Homework week 1

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Kent State University *

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21430

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Astronomy

Date

Feb 20, 2024

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PHY 21430 Frontiers in Astronomy Homework - Week 1 Instructions: Replace the Text in Orange with your answers. You can take up as much space as needed to answer, but please keep your answer colored orange to make it easier to grade. Upload your solutions to the Assignment in Canvas. The celestial sphere, constellations, and the appearance of the night sky. When you look at the sky on a clear night, you can see many stars. If you watch for hours, the stars maintain their relative separation from each other and move as a whole across the sky. An ancient way to envision the night sky and specify where to find particular stars is to imagine that all the stars are fixed to a sphere centered on Earth that can rotate with respect to the Earth. This celestial sphere does not accurately describe the location of the stars, but it does describe their appearance from Earth. The celestial sphere is often divided into constellations , patterns of a small number of visible prominent stars. These patterns (and stories about them) are passed down from ancient times. There are 88 such constellations. View this animation of the apparent motion of the celestial sphere . The animation also shows the motion of the Sun across the sky during the day (also depicted to be fixed to the celestial sphere ). Constellations are shown during both the day and night, but obviously they are actually only visible at night. The Sun and constellations of the Zodiac (familiar constellations Ares, Taurus , etc) are located along the ecliptic shown as an orange line. The celestial equator , projection of the Earth’s equator, is shown in grey. You can set the latitude and drag the sphere to change the orientation North, South, East, and West. Set the latitude to Kent’s location: approximately 41 degrees N and leave the directions North, South, East, West unchanged. Answer the following questions. 1. (1pt) Describe the motion of the stars as you watch through the night. (For example, pick a star --- how does it seem to move?) Write your answer here. 2. (1 pt) Why doesn’t Polaris (the north star) appear to move? (Polaris is first star in the handle of the constellation Ursa Minor or the “little dipper”). Write your answer here. 3. (1 pt) What is responsible for the apparent motion of the stars?

PHY 21430 Frontiers in Astronomy Write your answers here. 4. (1 pts) The sidereal day (1 revolution of the Earth with respect to the stars) is 23 hrs 56 minutes, and the solar day (one revolution with respect to the sun) is 24 hrs. This means that a star rises 4 minutes earlier each day. If Orion rises at 9:00pm on Sunday, on what day of the week will it rise at 8:40 pm? Write day of the week here. 5. (2 pts) Name something that can help you identify the ecliptic : during daylight: Replace Text at night: Replace Text 6. (1 pts) Set the latitude to 90 degrees N to show the appearance of the sky if you were standing on the north pole. On the north pole, Polaris is directly overhead. What fraction of the celestial sphere can you see from the north pole over a 24 hour period? Write percentage here. 7. (1 pt) Set the latitude to 0 degrees to show the appearance of the sky if you were standing on the equator. On the equator, Polaris is on the horizon. What fraction of the celestial sphere can you see from the equator over a 24 hour period? Write percent here. Placing the sun and all the stars on the celestial sphere is misleading because (of course) the sun and all the stars are not the same distance from the Earth. 8. (1 pt) Explain why the light we see from each star of the big dipper (for example) has left the star at a different time. Write your answer here. 9. (1 pt) When looking at the big dipper, the light we see left the star Alkaid Replace with a time in years before the light left the star Megrez . (Which is kind of incredible!)

PHY 21430 Frontiers in Astronomy 10. (2 pts) A time lapse exposure of the night sky is shown in the photo below. Estimate the exposure time used to take this picture. Write time here. Justify your answer.

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PHY 21430 Frontiers in Astronomy Phases of the Moon At different times over the course of approximately 29.5 days (Moon’s synodic period ), differing amounts of the surface of Moon can be seen in the sky (phases of Moon). https://moon.nasa.gov/moon-in-motion/moon-phases/ In this exercise you will use a simple model of the Sun, Earth, and Moon that illustrates how the relative positions of these objects affects how we see Moon here on Earth. This model does not take into account the orbital motion of the Earth. Run the Phases of the Moon simulation . In addition to the sunlight, Earth, and Moon, a light gray wedge shows the regions on the surface of Earth that at that time that can see Moon. The green dot represents a point on the surface of Earth, and when this dot lies in the light gray wedge an observer at that position can see Moon. In addition, there are two sliders: Orbit Angle that manually controls the position of Moon and Local Time that controls the position of the green dot on the surface of Earth. 1. (2 pts) Write down the orbital angle for the following: New Moon: orbital angle First Quarter: orbital angle Full: orbital angle Third Quarter: orbital angle 2. (2 pts) For each phase you were asked about in Question 1, determine the approximate time of day when Moon in that phase would be directly overhead for an observer on the equator of Earth. Write this time next to your drawing of each phase. You may use the Local Time slider to move the green dot into the proper position so that Moon is overhead. New Moon: time overhead First Quarter: time overhead Full: time overhead Last Quarter: time overhead

PHY 21430 Frontiers in Astronomy 3. (4 pts) Use your answers to the previous questions (and the computer simulation if needed) to determine the times during which each of Moon's phases are visible. An observer on the equator, the green dot, can see Moon when light from Moon reaches the observer. Fill in the table below. Phase rising and sets Rising Time Setting Time New Moon Rising Time Setting Time Waxing Cresent Rising Time Setting Time First Quarter Rising Time Setting Time Waxing Gibbous Rising Time Setting Time Full Rising Time Setting Time Waning Gibbous Rising Time Setting Time Last Quarter Rising Time Setting Time Waning Cresent Rising Time Setting Time

PHY 21430 Frontiers in Astronomy Solar and Lunar Eclipses A solar eclipse occurs when the Sun is directly in the Moon’s shadow, and a lunar eclipse occurs when the Moon is directly in the Earth’s shadow. 1. (1 pt) From the simple two-dimensional model we have studied so far, it might seem like lunar and solar eclipses should happen quite frequently. In fact, if the moon, earth, and sun were really always in a common plane then eclipses should occur once per month. Specifically, a lunar eclipse would occur every time the moon is in replace with phase phase, and a solar eclipse would occur every time the moon is in replace with phase phase. As you are no doubt aware, lunar and solar eclipses do not occur every month. To see why they don’t, run the Solar Lunar Eclipse program . This program shows the earth orbiting the sun and the moon orbiting the earth in the lower panel. It also shows a view of the sky as seen from Earth (showing the moon, sun, and background stars) in the upper panel. This view shows the Sun moving along the ecliptic (blue line). The path of the moon is shown by the green line. Notice that a solar and lunar eclipse (when they occur) will show on the image of the Sun and Moon, respectively. Notice that the plane of the moon’s orbit is slightly tilted with respect to the plane of the Earth/Sun orbit. You can drag the orbit to change the viewing angle to see this . (This is important to understand the frequency of eclipses.) As you run the simulation, pay attention to where the Moon is with respect to the ecliptic (upper panel) when the Moon is New and when it is in the Full phase (lower panel). 2. (2 pts) The first eclipse that occurs is a lunar eclipse (indicated by the orange sector in the lower panel). What two things need to occur simultaneously for a lunar eclipse to occur. Write your answer here. 3. (2 pts) The next eclipse that occurs is a solar eclipse (indicated by the other orange sector in the lower panel). What two things need to occur simultaneously for a solar eclipse to occur. Write your answer here.

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