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Dec 6, 2023

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3.1. MAPPING THE SOLAR SYSTEM FROM EARTH – KEY 47 3.1 Mapping the Solar System from Earth – KEY Courtesy of Adams and Slater and CAPER Team Part I: Rising and Setting Times to Sun Noon Figure 1-a: Observer positions on Earth. (Observer is at Equator) As seen from above, Earth appears to rotate counterclockwise. Figure 1-a shows a top view of Earth and an observer at noon. Note that our Sun appears overhead when standing at the equator. This is a crucial diagram that you will refer to in the rest of this assignment! 1. In Figure 1-a , sketch and label the positions of the observer and his horizon at midnight, 6 PM (sunset) and 6 AM (sunrise). The top of each observer’s head is pointed to the meridian direction in space. For example, at 6 PM the observer’s meridian is oriented directly to the left of this figure. Note that the horizon spins (rotates) with the observer! 2. Consider Figure 1-b , which shows Earth, Moon, Mars, Mercury, and Venus. At what time would each of these sky objects be highest (on the meridian)? Remember that Earth spins counterclockwise when viewed from above. [ Hint: Make use of Figure 1-a ] Time Overhead: Venus: Moon: Mars: Mercury: Sun Figure 1-b: Orrery 6 PM sunset Midnight 6 AM sunrise Noon 6 AM sunrise Venus Mercury Mars Noon. Venus is in same direction as Sun. I drew the noon observer from Figure 1a onto Figure 1b. Midnight. At midnight observer is facing down toward bottom of Figure 1-b. 6 AM (sunrise). I drew the 6 AM observer from Figure 1a onto Fig 1b. arrow is meridian between 6 AM and noon. Mid-morning. Mercury is between Mars and Sun on sky, so meridian time is between that for Mars and Sun. East West East West East West East West
48 Mapping the Solar System from Earth 3. If Earth spins 360 in 24 hours, that means that each sky object is visible for about 12 hours. What time will the sky objects shown in Figure 1-b rise and set? Complete the table below (and refer back to Figure 1-a!). Each member of your team should fill in the data for one sky object. 12 AM is midnight, and 12 PM is noon, but use “noon” or “midnight” instead of 12 PM and 12 AM. (Recall that an object is at its highest altitude when it is on the meridian .) Sky Object Rise Time Time on Meridian Set Time Sun 6 AM Noon 6 PM Venus 6 AM Noon 6 PM Moon 6 PM Midnight 6 AM Mars Midnight 6 AM Noon 4. Using complete sentences, explain why our Sun is not visible at midnight. Add a sketch of Earth, Sun, and observer in the space provided to support your explanation. Narrative At midnight we are facing directly away from the Sun (our meridian is oriented opposite the Sun toward the outer part of the solar system). At midnight the Earth blocks our view of things roughtly in the same direction as the Sun and we can only see things that arepositioned toward the outer part of the solar system. Sketch HORIZON above horizon (things visible) below horizon (things blocked by Earth) Sun Part II: Converting Geocentric to Heliocentric 5. Figure 2-a on the next page shows the horizon view of the first quarter Moon and Saturn visible at sunset. On the orrery shown in Figure 2-b, you will sketch and label the position of Jupiter, Moon, and Saturn. (1) First use an arrow to indicate the direction to the Sun in Figure 2-b. (2) After drawing the arrow, indicate the position of the observer at sunset. ( Recall figure 1-a: at NOON, the observer is facing directly toward the Sun and the Earth spins counter-clockwise.) (3) Draw the observer’s horizon at sunset. (4) Sketch and label the position of Jupiter, Moon, and Saturn. ( Recall the observer is pointed directly toward an object if the object is on the observer’s meridian—due South.) (5) After completing the diagram, complete the table. 12 AM is midnight, and 12 PM is noon, but use “noon” or “midnight” instead of 12 PM and 12 AM.
Mapping the Solar System from Earth 49 South East West x zenith Figure 2-a: Horizon View at sunset (6 PM) Saturn (rising) Moon to Sun at sunset Jupiter Earth Saturn orbit Jupiter orbit Figure 2-b: Orrery NOT drawn to scale! Sky Object Sun Jupiter Moon Saturn Rise Time Set Time 6 AM 6 PM Noon Midnight Noon Midnight little before 6 PM little before 6 AM to Sun (and noon meridian) remember Earth spins counter-clockwise 6 PM sunset meridian direction HORIZON Person facing south sees Saturn on his left. Horizon line spins in counter- clockwise direction. Moon Jupiter Saturn I also drew in the observer and his horizon line. Meridian goes through exact south and zenith. dotted line is meridian arc Jupiter and Moon are on the meridian (or very close => observer’s part of Earth is pointed right toward the Moon and Jupiter. 6. If Neptune is visible on the meridian in the southern sky at sunrise (6 AM), sketch the relative positions of Sun, Earth, Neptune, and observer with his horizon in an orrery in the space below. ( Recall figure 1-a: at NOON, the observer is facing directly toward the Sun and the Earth and horizon spins counter-clockwise—so what direction are we facing at 6 AM? Also the observer’s part of Earth points toward whatever object is on the meridian.) To Sun Earth 6 AM sunrise Neptune meridian of 6 AM person If Sun is at the bottom of the figure, then rotate Figure 1-a 180º so person is facing toward the left side at sun rise. Direction person is facing is the direction of the meridian, so Neptune should be in that direction (i.e., to the left side of the picture). HORIZON Horizon rotates counter-clockwise
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50 Mapping the Solar System from Earth Part III: Converting Heliocentric to Geocentric Figure 3-a: Orrery comet orbit 7. Figure 3-a shows the position of Mercury, Venus, Earth, Mars, Moon and a comet in an orrery diagram. On the horizon diagram, Figure 3-b , sketch and label the positions of Mercury, Venus, Mars, Moon and the comet at midnight . (In Figure 3-a which direction is the observer facing at midnight ?) Figure 3-b: Geocentric Horizon View at Midnight South East West x zenith In Figure 3-a, the observer is facing to the right side of the figure (I drew her in). Her meridian is oriented to the right side of the figure so East is on her left toward the comet. Horizon line rotates counter-clockwise! HORIZON comet (rising) First quarter Moon (setting) Mars Mercury and Venus are below the horizon (not visible) East West comet Mercury Venus Moon Mars Draw the positions of the objects in the sky as we would see them from on the ground, i.e., translate Figure 3-a to Figure 3-b. If an object is below the ground at midnight, be sure to explicitly say so or draw it and label it below the ground. Need to note that Mercury and Venus are below the horizon because question includes them in the instructions! 8. Venus is often called the morning star or evening star. Why is it never seen at midnight? Why is it always the case that it is below the horizon at midnight? At midnight we (our part of the Earth) are pointing directly away from the Sun and we can only see things that are farther out from the Sun than we are. Venus’ orbit is smaller than ours and never carries Venus to beyond the Earth’s orbit. Venus always appears near the Sun because its orbit is inside our orbit. The orbit size is the CAUSE. To say that Venus is below the horizon or it has already set begs the question of why that is ALWAYS the case at midnight.