Lab3_CelestialSphereII_Worksheet_F19

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Astronomy

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Oct 30, 2023

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PHYS 1403 Lab 3: THE CELESTIAL SPHERE II Worksheet Name: Vanessa Van Ark CWID: 100600489 OBJECTIVES This exercise teaches you some important facts about the celestial sphere and the meaning of the terms right ascension, declination, altitude and azimuth. By exploring the Stellarium software, you will see what these terms mean. You will learn how to identify the location of various stars and planets. Additionally, you will also learn about the causes for the different seasons and how your location on earth determines the seasonal changes. EQUIPMENT “Stellarium” software INTRODUCTION One significant change that takes place every day is the rising of the Sun. For this reason, the ancients used to measure time in solar days, the time from sunrise to sunrise. The motion of the Sun, Moon and stars across the sky in a day is called diurnal motion, which takes 24 hours to complete. But if you carefully mark the position of some stars and watch them from day to day, you will see that they are in a slightly different position than they were 24 hours earlier. A period of time measured from when a star is in a particular location to when it is in that same location again is called a sidereal day, and it is slightly shorter than a solar day. This difference is caused by the rotation of the Earth about the Sun. This motion of the Earth causes a constantly changing perspective of the stars. Each year the Earth moves around the Sun once, so the perspective will return to the original in 365.242 days - a tropical year. So, the stars will advance 360 degrees in this period. If we do the math, we find that they will advance by about 3.9 minutes (of time) every day. This means that if a star is at a precise location in the sky at exactly a given time today, tomorrow it will be at that same precise place in the sky 3.9 minutes earlier. If we watch the apparent path of the Sun in the sky carefully we will find that its path is more northerly in the summer, and more southerly in the winter. After a full year the Sun will return to its original position in the sky. The apparent path of the Sun through the sky is known as the ecliptic and is inclined to the equator by 23.5 o . This tilt is due to the fact that the Earth is tilted on its axis by 23.5 o . The constellations along the path of the ecliptic are called Zodiacal constellations. These constellations have been considered important historically because, by measuring the location of the Sun on the 1

ecliptic, the seasons are measured year to year. This tilt of the axis is what causes the seasons. As we have seen, the path of the Sun through the sky is more northerly in the summer and more southerly in the winter. The Sun is at its most northerly point around June 21, which we call the Summer Solstice. At this time, the Sun will be directly over the Tropic of Cancer, 23.5 o north. When it is at its most southerly point, it is the Winter Solstice which occurs around Dec 21. At this time, the Sun will be directly over the Tropic of Capricorn, 23.5 o south. These points are named for the constellations the Sun used to be in when these events occurred. If you stop to think about it for a moment, you will realize that this means there are two times a year when the Sun will be directly over the equator. If the Sun is over the northern hemisphere in summer, and the southern hemisphere in the winter, it must cross the equator. When the Sun is moving northwards and is over the equator, we have the vernal equinox, around Mar 21. And when it is moving southwards and is over the equator, we have the autumnal equinox, around Sep 22. Due to this apparent motion of the Sun in the skies, the amount of sunlight we receive is not constant. A circle of light in the sky will make a circle on the ground only if the source is directly overhead. If the light comes in at an angle, then the light will make an ellipse on the ground. As the angle gets closer to horizontal, the ellipse will get larger. This means that the same amount of light illuminates a greater amount of area. The smaller the circle the hotter the ground gets, and since the hot ground heats the air, the hotter the air gets. In the summer, the Sun is closer to being directly overhead and heats the ground more. There is not enough time at night for the ground to lose as much heat as it absorbs during the day, so summers are hot. In the winter, the Sun is low in the sky and the sunlight has to warm a greater area of ground. The ground loses more heat during the long night than it can absorb during the short day, so the winter is cold. This also explains why shadows are long in the winter and short in the summer. It is also this tilt of the axis that controls the length of the day. The Earth in space has one-half of its surface illuminated by the Sun, and one-half is in shadow. As the Earth rotates, points on the surface pass from the lighted portion into the shadow portion, and back into light, thus making periods of night and day. But since the Earth is tilted, the North Pole on the summer solstice is pointing towards the Sun and never enters the shadow half (nighttime). This means the North Pole experiences twenty-four hour long daylight. On the summer solstice, this condition will be true all the way to 23.5 o from the pole. The most southerly point from the North Pole that experiences a twenty-four hour daytime on the summer solstice is the Arctic Circle, located at 66.5 o north. For locations south of the Arctic Circle there will be a nighttime, but it will be the shortest nighttime of the year and the daytime will be the longest. Figure 1 shows the situation at the summer solstice. The North Pole is pointed 2

towards the Sun and everything north of the Arctic Circle is in 24-hour sunlight. The South Pole is pointed away from the Sun and everything south of the Antarctic Circle is in 24-hour darkness. Figure 1 As the Earth rotates about the Sun, the darkened half of the earth will travel northward so that by the time we reach the fall equinox, the darkened half passes directly through both poles and everywhere on Earth experiences twelve hours of night and twelve hours of daytime. The poles are opposite of each other in more ways than one. When the North Pole is in summer, the South Pole is in winter, and vice versa. Likewise, on the north’s fall equinox, the South Pole is experiencing its spring equinox. So the North Pole is seeing its one sunset of the year, while the South Pole is seeing its one sunrise. As the Earth continues to rotate about the Sun, more of the northern hemisphere will be in darkness and more of the southern hemisphere will be in light. So the nights will be getting longer in the north, until we reach the winter solstice. On this day the north pole will be pointing directly away from the Sun and the darkened hemisphere of the Earth will cover the maximum amount of the northern hemisphere. The darkness will again extend 23.5 o from the pole to the Arctic Circle. Places north of the Arctic Circle will be experiencing the longest night of the year. Figure 2 shows this situation. The Earth is 3

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now located at the winter solstice, six months after (or before) the situation in Figure 1. The Earth continues to point in the same direction in the sky, but because of the Earth’s rotation about the Sun, the Sun is now located on the opposite side of the Earth. Continuing towards the spring, or vernal, equinox, we see the same effect in reverse. The nights get shorter as the Sun gets higher in the sky and the poles see their one sunrise or sunset of the year on the equinox. The Earth continues on its path until we are back at the summer solstice and the cycle begins again. The closer you are to a pole, the more extreme the seasons. The nights are longer in the winter, and the daytime is longer in the summer. Since the two hemispheres experience opposite seasons, the equator in between must always experience the midpoint between these two. As a result, the equator experiences twelve hours of night and twelve hours of daytime every day. Figure 2 4

PROCEDURE Enter you answers to each question in the data tables and yellow highlighted areas below. When completed, please upload this file to Canvas using the designated submission link on the Modules page. A. PRELAB QUESTIONS 1. What causes the seasons? Earth’s tilt and its orbit around the sun 2. How long would nighttime be on Sep 22 if you were standing directly on the Arctic Circle? 12 hours? 3. If the longest daytime of the year is on the summer solstice, why are the hottest days of the year about six weeks later? Earth takes time to heat up and cool down, seasonal temperature lag. 4. What is the vernal equinox? Day and night are about the same, marks the day of spring. 5. How can it be true that half the Earth is in light all the time, if during the winter some part of the northern hemisphere is in 24 hour darkness? Due to its rotation half the earth is always lit. 6. Why are shadows longer in winter? Sun is lower in the sky. B. EXERCISE In this exercise you will be using Stellarium in order to familiarize yourself with the celestial sphere. Start the program (just as you did in Lab 2. If for some reason you did not do Lab 2, see the Lab 2 worksheet for instructions on starting up Stellarium), you should see a scene representative of the sky conditions outside. If it is still daylight outside, you will see daylight on your computer screen; and if it is night outside, you will see night on your computer screen. Since, in this lab, we are interested in what the sun is doing relative to the ground, we need to have both the atmosphere and ground on the screen. Although you can follow the instructions in the Lab 2 worksheet for turning the 5

atmosphere and ground on and off, you can quickly do this by clicking the “Atmosphere” and “Ground” icons that appear at the bottom of the screen when you move your cursor there. First, we want to see how the sky will look from a particular place on Earth. The first place we wish to go is the North Pole. To do this, open the “Location window”. Since the North Pole is not an option on the location list, we must set our location manually. In the box labeled “Latitude”, set the degrees to 90 and press “Enter”. 7. What is the declination of the Sun on today’s date? If the Sun is below the horizon on today’s date, you can move to it using the “Search window”. Declination = -23.44 degrees 8. You can find how many hours of daylight there are on a particular day by watching the Sun move across the sky. If you move your cursor to the bottom of the screen, a horizontal menu appears. On the right hand side are the time flow controls: “Set normal time rate” (play/pause), “Increase time speed” (fast-forward), and “Decrease time speed” (rewind). You can start and stop time, and run it forward and backward, by using these controls. Run time forward until the Sun dips below the horizon. Note the time of day that this happens. Next, run time backwards until the sun dips below the horizon again. Note this time as well. The number of hours between these two times is the number of hours of daylight on this date. How many hours of daylight are there today at the North Pole? Hours of daylight = 0, polar night 9. Where do you see the celestial equator? along the equator 10. Where do you see the north celestial pole? directly overhead Now go to Quito, Ecuador (latitude = 0 o ). Use the Location window to select this city from the list. 11. What is the Sun’s declination on today’s date? Declination = -23.44 12. How many hours of daylight are there today? 6

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Hours of daylight = 12 hours 13. Where do you see the celestial equator? directly overhead 14. Where do you see the north celestial pole? on the horizon Now, use the Location window to go back to Plano. 15. You can adjust the date by clicking the “Date and time” icon in the vertical menu at the left of your screen. For the each of the following dates, find the Declination of the Sun, the Altitude of the Sun above then nearest horizon (at local noon), and the number of daylight hours. Date Declination of the Sun Altitude of the Sun Daylight hours June 21 23.44 degrees 66.56 degrees 14 hours Sep 21 0 degrees 43.56 degrees 12 hours Dec 21 -23.44 degrees 29.91 degrees 9.5 hours Today -.02 degrees 50.26 degrees 12 hours Now use the Location window to go to Murmansk, Russia 16. For the each of the following dates, find the Declination of the Sun, the Altitude of the Sun above then nearest horizon (at local noon), and the number of daylight hours. Date Declination of the Sun Altitude of the Sun Daylight hours June 21 23.44 degrees 47.13 degrees 24 hours Sep 21 0 degrees 23.44 degrees 12 hours Dec 21 -23.44 degrees -0 degrees 0 hours Today 0 degrees 24.67 degrees 12 hours Now use the Location window to go to Quito, Ecuador 17. For the each of the following dates, find the Declination of the Sun, the Altitude of the Sun above then nearest horizon (at noon), and the number of daylight hours. Date Declination of the Sun Altitude of the Sun Daylight hours June 21 23.44 degress 90 degrees 12 hours Sep 21 0 degrees 90 degrees 12 hours 7

Dec 21 -23.5 degrees 66.5 degrees 12 hours Today 4 degrees 86 degrees 12 hours Now go back to Plano, TX. Open the Sky and viewing options window, and click on the “Sky” tab. Under “Planets and satellites”, check the boxes marked “Show planets” and “Show planet markers”. This should display planet labels on the sky. Now set the time to sunset. 18. Which planets are visible in the sky at sunset? mercury, mars, neptune 19. Advance time forward 1 hour. Have any of the planets set yet? Which ones? mercury How about after 2 hours? mars How about after 3 hours? Now set the time to sunrise. 20. Which planets are visible in the sky at sunrise? mercury, venus, jupiter, neptune, uranus Okay, finally, look at the planets you have listed so far. Are there any planets that you weren't able to see at either sunrise or sunset? These planets are currently too close to the sun to be easily observed. 21. Which planets are too close to the sun in the sky to be seen right now? saturn 22. If there are planets too close to the sun in the sky to be seen, are these planets actually physically right next to the sun (i.e. are they hovering right next to the sun, burning up from all of the heat)? no they are not physically right next to the sun 8

23. If your answer to 22 was 'no' explain how they can appear to be right next to the sun, if they're not really physically close to it. If it was 'yes', explain how can they be that close without being destroyed. it’s about perspective, they can appear closer or further in the sky while orbiting around the sun. 9

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