Penn State Astronomy 11 Laboratory

Transcription

1 Penn State Astronomy 11 Laboratory Fall 2002 / Spring 2003 The Pennsylvania State University Current editor: Michele Stark Authors: Many past and present ASTRO 11 TAs and instructors have contributed to this work, including... David Andersen Roger Bartlett Jason Best Lee Carkner David Chuss Donald Driscoll John Feldmeier Mena Ferraro Rajib Ganguly Jason Harlow Ian Hoffman Anna Jangren Karen Lewis Suzanne Linder Phillip Martell Michael Sipior Michele Stark Dan Weedman Michael Weinstein Darren Williams

2 Copyright c 2002 by the Department of Astronomy & Astrophysics, The Pennsylvania State University Copyright c 2002 by Hayden-McNeil Publishing, Inc. on illustrations provided All rights reserved. Permission in writing must be obtained from the publisher before any part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system. Printed in the United States of America ISBN Hayden-McNeil Publishing, Inc Clipper Street Plymouth, MI Stark F02 ii

3 Astronomy 11 Syllabus A. Along with this laboratory packet, you need to purchase a planisphere from the bookstore which will help you to locate stars and constellations this semester. You will also need a calculator capable of scientific notation, and a small flashlight with some type of red filter on it (i.e., covered with red cellophane, a red balloon, red nail polish, etc.). B. Students will be required to prepare a written report for each lab, based upon answering specific exercises and questions in the notebook. It is recommended that as much of this write-up as possible be done during the lab meeting time, while instructors are available to answer questions. C. Students must be prepared to go onto the roof of Davey Lab for observing with the telescopes on any evening. Every lab will be expected to attempt observing until all of the objects in the observing notebook are seen and described! This is an ongoing assignment that is not optional; it is required. If the night is clear, it will usually be cold. Always bring adequate warm clothes for going outside during the lab. D. Laboratory activities this semester will include the following. Additions, subtractions, and corrections to this list are likely. The labs may be done out of order. 1. The Semester Observing Project (page 1) Observations of the Moon, planets, stars and galaxies will be collected at the end of the semester. 2. The Changing Sky (page 7) Use of the computer program Skyglobe to find different seasonal constellations, and to demonstrate nightly and annual changes in the sky. 3. The Scale of Things: How Big Is It? (page 15) A summary of the scale of things, from the solar system to the universe, using scale models and analogies. 4. Angles, Navigation, and Data Analysis (page 21) Celestial navigation and data analysis, using observations in the planetarium. 5. Planetary Orbits and Kepler s Laws (page 29) An examination of Kepler s three laws which describe the motions of the planets using the program Orbit Maker. 6. Parallax and the Distances to the Stars (page 39) Parallax concepts and their use for measuring distances to the stars. 7. Spectroscopy of Stars and Galaxies (page 45) How we use spectroscopy to tell us the chemical content, velocity, and physical properties of distant stars and galaxies. 8. The Inverse-Square Law of Light (page 51) Use of light meters to learn about the inversesquare relation for light. 9. Understanding the Stars (page 57) The luminosity-temperature diagram, using data on the closest and brightest stars, and what it shows about the nature of the stars. 10. The Lives of the Stars (page 63) Stellar evolution and evolutionary states using astronomical data and luminosity-temperature diagrams. 11. The Structure of the Milky Way Galaxy (page 69) Structure of our Milky Way Galaxy through the study of globular clusters and young groups of stars. 12. The Local Group and the Hubble Deep Field (page 77) Galaxy locations, distance measurements, and a look into the past using images from the Hubble Space Telescope. 13. Distances to Galaxies (page 83) Visits to various web pages illustrate how to estimate the large distances to other galaxies. 14. Distant Galaxies and the Expanding Universe (page 87) Measurements of distant galaxies and a derivation that the universe is expanding. Also, we determine the age of the universe. 15. The Search for Extraterrestrial Intelligence (page 93) Using the Drake Equation to estimate the number of other civilizations in our galaxy. 16. The Moon and Its Phases (page 97) the phases of the Moon and the relationship between the Sun, Earth, and Moon. iii

4 The Greek Alphabet α A Alpha η H Eta ν N Nu τ T Tau β B Beta θ Θ Theta ξ Ξ Xi υ Υ Upsilon γ Γ Gamma ι I Iota o O Omicron φ Φ Phi δ Delta κ K Kappa π Π Pi χ X Chi ε E Epsilon λ Λ Lambda ρ P Rho ψ Ψ Psi ζ Z Zeta µ M Mu σ Σ Sigma ω Ω Omega The Pleiades Open Star Cluster (see Lab 10, page 63) M15 Globular Star Cluster (see Lab 10, page 63) iv

5 I. Objective PENN STATE ASTRONOMY LABORATORY # 1 SEMESTER OBSERVING PROJECT Over the course of the semester, you will have the opportunity to observe many things, thereby imitating astronomers throughout history. Although contemporary astronomy is largely an indoor science, visual and telescopic observations are fundamental. Everything we think we know about the universe is either supported by observations or hinges on the support of future observations. Most of the observations you will make this semester will be similar to those that have been made by countless numbers of astronomers throughout history. However, they will be unique to you, and give you the opportunity to discover the nature of the universe for yourself. Students often ask, What is a good observation? or What should I draw? Frustrated Astro 11 instructors typically respond, Draw what you see. The lesson is clear. An observation will depend on an observer s eyesight or other equipment used to make the observation, and one s ability to sketch in the dark. Even with this element of uncertainty, however, everyone s sketch of a Full Moon should be circular, the Andromeda Galaxy should not look like Jupiter, and the North Star should always be drawn roughly North. You should strive to record what you see as accurately as possible, but only in as much detail needed to clearly distinguish your object from another. You need not draw every star in Orion to obtain the general shape, for example. One note: You will see in Lab #2 that the position and visibility of the stars depends greatly on when you are doing your observing. In order to be acceptable, every drawing MUST have the following information: 1. The date, 2. The time, 3. The direction you are facing and the directions to your left and right 4. A label of what you have drawn. Without this information, you have only made a drawing, not an Observation that contains useful astronomical data! II. Exercises The semester observing project will consist of three activities. 1. naked eye observations of stars, constellations and planets 2. telescopic observations using the telescopes on the roof of Davey Lab 3. naked eye observations of the Moon and its phases Each activity is described in more detail on the following pages, along with checklists to help you keep track of what you have and haven t done. Good Luck! 1

6 All observations will be collected at semester s end. You only need to turn in one observation of each object, but you are encouraged to observe objects more than once until you feel that your sketch is a good one. Observations will be graded on completeness, accuracy, and clarity. You will have a planisphere, which can be purchased from the bookstore, to help you find stars and constellations. Most observations can be done during class time, weather permitting, but many must be done outside of class time. For out-of-class observations, you are encouraged to observe on your own or with a friend in a relatively dark area. Take advantage of any opportunity to observe since it is cloudy over 70% of the time in State College. Enjoy your semester in Astro 11! Activity 1: Naked Eye Observations of Stars, Constellations and Planets, Checklist Fall Semester Ursa Major (Big Dipper) Ursa Minor (Little Dipper) with Polaris Auriga (the Charioteer) with Capella Cepheus (the King) Cassiopeia (the Queen) Cygnus (the Swan) with Deneb Boötes (the Herdsman) with Arcturus Lyra (the Lyre) with Vega Pegasus (the Winged Horse) with the Great Square Perseus (the Warrior) Taurus (the Bull) with Aldebaran Scorpius (the Scorpion) with Antares Sagittarius (the Archer) Summer Triangle with Deneb, Vega, and Altair Aquila (the Eagle) with Altair Virgo (the Maiden) with Spica Hercules (the Strongman) Spring Semester Ursa Major (Big Dipper) Ursa Minor (Little Dipper) with Polaris Auriga (the Charioteer) with Capella Cepheus (the King) Cassiopeia (the Queen) Cygnus (the Swan) with Deneb Boötes (the Herdsman) with Arcturus Lyra (the Lyre) with Vega Pegasus (the Winged Horse) with the Great Square Perseus (the Warrior) Taurus (the Bull) with Aldebaran Orion (the Hunter) with Betelgeuse and Rigel The Pleiades (the Seven Sisters) Leo (the Lion) with Regulus Canis Major (the Big Dog) with Sirius (the brightest star in the night sky) Canis Minor (the Little Dog) with Procyon Gemini (the Twins) with Castor and Pollux 2

7 Space has been left at the bottom as your instructor may suggest other objects, such as planets or comets, which are only visible at special times. Also note that the shapes of these constellations are subject to interpretation. The constellation of Ursa Major has been identified both as a large animal and a kitchen utensil. Which is it? Again, the best rule of thumb is to see for yourself. If you see a teapot instead of an archer when observing Sagittarius then remember it as a teapot. When lying on its side, Orion may look to you like a giant bow tie rather than a hunter; feel free to use your imagination. Your sketches for Activity 1 will be semicircular sketches of the sky as shown in the sample sketch on the following page. The semi-circle is used to depict the half of the sky that you are facing. The horizon is depicted by the flat portion of the semi-circle. Objects seen directly overhead should be drawn at the top of the frame. The corners of the semi-circle are reserved for objects seen on the horizons directly to your left and right. Since the sky you observe depends on date, time, direction, and observing locale, you must record this information near all sketches. You may include as many stars, constellations, and planets in one sketch as you wish without making the sketch incomprehensibly congested. All objects MUST be clearly labeled. Sample Sketch for Activity 1 Naked Eye Sketch Title: Summer Triangle & Moon Phase Observing Site: Date and Time: Mon, Sept 24, 2001, 8:30pm Sky Condition: Overhead Old Main Lawn very clear!! Vega Deneb Moon Altair The Summer Triangle E Your Left S In Front W Your Right Description: Drawing made from lawn of Old Main. Sky was clear, but bright, only a few stars other than those in the summer triangle were visible. Moon was half full, with right side (west side) illuminated. 3

8 Activity 2: Telescopic Observations of Planets, Galaxies, Stars and Clusters; Checklist Fall Semester Mizar and Alcor in Ursa Major (double star) Albireo in Cygnus (double star) M13 in Hercules (a globular cluster) The Andromeda Galaxy (M31) Spring Semester Mizar and Alcor in Ursa Major (double star) The Orion Nebula The Pleiades (an open star cluster) M15 in Pegasus (a globular cluster) Again, space has been left intentionally blank for planets or other objects which may be visible at special times. A sample observation for Activity 2 is given below. Telescopic observations capture a very small portion of the sky, and thus should not be semicircular. Draw your observations within a circle that represents the edge of your field of view. The same rules for time, date, etc. apply here. Sample Sketch for Activity 2 Telescope Sketch Title: Saturn & Titan Observing Site: Date and Time: Tues, Nov 27, 2001, 9:00pm Sky Condition: Davey Lab Roof clear Description: Looking through 8 inch telescope on the roof of Davey Lab. Saturn was yellowish grey. The rings were bright and visible. Titan looked just like a white dot, much like a star. Saturn Titan 4

9 Observing Template for Lab 1 (Please photocopy or reproduce manually as necessary) Naked Eye Sketch Title: Date and Time: Overhead Observing Site: Sky Condition: Your Left In Front Your Right Description: Telescope Sketch Title: Date and Time: Observing Site: Sky Condition: Description: 5

10 Activity 3: 10 Naked Eye Observations of the Phase of the Earth s Moon For this activity you will sketch the shape, appearance, and position in the sky of the Moon on different dates. These observations may be done outside of class time; just go outside whenever it s clear and look around for the Moon. As the Moon orbits the Earth once every month, we see the side of it that is illuminated by the sun from different angles. That is what causes the Moon to appear to go through phases. Each phase corresponds to a different angle between us (Earth), the Moon, and the Sun. For example, Full is when the Earth sits between the Moon and the Sun; at that time, the illuminated half of the Moon is facing us. If the Moon, Earth, and Sun make a right angle, then we see only half of the side of the Moon illuminated by the Sun, and this is called first or third quarter phase (depending on which side of the Moon is lit). Each observation of the Moon must include: 1. date and time of the observation 2. description of observation 3. sky conditions 4. compass directions 5. sketch of the moon s location in the sky use a naked-eye constellation observation template for this (see example on page 3) 6. sketch of the shape of the moon Your instructor will provide you with the details of which phases to observe and/or when you should make these observations. Since the Moon is observable during the day and night, try to make at least three day-observations of the Moon. If the moon is only partially illuminated, make a careful note of which side, left or right, is lit. 6

11 PENN STATE ASTRONOMY LABORATORY # 2 THE CHANGING SKY I. Objective You may not be aware of it, but the appearance of the sky is constantly changing. Which stars and constellations you can see at night depends greatly on both the time, date, and location from which you do your observations. In this lab, we will try to understand why the sky is different at different times. II. Exercises: Rotation of the Earth During the course of a night or a year, the stars appear to change their positions in the sky. This is not due to the stars moving through space, but rather the fact that the Earth is moving and we are moving with it. In this exercise, we will use the computer program Skyglobe 1 to investigate these apparent motions. Be sure to notice these motions yourself during your observations of the real sky as you complete your semester observing project! We see two distinct types of motions in the sky caused by the two different motions of the Earth. The first motion is the rotation of the Earth about its axis, which runs through the North and South Poles. This rotation produces the diurnal motion of the sky, that is, those motions we see throughout a day (or night). The most familiar example of this motion is day and night. The Sun rises in the east when the Earth rotates us around so that the Sun is shining down on us. It sets in the west every day because we have rotated with the Earth so that we are in the shadow of the Earth on the other side. The stars in the sky exhibit the same kind of motion. Every night, stars will also rise in the east above the horizon and then set in the west as they pass below the horizon and behind the Earth. a. Based on the information given above, answer the following: Suppose you see a star in a certain part of the sky (say, low in the south-east). About how many hours will pass before you will observe that same star in the same position in the sky? ** Now log on to your computer and activate the Skyglobe program as your instructor demonstrates. The map you see before you is a map of the sky, as it appears now, from State College, as if you were facing south. ** Let s take a look at some of Skyglobe s buttons and features, the buttons and bars surrounding the map. You may want to spend a few minutes messing around with these features to get a feel for the program. 1 Skyglobe software 1997, by Mark A. Haney, a Shareware product of KlassM Software. 7

12 Skyglobe features: ADVISORY: Double-clicking on any button causes the action to repeat rapidly ( Turbo ), and the program s settings run wildly away from you. Do multiple clicking SLOWLY, except where indicated. To cancel a Turbo, click on the button once. On TOP The date and time is indicated, time is 24-hr based. (13:00 means 1:00 PM.) Z Zoom in (left mouse button) or out (right mouse button) to view less or more of the sky in your window. M Magnitude: Add or subtract dimmer stars (right/left mouse button). On BOTTOM The NESW directional bar: click here to change your view to other compass directions. At RIGHT The various icons here add or subtract certain features from the map. Try them all. You can add or remove constellation pictures, planets, star names, the horizon, and other map features with the left mouse button. The right mouse button here adjusts the completeness of the info shown. For example, clicking on the Vega icon with the left mouse button will turn star names on and off, but the right mouse button will include the names of dimmer and dimmer stars. At LEFT These buttons allow you to change the time of your observation. 1, 5, 10 : Advance time by 1, 5, or 10 minutes (left mouse button = forward in time, right mouse button = backward in time). H, D, W, M, Y : Advance time by one hour, day, week, month, year (left/right mouse button = forward/backward in time). E : Enter any time and date. R : Reset to the current time and date. Once you have reset, click R again to disengage otherwise it will periodically reset you, when you don t necessarily want it to! (Another, way to reset everything is to restart the whole program.) ** Having familiarized yourself with the program, click (SLOWLY), with the left mouse button, on the arrow at the bottom ( ), until the horizon looks flat. ** On the top border of the window, you will see the letter Z (for zoom) and a number. Click (SLOWLY) on the Z with the right mouse-button to bring the zoom number down to 1.5. If you overshoot 1.5, use the left mouse-button to regain it. One important star is the North Star or Polaris. It is (almost) directly above the North Pole so that it appears fixed while all the other stars appear to rotate about it. b. Go to a north view of the sky and click on the H button (at left) with the left mouse button, slowly (this advances the time of observation by hourly increments). Watch the stars, particularly the constellation Ursa Minor (the Little Dipper). Do the stars rotate clockwise or counterclockwise around Polaris? 8

13 Set the date and time to today, 21:00 (9 PM). c. Face each of the four compass directions in turn, by clicking on the N, E, S, and W letters that appear at the bottom of the window. For each direction, list two bright stars that appear near the CENTRAL portion of the view (eight stars in all). Mention the names of the constellations that contain these eight stars. Do the following for EACH of the eight stars that you listed in part c. d. Set the date and time to today, 21:00. Locate the star by facing the correct direction. Now, double-click on the 1 (at left) with the left mouse button, to move forward in time. Follow the motion of the star (if the star moves off the side of the view, you may have to face another direction to find it again). Stop the motion of the sky at 3:00 tomorrow morning (six hours after you started). Where is the star now? (North, south, east, or west? High or low in the sky? Has the star passed below the horizon?) ** Now move forward in time more quickly by double-clicking on 10 (at left) with the left mouse button. While the sky is wheeling around, click on the N, E, S, W letters (at bottom) to look at this diurnal motion of the stars. (Also note the rising and setting of the Sun.) e. Describe the overall motions of the stars as the Earth rotates, when facing north, east, south, and west. 9

14 III. Exercises: Revolution of the Earth The second motion is the revolution of the Earth about the Sun. This rotation produces the annual motion of the sky, that is, those motions we see throughout the year. Because of the Earth s motion around the Sun in a year, the Sun APPEARS to move through the constellations, around the sky, slowly, over the course of one year. The path it appears to take is called the ecliptic. Therefore, the plane of the Earth s orbit is called the ecliptic plane. ** Reset Skyglobe to today, at 21:00. Face the northern part of the sky. Now move forward in time by 3 months, by slowly clicking three times on the M (at left) with the left mouse button. Notice that each step forward shows the night sky at the same time of night (21:00), but one month later. f. Quantitatively compare the motion you see in the north sky over three months (always looking at 21:00), to the motion you saw over six hours in one night (part b). Do the stars move in the same way? in the same direction? by the same amount? Again set the date and time to today, 21:00, but this time face south. g. Over the course of three months (always looking at 21:00), which way do the stars appear to move towards the east, or towards the west? h. If you always look at 21:00, in how many months will the stars be in the exact same positions as they were today at 21:00? Find out using Skyglobe. 10

15 To help visualize the annual motion of the stars, perform the following thought-experiment (parts i and j). i. Draw a circle to represent the orbit of the Earth and put the Sun at the center. Draw four small circles to represent the Earth during the four different seasons. Label the top point Spring, the left point Summer, the bottom point Fall, and the right point Winter. Darken the side of the Earth which is not being illuminated by the Sun. On each of the four Earths, draw a stick figure or mark representing a person observing the sky at midnight, and at sunset. Label these marks clearly. (NOTE: To draw this correctly, you need to know that the Earth rotates and revolves in a counter-clockwise fashion, as seen in this diagram.) j. At sunset on New Year s Day, you observe a star at its highest point in the sky. At midnight that night, you see it low toward the western horizon. Later in the year, you see the same star at sunset on April Fool s Day. Where is it in the sky? (Use your drawing in the last part as a reference. Keep in mind that for a person standing outside at sunset, the Sun is always in the western part of the sky! Also keep in mind that stars are VERY far away to draw the above diagram to scale, the star would need to be drawn many miles away from the Sun and the Earth.) 11

16 k. Review your answers to parts f, g, and h. Do they make sense in the context of the thought-experiment in parts i and j? (Please do not simply answer yes or no elaborate!) IV. Exercises: Phases of the Moon Because of the Earth s motion around the Sun in a year, the Sun APPEARS to move through the constellations, around the sky, slowly, over the course of one year. The path it appears to take is called the ecliptic. Therefore, the plane of the Earth s orbit is called the ecliptic plane. The Moon orbits the Earth about once a month ( moon th) in a plane close to, but not exactly aligned with, the plane of the ecliptic. The phase of the Moon depends on how much of the Moon s illuminated side is angled toward us, and thus it depends on the orientation of the Moon, Earth, and Sun. Another thought-experiment: l. Draw a circle representing the Moon s orbit with the Earth at the center. Draw an arrow indicating which direction the Sun is in, and darken the appropriate side of the Earth. Now draw four circles representing four different points in the Moon s orbit as before. Darken the appropriate side of each Moon and label their phases: New Moon, First Quarter, Full Moon, and Last Quarter. Mark on the Earth the position of a person observing the evening sky (a little after sunset). 12

17 ** Reset the time on Skyglobe to 8:00 AM, this morning. ** View the eastern sky. The Sun should appear there. We will now seek the date of the next New Moon. ** Go forward by days (by clicking slowly on the D at left, with the left mouse button) until the Moon appears very close to the Sun. (Again, use the right mouse button to backtrack in time, if you need to.) That will be the date of New Moon. ** Observe the rising of the Sun & Moon by using the 10 button. Go back or forward as necessary until the Moon is very close to the horizon. m. What time does the New Moon rise? Why is the New Moon not visible in the night sky? ** Now click once on W to advance a week (when the moon will be in the NEXT phase, First Quarter), then click on H slowly a few times until you see the moon rise. Then use the 10 button to get the exact time of moonrise. (Repeat as necessary to answer the next question.) n. At what time does the First Quarter Moon rise? The Full Moon? The Third Quarter Moon? Can you see the First Quarter Moon at sunrise? Can you see a Third Quarter Moon an hour after sunset? A solar eclipse occurs when the Moon passes between the Sun and the Earth, casting a shadow on the face of the Earth. A lunar eclipse occurs when the Earth passes between the Moon and the Sun, casting the Earth s shadow on the Moon. o. What phase is the Moon in during a solar eclipse? How about during a lunar eclipse? Refer to the diagram in part l. p. Why do you think we don t have eclipses every time the Moon is in those phases? (This is a subtle, yet important, point you may want to check your answer with your instructor.) 13

18 l. Summarize the facts and ideas presented in this lab, including any additional questions you may have. 14

19 I. Objective PENN STATE ASTRONOMY LABORATORY # 3 THE SCALE OF THINGS: HOW BIG IS IT? When you look up at the planets and stars, you are seeing things that are very far away. The universe is a very big place. How big is it? If we were able to zoom out, and look back in at the Earth and at its place in the solar system, or look at the solar system in the galaxy, what would it look like? In this lab we will calculate the relative sizes of the various structures in the universe by making scale models. We will try to comprehend the hugeness of space. II. Exercises We begin our exploration of the universe with the Earth: a ball of rock, mostly covered by water, that is 13,000 kilometers (km) in diameter. Gravity pulls things on the surface toward the center, and we live up on the surface. Your instructor will show you something a volleyball, an orange, maybe something really weird that represents a scaled down model of the sun. In real life the sun is a huge ball of hydrogen gas 1,400,000 km in diameter. (That s km, or a little less than a million miles). a. Draw an Earth which is approximately the correct size relative to the model used for the sun. Explain your calculations and the scale transformations that you use to make this drawing. 15

20 The sun is 150,000,000 km away from the Earth (that s km, or 150 million km). b. Using the same scale as for part a., determine the distance that should be between your drawing of the Earth and the instructor s model of the sun. Explain your calculations. Assign two volunteers to hold the Earth drawing and the model of the sun the correct distance apart. Now we ll use a smaller scale to visualize the solar system (the sun and its nine planets). Below is a scale drawing of the inner solar system: the sun, Mercury, Venus, Earth, and Mars. Astronomers often use a distance called the Astronomical Unit, or AU, to represent the average distance between the sun and the Earth (1 AU = km). The outer planets are more distant from the sun, and would be located off the page: Jupiter, Saturn, Uranus, Neptune, and Pluto. Sun Mercury Venus Earth Mars c. If this drawing represents the actual size of the inner solar system, how far away would Jupiter (5.2 AU) be? How about Neptune (30.1 AU)? Name an object that s about the same size as the orbit of Neptune on this scale. Show all work, and be sure to explain how you got your answers. 16

21 The star Vega is one of the brightest in the summer sky. Its distance is so great that light itself, which travels 300,000 km every second, takes 27 years to travel from Vega to the Earth. Thus the distance to Vega is 27 light years (a unit of DISTANCE). The star Deneb appears almost as bright but is at least 1,600 light years away. Astronomical distances are enormous; light takes 8 minutes just to get from the sun to the Earth. Note therefore that 1 AU is equal to 8 light minutes or light years. d. If the entire universe was shrunk down to the same scale as in part c., what would be the scaled distances to Vega and Deneb? That is, if you placed the sketch of the inner Solar System on the ground and had to walk the correct distance to get to Vega or Deneb, how many kilometers would you have to walk? Show all work and explain all of your calculations. Also, please complete the following sentence: To a make a scale model of our Solar System and the stars Vega and Deneb, to the same scale as the diagram in part c., I would need to place the Sun in State College, and the stars Vega and Deneb in (some town) and (some other town). All of the stars we can see in the sky are part of our Milky Way Galaxy, a huge collection of stars of diameter about 100,000 light years. All the stars in the Milky Way, including our sun, are held together by mutual gravitational attraction. The Milky Way would be disk shaped if we could travel outside it and look back, and brighter stars would form a nice spiral pattern when viewed from above. The sun is located about 2/3 of the way out from the center toward one side of the disk. A sphere of radius 1,600 light years (the distance to Deneb) would enclose most of the stars we can see with the naked eye in the night sky. e. Choose a scale, and make a sketch of the Milky Way Galaxy on the back of this sheet. (You may represent the Milky Way as a plain old circle nothing fancy is needed.) Put a dot where the sun should be, and draw a circle around the sun, whose radius is the correct scaled distance from the sun to Deneb. This circle represents our local neighborhood of stars that can be seen with the naked eye. Be sure to show how you determined the diameter of your Milky Way sketch, and the radius of your circle around the sun. 17

22 Here you may draw your sketch for part e. 18

23 The observable universe is teeming with galaxies. Now, we think the universe is about 15 billion ( ) years old (see Lab 14). (That s about 3 times the age of the Earth and Solar System, which we measure to be 4.6 billion years old.) Since light can only travel at the speed of light, and the universe did not exist more than 15 billion years ago, the farthest we can ever hope to see with the largest telescopes is 15 billion light years. In this sense, the radius of the sphere around us which is the observable universe is light years. f. If the Milky Way Galaxy were as small as a piece of paper (20 cm in diameter), how far away would the most distant galaxy observable be located? Show your calculations clearly. g. Put it all together by imagining two trips by rocket or some other sort of spacecraft. One is a trip to the sun. The other is a trip to the most distant observable galaxy. How many times longer is the second trip? 19

24 h. Summarize the facts and ideas presented, including any additional questions you may have. 20

25 I. Objective PENN STATE ASTRONOMY LABORATORY # 4 ANGLES, NAVIGATION, AND DATA ANALYSIS In this lab, you will learn how to measure angular differences in positions, how to use this skill for celestial navigation, and what the scientific concept of a measurement means. II. Exercises Your instructor will tell you why the angle of Polaris above the horizon is the same as your latitude (how far north or south of the Equator you are). Observations will be made in the planetarium to recreate an attempt at celestial navigation. For the first set of observations, your instructor will set the sky to the way it would appear tonight at 9 PM in State College. a. Use the simple sextant provided to measure the altitude of Polaris, in degrees, above the northern horizon. Your answer should correspond to the latitude of State College, or about 41 degrees. Practice with the sextant until you get about this answer. For maximum accuracy, make your observation from as close to the center of the planetarium as possible. Write down your best measurement. Your instructor will now set the sky as it would appear from a different latitude on Earth at the same time tonight. Your challenge is to determine your latitude from celestial observations, as accurately as you can. Imagine you are the navigator of a ship travelling from Europe to America, and you need an accurate latitude measurement to land the ship successfully. b. Make your observation of the altitude of Polaris at the new position. List your value as precisely as you can estimate it, within fractions of a degree if possible. c. Explain in detail what factors (at least 3) you feel most affect the precision of your measurements. (Do not simply say human error or instrument error, describe what specifically about humans and instruments can lead to errors.) 21

26 Everyone s measurements will now be compared to each other. They will all be somewhat different from each other, because all measurements are subject to error. Whenever an experiment is done, the measurements will be either too high or too low, compared to the correct value. Most of the time, it s just as likely that someone will be too high as too low. So the mean, or average, is a good estimate of the correct answer. The mean is calculated by adding up all of the measurements, and dividing the sum by the total number of measurements. Next, we d like to estimate how accurate our answer is. One way to estimate the amount of error in a group of measurements is to look at how they are spread out. Let s look at a few examples, taken by imaginary classes doing the same experiment. If the classes latitude estimates looked like this: Class A: 25,26,27,26,24,27,25,28 Class B: 15,34,18,41,32,37,20,26 you d probably think that the mean latitude of class A is fairly accurate. Because many people are getting similar answers, and the spread of measurements are small, you tend to believe their results. On the other hand, class B s measurements have a bigger spread, which usually means that their numbers are less accurate. From their measurements, it s hard to tell what the correct latitude is. A way to measure this spread in a set of data is the standard deviation. To find the standard deviation of a set of data, follow these instructions: 1. Find the mean of your data. 2. For every measurement, take it, subtract the mean from it, and square the result. 3. Add up all of these squared terms (called the sum of the squared residuals). 4. Divide by: [the number of measurements minus one]. 5. Take the square root of that result. That is the standard deviation! The standard deviation gives you an estimate of the error inherent in a measurement. This means that we don t believe our result to any better than a standard deviation. Anyone who gives you a scientific estimate without any error is trying to sell you something... (Another meaning of the standard deviation: approximately 68% of the measurements should be within one standard deviation of the mean value see part e.) 22

27 d. Use everyone s measurements of the unknown latitude, and follow the list of instructions given on page 22 to find the mean and the standard deviation of the data set. Show all your calculations (use a separate sheet if necessary). 23

28 e. Determine if your measurement falls within one standard deviation of the mean value. (To do this, subtract your measurement from the class average. Compare the absolute value of the result of this calculation with the standard deviation calculated above.) f. Convert the standard deviation from degrees to kilometers (km), explaining how this conversion is done (remembering that there are 360 degrees in the circumference of anything and 40,000 km in the circumference of the Earth). g. Find the difference between the class average and your own measurement, convert this difference from degrees to kilometers (using the same conversion as in the previous question), and see how far away your measurement of the latitude was from the mean, in kilometers. Explain clearly the different steps in this calculation. 24

29 h. Illustrate on the map: 1. where your ship would come ashore if the class average is the correct value, 2. the range of uncertainty of landfall (as given by the standard deviation), and 3. where your own measurement would have indicated a landing. 25

30 Now, let s put everything together. Let s take an imaginary trip to Planet X. A diagram of Planet X is shown below. Your spaceship lands and you want to find out where on the planet you are. So you look up and notice that none of the stars rise or set. Instead, they travel in circles that are parallel to the horizon. All the stars seem to rotate about a stationary point directly above your head. Planet X N S i. What are your possible landing spots (name both)? Pick one of these spots and label it on the diagram above as your landing site. Label it with an L. (In the following questions, this point will be referred to as point L.) You decide to explore Planet X a bit. So, you move 5,000 km in one direction from your landing site (L). At this new site, you find that some stars rise and set while others do not. All of the stars seem to rotate about a stationary point that is 45 above your horizon. The stars that are near this point are the same stars that you saw at your landing site. j. What is your new latitude? Label this new site on the diagram above with a 1. k. What is the planet s circumference? (Hint: What fraction of the circumference have you moved around?) 26

31 Let s now imagine a different case. Let s start again at your landing spot, L. Let s say that you still move 5,000 km in one direction from your landing spot. This time, however, you notice that all of the stars rise straight up in the east and set straight down in the west. You also notice that the stars appear to be rotating around two stationary points: both are on the horizon one is due north, and one is due south. l. What is your latitude now? Label this new site on the diagram above with a 2. What is the planet s circumference in this case? Let s do this again. Starting again at point L, you move 5,000 km as before. But, now you find that some stars rise and set while others do not. All of the stars seem to rotate about a stationary point that is 30 above your horizon. However, the stars that are near this point are not the same stars that you saw at your landing site, L. m. Label this site on the diagram above with a 3. What is the planet s circumference in this case? Let s repeat this one more time. You move 5,000 km from point L as you did before. Now you notice that none of the stars rise or set. All the stars seem to rotate about a stationary point directly above your head. These stars, however, are totally different from the stars that you saw at your landing site, L. n. Label this site on the diagram above with a 4. What is the planet s circumference in this case? 27

32 o. Summarize the facts and ideas presented, including any additional questions you may have. 28

33 PENN STATE ASTRONOMY LABORATORY # 5 PLANETARY ORBITS AND KEPLER S LAWS I. Kepler s 1 st Law: Planets orbit the sun in ellipses (with the sun located at one of the foci) Here s an ellipse: x focus a b focus x Semi-Major Axis (a): Half the length of the longest dimension Semi-Minor Axis (b): Half the length of the shortest dimension Eccentricity (e): A number between 0 and 1 that describes how squashed the ellipse is (an ellipse with a small eccentricity, near 0, is very round, whereas an ellipse with a large eccentricity, near 1, is very elongated) Here are some ellipses for you: Questions (note: you do not need to measure anything, this is qualitative) a. List these ellipses in order of INCREASING eccentricity (i.e., write: 1, 2, 3, or 3, 2, 1, or... ). b. List these ellipses in order of INCREASING semi-major axis (i.e., write: 1, 2, 3, or 3, 2, 1, or... ). 29

34 II. Kepler s 2 nd Law: The line between a planet and the Sun sweeps out equal areas in equal times. One Month One Month Sun Planet Planet s Orbit This law is a bit strange as stated, however, its meaning should become clear soon. In a weird way, it qualitatively describes the speed of a planet at different parts of its orbit. Using Orbit Maker 1, set up the following orbit. The Sun (or some other star) is represented by star1, and star2 is a planet. Adjust the Scale setting so that you can see the whole orbit, and set the Step value so that one orbit is completed in a reasonable amount of time. Name Mass x y z v x v y v z star1 (Sun) star2 (planet) c. As you watch the planet orbiting around the Sun, describe the shape of its orbit. According to Kepler s 1 st Law, the Sun is located at one of the foci of the planet s elliptical orbit. What is located at the other one? d. Does the planet travel at the same speed during the entire orbit? If not, describe how its speed changes at different points in its orbit (i.e., describe where it is when it s going fastest, and where it is when it s going slowest). Where does the planet spend most of its time close to the Sun, or far from the Sun? 1 Orbit Maker software 1996, by Charles Meegan, distributed by Zephyr Services. 30

35 Adjust the Step value so that it takes roughly 60 seconds for the planet to complete its orbit. Reset the orbit. e. Draw an ellipse that roughly corresponds to the ellipse on the screen. Include the location of the Sun and the initial location of the planet (please label these points). Start the motion; let the planet orbit for about 5 seconds then stop it. Mark its new position on your ellipse. Keep incrementing its orbit by 5 second intervals and continue to record its position each time, until the orbit is complete. Draw lines between each location of the planet and the Sun (just like in the figure at the beginning of this section). f. Look at the area contained in each sector (between two lines). Are they comparable (the same)? How does this fit in with Kepler s 2 nd Law? Based on your observations, do you think Kepler s 2 nd Law is correct? How does Kepler s 2 nd Law of equal areas in equal times relate to your observations in question d. about the changing speed of the planet in its orbit? 31

36 III. Kepler s 3 rd Law: For any planet in the Solar System, P 2 = a 3 where: P = orbital period (how long it takes to finish one orbit) in YEARS (Earth-years, that is) a = semi-major axis (the average distance between the Sun and the planet) in ASTRONOMICAL UNITS (AU) This law describes quantitatively how a planet orbits the Sun. It says that as the average distance between the planet and the Sun INCREASES (or as a gets larger), the time it takes for the planet to complete its orbit also INCREASES (P gets larger). All right, let s make the Solar System. Well, part of it, anyway... Enter these settings ( star1 = Sun, star2 = Venus, star3 = Earth, star4 = Mars, star5 = Jupiter): Name Mass x y z v x v y v z star1 (Sun) star2 (Venus) star3 (Earth) star4 (Mars) star5 (Jupiter) g. Reset the screen and notice where the Earth ( star3 ) is on the right side along with all the other planets. Start the planets orbiting, let the Earth make a complete orbit, then stop the motion; notice where the other planets are in their orbits. Which planets have completed at least one orbit? Where is Jupiter ( star5 ) along in its orbit? (Has it gone very far?) Which planets complete their orbits the fastest: those closer to the Sun (inner planets), or those farther away (outer planets)? h. How does the motion you see relate to Kepler s 3 rd Law (the equation P 2 = a 3 )? Does what you see match what the equation predicts? (What does the equation predict? HINT: The x parameter in Orbit Maker is related to the distance from the Sun, measured in AU s.) 32

37 IV. Orbital Mechanics These next parts of the lab show how different physical parameters affect the shapes of planetary orbits. To begin, rerun the planet from Section II again; here are its Orbit Maker settings: Name Mass x y z v x v y v z star1 (Sun) star2 (planet) Make sure that you can see the whole orbit, and that the planet takes a reasonable amount of time to complete its orbit. Watch the planet orbit for a moment you will be comparing the period and shape of this orbit to other ones. i. First, let s increase the mass of the Sun and see what affect that has on the orbit of the planet. Change Orbit Maker so that it has the following settings (Be Sure To Use The Same Scale And Step Values That You Had For The Previous Orbit!): Name Mass x y z v x v y v z star1 (Sun) star2 (planet) Study the orbits carefully, then fill in the following table to indicate which of the two planets has the largest and smallest values for each of the orbital properties listed. planet with normal Sun planet with massive Sun Orbital Property Semi-major Axis Period Initial Velocity Eccentricity j. Now let s see how eccentricity affects the orbits. Change Orbit Maker to these settings. (NOTE: the Sun s mass is back to normal.) Name Mass x y z v x v y v z star1 (Sun) star2 (planet1) star3 (planet2) star4 (planet3) This time play around with the Scale and Step and adjust accordingly. that you can entirely see all three orbits. Make sure 33

38 Study the orbits carefully, then fill in the following table to indicate which of the three planets has the largest, middle, and smallest values for each of the orbital properties listed (or if more than one have the same properties, then indicate that it is the same as star ). star2 (planet1) star3 (planet2) star4 (planet3) Orbital Property Semi-major Axis Period Initial Velocity Eccentricity k. Now examine how different initial velocities affect the orbits. Change Orbit Maker to these settings. (NOTE: the initial velocities, v y, are different, but the distances, x, are the same.) Name Mass x y z v x v y v z star1 (Sun) star2 (planet1) star3 (planet2) star4 (planet3) Study the orbits carefully, then fill in the following table to indicate which of the three planets has the largest, middle, and smallest values for each of the orbital properties listed. star2 (planet1) star3 (planet2) star4 (planet3) Orbital Property Semi-major Axis Period Initial Velocity Eccentricity l. Now, to determine how different starting positions affect the orbits, create these settings. (NOTE: this time, the distances, x, are different and the velocities, v y, are the same.) Name Mass x y z v x v y v z star1 (Sun) star2 (planet1) star3 (planet2) star4 (planet3) As with the previous problem, study the orbits carefully, then fill in the following table to indicate which of the three planets has the largest, middle, and smallest values for each of the orbital properties listed. 34

39 star2 (planet1) star3 (planet2) star4 (planet3) Orbital Property Semi-major Axis Period Initial Velocity Eccentricity m. Summarize your observations from Section IV by explaining which physical factors (semi-major axis, period, initial velocity, eccentricity, and/or mass of the sun) affect the size, shape, and period of the orbit, and in what manner they are affected (i.e., it makes the property bigger/smaller, faster/slower, etc.). 35

40 V. Optional Section: Binary Star Systems, and Fiddling with the Solar System (not a good idea!!) This section is qualitative questions dealing with some really weird star systems. Not all star systems are nice like our own Solar System, some have very strange and unusual orbits (but they can still be described by modifications of Kepler s Laws!). The following are just a few examples. n. Here is a binary star system (two stars orbiting each other), with one star a lot more massive than the other. Create these settings in Orbit Maker: Name Mass x y z v x v y v z star star Describe what the orbits in this star system look like. o. Now enter these settings for another binary star system, which is made up of two stars that are the same mass: Name Mass x y z v x v y v z star star Describe what the shapes of the orbits in this system are like (are they still ellipses? how do their semi-major axes compare?). Compare it to the system in question n. 36

41 p. There has been a lot of talk about planets discovered around other Sun-like stars (extra-solar planets). These new solar systems are very different from our own. Almost all of them have planets the mass of Jupiter (or larger) in orbits much closer to their star than Jupiter is to our Sun. Additionally many of these planets have very elliptical orbits. We are going to magically transport one of those extra-solar planets to the Solar System and let it orbit around the Sun with the other planets. Your job will be to see what effect it has on the orbits of the inner planets (Venus, Earth, and Mars). Here are the settings for the inner Solar System planets again: star1 is the Sun, star2 is Venus, star3 is the Earth, and star4 is Mars. This time, star5 will be the extra-solar planet. Enter these settings into Orbit Maker: Name Mass x y z v x v y v z star1 (Sun) star2 (Venus) star3 (Earth) star4 (Mars) star5 (massive planet with small, eccentric orbit) Let Orbit Maker run, watch how the system changes. Record your observations. (Note: increase the Step value so the planets orbit really fast, also try turning the trails on and off periodically to get a better sense of how the orbits change.) Here are some things to consider in your observations: What effect does this new planet have on the inner Solar System? What is the ultimate fate of Venus? What about Mars? How about the Earth? Does this new planet make the Solar System a nice place to live? What do you think happened to any possible Earths that may have been formed in that planet s own solar system? Any other comments? After the system has settled down, zoom in on the Sun (go to something like Scale = 1 AU). What effect does this new planet ( star5 ) have on the Sun? (Note: astronomers can observe this effect by carefully watching other stars, and are using it to find more extra-solar planets they can actually see this effect as varying Doppler shifts in the spectra of the star.) (Continue on next page if needed.) 37