lab02-2

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University of Missouri, Columbia *

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Apr 3, 2024

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Name __________________________________ ID __________________________________ Astron 1010 SP 2023 Lab #2 This lab has three parts: I. Introduction to Stellarium (15 points) II.Reason of Seasons (25 points) III.Formation of Planets in Our Solar System (20 points) You need the software Stellarium to finish this lab. You can download it from https://stellarium.org/ to your laptop. The due date of this lab is March 16th (Thursday), 2023 . You can finish most part of the report with handwriting and sketches (Note: Illegible handwriting or sketches to me would be scored zero). But some questions require TYPED answers. Print out your answers and attach them to the report. Submit your report to the instructor. Page of 1 14

Name __________________________________ ID __________________________________ P ART I: I NTRODUCTION OF S TELLARIUM (15 P OINTS ) 1. Install and launch the program Stellarium ( https://stellarium.org/ ). • The program has two navigation panels which appear when you mouse over: one on the left and another at the bottom of the screen. • There are also several hotkeys which turn on an off certain features. You can find a list of these in the Appendix of this document. 2. From the left panel, select the Location Window (F6) and search for Columbia, MO in the search bar (the one with the magnifying glass). Ensure that the red arrow on the world map moves to Columbia. Click the box to make this your default location. 3. Let's begin by pretending the Earth does not have an atmosphere so that we can see the stars even during the day. To do this, click "A" to turn off/on the atmosphere. 4. Orient your view to the East and observe how the stars move with respect to your horizon. You will want to speed time up slightly. To do this, click "L" twice . (You can return to normal speed at any time by hitting the "K" key.) 5. Describe the motion you observe as well as make a simple sketch (arrows) which indicate how the stars move for each cardinal direction. —— 4 points Description Sketch EAST E WEST W SOUTH S NORTH N Page of 2 14

Name __________________________________ ID __________________________________ 6. While oriented North, find Polaris (The North Star), it should not be moving like all the other stars. Draw it on your sketch. In Stellarium, select Polaris. This will bring up lots of information about the star in the upper left of your screen. Find the data entry labeled: "Az/Alt". This is the azimuth (direction) and altitude of Polaris. Record the altitude below. —— 1 point Altitude of Polaris: _____________________ Latitude of Columbia, MO: _________________ Determine the latitude of Columbia, MO as well and compare the two numbers. They should match within a degree of each other. This will hold true for any location in the northern hemisphere and historically a very useful navigational tool. 7. Orient yourself away from north in any direction and select a star at random. In the chart below record its altitude and azimuth every hour for 5 hours. Do not use the fast forward time button this time. Instead, advance time incrementally by one hour at a time. To do this, open the clock (F5) and click the small arrow above the hour position. (Note that the clock is in 24h format) —— 2.5 points Name of your star: __________________________ Time your observations began: ______________________ AZIMUTH ALTITUDE Page of 3 14

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Name __________________________________ ID __________________________________ 8. Create a graph of your altitude and azimuth in the space provided below. The y-axis should be altitude and the x-axis should be azimuth. You may scale this graph however it is convenient; in other words your altitude axis range does not have to start at 0 and go to 90 -- keep your ranges near your values. You may alternatively use Excel to plot your data if you know how. —— 2.5 points 9. Where would you expect to see the star 24 hours later from your first measurement? —— 1 point __________________________________________________________________________ 10. Why do stars appear to rise in the east, move across the sky, and set in the west every day? —— 1 point __________________________________________________________________________ Page of 4 14

Name __________________________________ ID __________________________________ 11. Change your location to another place on the world (another distant country or region) and repeat the observations in the N, S, E, and W. Sketch how the stars move. —— 3 points Location you picked: _____________________________________________ How has the movement of the stars changed? If they look very similar, what about your chosen location could be the reason for that? _______________________________________________________________________ _______________________________________________________________________ N S E W Page of 5 14

Name __________________________________ ID __________________________________ P ART II: S EASONS (25 POINTS ) 1. Launch Stellarium, and set your location to Columbia, MO. ( make sure your red arrow on the map is actually on Columbia ) 2. Select the Sky and Viewing Options Window (F4) button on the left-side navigation menu. Click on Markings and check boxes to enable the Ecliptic, Cardinal Points, and Meridian in the Celestial Sphere section. 3. Zoom out so your field of view (FOV) would be between 160 and 190 degrees. Now, you should be able to see the ecliptic line arching over the southern horizon. 4. Open the Date and Time window (F5) and set the date to Today (i.e., the day you are working on this part) and set time to 6 AM . Advance time to see how the sun is rising and setting on your eastern and western horizon. You will see that the sun always follows the Ecliptic which is an apparent path of the sun in our sky. You should turn off the atmosphere (A) to read Sun data easier. —— 4 points Remember, when sun rises and sets, its altitude is 0 degree. Write down today’s date: _________________ Does the Sun rise due east (E 90°) and set due west (W 270°) today? Yes / No What is the azimuth of the sun when it is rising in the eastern horizon? ______°_____’ What is the azimuth of the sun when it is setting in the western horizon? ______°_____’ What time did the sun rise? (rising is defined as the Sun having an altitude = 0 o in the East) _____hr_________min What time did the sun set? (setting is defined as the Sun having an altitude = 0 o in the West) _____hr_________min What was the altitude of the sun when it crossed the Meridian? _______°________’ Tip: Keep the time window (F5) permanently up in the lower right of your Stellarium and simply advance time manually!! Also, you can use the Key K or 7 to stop time from automatically running. Page of 6 14

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Name __________________________________ ID __________________________________ 5. Use Stellarium to fill out the rest of the table (6 points) : When was the longest day? _____________________________ When was the shortest day? ____________________________ When did the sun spend an equal amount of time below and above the horizon? ________________ On which day are the sun’s ray’s most intense? _______________________ * When the sun spends the equal amount of time above and below the horizon, we call it the equinoxes: Vernal (spring) equinox in March and Autumnal (fall) equinox in September. The sun always spends the least time above the horizon in the northern hemisphere in December on Winter Solstice. And the sun spends the most time in our sky in June on Summer Solstice. Next, we want to determine which effects of the Earth’s tilt contribute to our seasonal changes the most. To do this, we will be measuring the sun’s altitude each hour throughout the day for two days of the year. Once in summer, once in winter. From this, we want to know a few things: How long was the sun up that day, how intense was the sunlight at each hour, and the cumulative amount of solar energy we received over that day. We learned in lecture that the angle at which the sun hits the ground has an effect on the amount of light per square meter received and can be absorbed for heat. (We will be ignoring the albedo and assume all light is absorbed) The flux of the sun at Earth’s distance is 1340 Watts per square meter. This means if the sun were at zenith (altitude=90 o , i.e.: the ground directly facing the sun) then a square meter of ground would absorb 1340 joules of energy per second. (A Watt is a Joule/second). This decreases with lower altitudes of the sun based on the following equation: In our experiment, we will be using a different unit for the sun’s energy. We will be using MegaJoules per hour per square meter, since we will be taking hourly measurements instead of measurements every second. In this case, the flux of the sun is: 4.824 MJ/hr/m 2. Month Date (2023) Azimuth of the sun at (degrees) Time of (hours and minutes) Total time above the horizon Altitude at the meridian (degrees) sunrise sunset sunrise sunset March 20 June 21 September 23 December 21 sin( ) received sun Energy Altitude Flux = × Page of 7 14

Name __________________________________ ID __________________________________ The two days we will be measuring are January 1, and July 1 in 2023. Start by finding sunrise, advance time 30 minutes, take your altitude measurement, and then advance hour by hour until the sun sets . Fill in the table below. Unless you are comfortable taking the sine of an angle, you should use the sin(x) table that I uploaded to CANVAS instead of calculating the sine of the altitude yourself. (note: Not all of the rows may be filled) For example: If the sun rose at 6am, your first measurement would be at 6:30am. Then 7:30am, etc. January 1 (4 points) Time Altitude Sin(Altitude) Energy Received Page of 8 14 (10)

Name __________________________________ ID __________________________________ July 1 (4 points) Now, we need to sum up all of the energy received throughout the day as well as the length of day. —— 3 points Total Daylight Hours: Jan 1st ______________________ July 1st______________________ (simply count how many measurements you have, answer in units of hours) Total Energy Received: Jan 1st ______________________ July 1st ______________________ (add up column 4, answer is in units of Mega Joules per square meter or MJ/m 2 ) Average Energy / Hour: Jan 1st ______________________ July 1st ______________________ Time Altitude Sin(Altitude) Energy Received Page of 9 14

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Name __________________________________ ID __________________________________ Questions (4 points): Please submit TYPED answers for the following questions. Handwriting is not accepted! You can attach your answers in the end of the lab report. Label them clearly (i.e., Section II, Question I and II). I. Discuss your results of the solar irradiance experiment. Include a comparison of total energy on both days and how it relates to seasonal variation in temperature. How many hours in July did it take to equal the total daily energy in January? What are the two effects of Earth's tilt at play here and which do you think is more significant regarding energy absorption by the Earth? II. If the Earth had no tilt: (a) Would you expect there to be seasons at all? Explain . (b) Would you expect more northern (and far southern) latitudes to be cooler/ warmer/the same temperature as equatorial latitudes? Explain . (you may draw a picture to help explain) Page of 10 14

Name __________________________________ ID __________________________________ P ART III: W HY ARE T HERE T WO T YPES OF P LANETS ? (20 P OINTS ) For this section, I want you to find out the physics behind the separation of Terrestrial planets (Mercury, Venus, Earth, and Mars) and the Jovian planets (Jupiter, Saturn, Uranus, Neptune). In other words, why did the planets closest to the Sun form as low mass, rocky bodies while planets further out formed massive, gas giants? To do this, let us first map out the solar system based on the planets' distances from the Sun. However, instead of looking these values up, I want you all to determine a way to extrapolate through observation the distance of the outer planets from the Sun by simple observation using Stellarium and what you know from Kepler's 3rd Law (Chap 3.3 of your textbook). Typically in this class you have been given a cookbook of how the experiments are performed. However, I want you to do this one more independently. I will give you a hint: Distance from the Sun a = P 0.66 . (1) What value (a or P) in this equation can you easily measure by simple observation from Earth (provided you watched long enough)? —— 1 point (2) In Stellarium, find the following planets and take a note of their current locations. What reference would you use to record their locations? —— 1 point (Jupiter, Saturn, Uranus, Neptune) (3) For each planet, advance the time of Stellarium by year until the planet moves back to (almost) its original location. Write down the time it needs (You only need to be accurate to years). —— 4 points Jupiter: Saturn: Uranus: Neptune: (4) Using Kepler’s 3rd Law, convert the times in (3) into distances from the Sun and complete the table on the following page. —— 4 points Page of 11 14

Name __________________________________ ID __________________________________ T ABLE : D ISTANCES FROM THE S UN IN AU I can tell you that the reason for the difference between Terrestrial and Jovian planets is based upon the temperature at that distance from the Sun. In the previous page, there is a Mercury 0.387 Venus 0.723 Earth 1.000 Mars 1.524 Jupiter Saturn Uranus Neptune Page of 12 14

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Name __________________________________ ID __________________________________ graph of temperature vs. distance from the Sun. Place a mark of some kind to indicate where the planets fall on this graph based on their distance, label each mark with the name of the planet. Note: The x-axis of this graph is logarithmic. This means that each tick mark is not equally spaced on the graph. For example: The first section, each tick counts as 0.1, 0.2, 0.3, ... while the second section counts as 1, 2, 3, ..., then 10, 20, 30 .... ( 4 points ) Once you have marked your planets, determine what the temperature is between Mars and Jupiter (roughly): __________________ Celsius ( 1 point ) In the vacuum of space, hydrogen based compounds (such as water, ammonia, methane) freeze out of gaseous form into solid dust grains at around -120 Celsius . This is called the frost line. Draw a vertical line on the plot to indicate the distance of the frost line in our solar system. ( 1 point ) What is the distance of the Frost Line? __________________________ AU Discussion: With this information, describe the process by which planets are formed from the surrounding material, and explain the reason why the Jovian planets were able to obtain so much more mass than the Terrestrials. Remember: (1) Gas moves quickly since each particle has very little mass and is therefore harder to trap and hold on to compared to the slow moving, more massive dust particles. (2) To trap gas, what do you need at the beginning? —— 4 points Please submit a TYPED answer for this question. Handwriting is not accepted! You can attach your answer in the end of the lab report. Label it clearly (i.e., Section III, Discussion). Page of 13 14

Name __________________________________ ID __________________________________ A PPENDIX : A F EW H ELPFUL S HORTCUTS FOR S TELLARIUM Key: Description A: Turn on/off Atmosphere G: Turn on/off Ground L: Increase time speed (cumulative) J: Decrease time speed (cumulative) K: Set speed back to normal Space: Center on selected object Mouse scroll: Change field of view F3: Search for object F6: Location F5: Set Date/Time Arrow Keys: Look Right/Left/Up/Down C: Constellation lines V: Constellation labels F4 then under Markings -> Constellations -> borders: Constellation borders Alt+tab: Return to desktop without closing program (this works only on Windows) Page of 14 14

lab02-2

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