis points toward Vega. c. the axis points toward the Sun. Over the course of the year the orientation of the Earth’s axis does NOT change. It does slowly change with time due to precession, but this takes thousands of years (26,000 years for a full circuit). 21. If the Sun rises precisely due east, a. you must be located at Earth’s equator. b. it must be the day of either the spring or the fall equinox. c. it must be the day of the summer solstice. On the date of the spring and fall equinoxes, the Sun is at a declination of 0 degrees and so will rise/set due east/west. 22. The fact that we always see the same face of the Moon tells us that a. the Moon does not rotate. b. the Moon’s rotation period is the same as its orbital period. c. the Moon looks the same on both sides. The Moon exhibits what is known as synchronous rotation – it takes the same amount of time for the Moon to rotate once on its axis as it does for the Moon to orbit once around the Earth. As we will discuss later in the semester this is not a coincidence. EXAMPLE QUIZ QUESTIONS - ASTRONOMY 1010 – FALL 2021– CHAPTERS 2 & S1 23. The time from one spring equinox to the next is the a. sidereal day. b. tropical year. c. synodic month. A tropical year is the time period from one spring equinox to the next. This is about 20 minutes shorter than a sidereal year – which is the time it takes for the Earth to complete one full orbit around the Sun. 24. A star’s path through your sky depends on your latitude and the star’s a. declination. b. right ascension. c. both declination and right ascension. The star’s path through your sky depends on your location (latitude) and the star’s declination. The right ascension of the star tells you when during the year the star will be visible at night. 25. At latitude 50°N, the celestial equator crosses the meridian at altitude a. 50° in the south. b. 50° in the north. c. 40° in the south. At a latitude of 50°N, the North Celestial Pole will be at an altitude of 50° above the Northern horizon. The celestial equator will be 90° away which will put it at 90°-50°=40° above the southern horizon. 26. At the North Pole on the summer solstice, the Sun a. remains stationary in the sky. b. reaches the zenith at noon. c. circles the horizon at altitude 23.5°. At the North Pole on the summer solstice the Sun circles the horizon at an altitude of 23.5° and never sets. It never reaches the zenith (this only occurs in the tropics). 27. If you know a star’s declination, you can determine your latitude if you also a. measure its altitude when it crosses the meridian. b. measure its right ascension. c. know the universal time. If you know the altitude of a star when it cross the meridian and its declination then you can determine the location (altitude) of the celestial equator. Once you know the location of the celestial equator then the celestial pole is 90° away, and its height above the horizon tells you the latitude. 28. If you measure the Sun’s position in your local sky, you can determine your longitude if you also a. measure its altitude when it crosses the meridian. b. measure its right ascension and declination. c. know the universal time. If you know the local time (based on the position of the Sun) and you know the universal time (the time in Greenwich, England) then you can determine how many hours earlier or later your local time is relative to that in Greenwich. This then tells you your longitude – you are West if you are earlier and East if you are later, and the number of hours tells you how far east or west. Short-Answer Questions 29. New Planet. A planet in another solar system has a circular orbit and an axis tilt of 35°. Would you expect this planet to have seasons? If so, would you expect them to be more extreme than the seasons on Earth? If not, why not? Yes, you would expect this new planet to have seasons. These seasons would be more extreme than those on Earth. When the Northern Hemisphere of the planet was pointed toward the star, it would receive even more direct light than does our Northern Hemisphere, and when the Northern Hemisphere of the planet was pointed away from the star, it would receive even less light than does our Northern Hemisphere. Thus, the difference in the amount of light between the winter season and the summer season would be even more significant, and so the seasons would be more extreme. EXAMPLE QUIZ QUESTIONS - ASTRONOMY 1010 – FALL 2021– CHAPTERS 2 & S1 30. A Farther Moon. Suppose the distance to the Moon were twice its actual value. Would it still be possible to have a total solar eclipse? Why or why not? No, it would not be possible to have a total solar eclipse. At the moment both the Sun and the Moon subtend about half a degree in the sky. If the Moon were twice as far away, though, it would appear to be half as large (using the small angle formula). Since it would no longer subtend the full half-degree circle, it would not be able to completely block the light from the Sun. Only an annular solar eclipse would be possible. 31. Fundamentals of Your Local Sky. Answer each of the following for your latitude. The latitude of Statesboro is 32.4453° N a. Where is the north (or south) celestial pole in your sky? The north celestial pole is 32.4453° above the northern horizon. b. Describe the meridian in your sky, specifying at least three distinct points along it (such as the points at which it meets your horizon and its highest point). The meridian runs from the horizon due north, through the zenith (the point directly overhead), and then down to the horizon due south. c. Describe the celestial equator in your sky, specifying at least three distinct points along it. The celestial equator runs from the horizon due east, it crosses the meridian at an altitude of 90°32.4453°=57.5547° above the southern horizon, and then it connects to the horizon due west. d. Does the Sun ever appear at your zenith? If so, when? If not, why not? No, the Sun does not every appear at my zenith. The Sun only ever appears at the zenith in the tropics (at latitudes between 23.5°N and 23.5°S). The highest the Sun ever gets in the sky is on the Summer Solstice when it is 90°32.4453°+23.5°=81.0547° above the southern horizon. e. What range of declinations makes a star circumpolar in your sky? A star is circumpolar if it is within 32.4453° of the north celestial pole. This means stars with declinations ≥57.5547° are circumpolar. f. What is the range of declinations for stars that you can never see in your sky? I can never see stars with declinations within 32.4453° of the south celestial pole. This means stars with declinations ≤-57.5547° are never visible in the sky. Quantitative Problems: Be sure to show all calculations clearly and state your final answers in complete sentences. 32. Find the Sun’s Diameter. The Sun has an angular diameter of about 0.5° and an average distance from Earth of about 150 million km. What is the Sun’s approximate physical diameter? Compare your answer to the actual value of 1,390,000 km. Using the small angle formula, given that the sun has an angular diameter of 0.5 degrees and is 150 million km from the Earth: angular size physical size = 360 2πR angular size physical size = 2πR 360 0.5 physical size = 2π × 150 × 10 6 km 360 physical size = 1.309 × 10 6 km 1.309 × 10 6 km = 0.94 1.390 × 10 6 km We would derive the Sun to have a physical diameter of 1.31×106 km. This is about 0.94 times the actual physical diameter of the Sun. € EXAMPLE QUIZ QUESTIONS - ASTRONOMY 1010 – FALL 2021– CHAPTERS 2 & S1 33. Eclipse Conditions. The Moon’s precise equatorial diameter is 3476 km, and its orbital distance from Earth varies between 356,400 and 406,700 km. The Sun’s diameter is 1,390,000 km, and its distance from Earth ranges between 147.5 and 152.6 million km. a. Find the Moon’s angular size at its minimum and maximum distances from Earth. angular size physical size = 360 2π × distance physical size angular size = 360 × 2π × distance Size Moon = 3476 km Dist Moon−near =356,400 km Dist Moon− far =406,700 km physical size 3476 km = 360 × = 0.5588 2π × distance 2π × 356,400 km physical size 3476 km When the Moon is far: angular size = 360 × = 360 × = 0.4897 2π × distance 2π × 406,700 km When the Moon is near: angular size = 360 × b. Find the Sun’s angular size at its minimum and maximum distances from Earth. angular size physical size = 360 2π × distance physical size angular size = 360 × 2π × distance Size Sun = 1, 390, 000 km Dist Sun−near =147.5 ×10 6 km Dist Sun− far =152.6 ×10 6 km physical size 1, 390, 000 km = 360 × = 0.5399 2π × distance 2π ×147.5 ×10 6 km physical size 1, 390, 000 km When the Sun is far: angular size = 360 × = 360 × = 0.5219 6 2π × distance 2π ×152.6 ×10 km When the Sun is near: angular size = 360 × c. Based on your answers to parts a and b, is it possible to have a total solar eclipse when the Moon and Sun at both at their maximum distance? Explain. No, it is not possible. At the maximum distances the angular size of the Moon is 0.49° while that of the Sun is 0.52°. Thus, the size of the Moon is smaller than the size of the Sun, and so the Moon cannot fully cover the Sun (or fully block out all of the light from the Sun). As a result it is not possible to get a total solar eclipse – instead one will get an annular solar eclipse.
