A STUDENT’S HANDBOOK OF LABORATORY EXERCISES IN ASTRONOMY
Laboratory Manual for Astronomy 201 Search For Life in the Universe
Second Edition 2010 i CONTENTS ii
Contents
1 Introduction and Lab Outline 1
2 Visual Observations 5
3 Spectra and Remote Sensing 9
4 Mission to Mars 17
5 Extrasolar planets: Detection and Habitability 25
6 Search for Extra-Terrestrial Intelligence 36 CONTENTS iii 1 INTRODUCTION AND LAB OUTLINE 1
1 Introduction and Lab Outline
General Guidelines Lab Preparation • Read the lab ahead of time to be prepared.
• Always bring your notebook and a pen / pencil.
During the Lab • Be on time! Outlines with essential information are given at the start of a lab.
• Talk to your TA about problems and/or questions as soon as they come up - so you don’t fall behind.
• Discuss the lab with the students around you, but do your work independently!
• Complete as much of the lab write-up as you can while in the lab session. That way the information is fresh in your mind and you have the TA to answer questions.
• Check with your TA before you leave the lab to make sure you have performed all the require- ments of the lab and have adequate notes to complete the assignment.
After the Lab • Reports are due 48 hours after the end of the lab.
• Reports are to be dropped off in the boxes outside our lab room.
• Extensions for extenuating circumstances must be requested before the 48 hours deadline
• Late marks are deducted at a rate of one point per week.
• If you need help, call, email, or visit your TA; they exist to assist!
Lab Reports • In a black physics notebook (from Bookstore) or typed on the computer (in Word / etc).
• Do not plagiarize - we can tell! This is a serious offense, and you will get a 0 on the lab.
• Cite all your sources (full URL and date accessed for any web pages).
• Follow the lab report template (Section 3) and our “Tips and Tricks” (Section 2). 1 INTRODUCTION AND LAB OUTLINE 2
Tips and Tricks for Writing Successful Lab Reports in Astronomy If you are using a black physics notebook: • Write neatly in ink on the lined pages of your notebook.
• Underline titles and section headings for clarity.
• Use pencils, coloured pencils and rulers to make clear, large diagrams on the blank pages of your notebook.
• Number your pages and list labs in a “Table of Contents” at the start of your notebook.
• Fold and secure (tape) loose pages so the edges do not protrude.
If you are typing up your report on the computer: • Keep your labs in a folder after they are returned for future reference.
• Use your spell checker!
• Make sure equations and calculations are formatted so they are clear to the reader.
• It is OK to include diagrams, tables of data, graphs, and calculations done by hand.
In general, remember to: • Label tables, graphs, and figures so you can refer to them from your text.
• Remember to always include units!
• Label the axes of your graphs: what are you plotting, and on what scale?
• Label the rows and columns of your tables.
• Write in full sentences in the third person, past tense.
• Write a short evaluation of the lab content to give your TA immediate feedback on the lab and their teaching.
• If you are confused, just ask to see our sample lab reports or for extra details.
• Read the comments written by your TA on your returned labs for advice on how to improve. 1 INTRODUCTION AND LAB OUTLINE 3
Astronomy 201 Lab Report Template Keep in mind that another student should be able to reproduce the experiment from your report alone (ie. without the lab manual). A good lab report should convince your TA that you fully un- derstand the concepts and how they relate to the lab’s purpose; that you competently performed the entire experiment and made your own observations; and that you have properly made calculations and graphs to represent and interpret your data.
Sections of the Lab Report: Objective: (2 to 3 sentences) • State the main goals of the lab.
• What will be measured and/or learned, and why?
Introduction: (2 to 3 paragraphs) • Provide a context for the lab: why is it important?
• Introduce all background ideas, theories, and formulae used in the lab, with appropriate diagrams.
Equipment: (1 paragraph) • Describe the equipment and setup you used for each experiment.
• Include things like telescopes, cameras, lenses, thermometers, etc.
• Don’t worry about things like computers, pens, pencils, brains, etc...
Procedure: (1 paragraph, optional) • A brief outline of the major steps of the experiment and how its goals are achieved.
Experiment: (2 to 5 pages written, plus graphs, tables, diagrams, calculations) This section can be split up into sub-sections with the same section headings as the major com- ponents of the lab manual. Basically, this section allows you to write your lab in “chronological order”, combining detailed procedure with results, calculations, graphs, and analysis for each major step of the lab. Present and discuss:
• Experimental steps performed.
• Data gathered or measurements made.
• Graphs made based on observed and/or calculated data.
• Answers to any questions posed in this section of the lab manual. 1 INTRODUCTION AND LAB OUTLINE 4
Conclusions: (1 paragraph) • Rephrase your major results
• Relate your results to the main objective of the lab and their importance to the search for life in the Universe.
Evaluation: (2 to 3 sentences, optional) • Comment on the pitfalls/highlights of the lab
• General feedback to your TA (ie. spoke too quietly, introduction felt rushed, etc) 2 VISUAL OBSERVATIONS 5
2 Visual Observations
OBJECTIVE The objective of this laboratory exercise is to introduce the student to the essentials of astronomy – planets, stars, galaxies, nebulae, and telescopes – through the observation of the night sky.
EQUIPMENT Telescopes At night the brightness of the faintest star which you can see is limited by the size of the pupils of your eyes. Your pupils dilate in the dark so that more photons (bits of light) can get into you eye. In the dark your pupil is about 1 cm in diameter (0.5 cm radius) and has an area (πr2) of 0.79 cm2. If the pupil of your eye were three centimetres in diameter (1.5 cm in radius) you could see stars nine times fainter. For this lab we will give you a telescope, which concentrates all the light which falls on a mirror 10 cm in radius into a beam small enough to fit in your eye. These telescopes also magnify about 45 times and have a field of view of 1 degree. Your instructor will show you the parts of the telescope and explain their function. You will be shown how to use the telescope. Make sure you understand the use of the instrument before you use it in the dark.
• Draw a diagram of the telescope showing the essential parts: primary mirror, secondary mirror, eyepiece, focuser, mount and finder.
• In a sentence or two describe and explain the function of these parts.
• Draw on your diagram the path followed by the incoming light.
• How much brighter will your telescope make the stars appear relative to your unaided eye?
Our telescopes can moved under computer control. The telescopes must be told the accurate time and properly aligned on two stars at the beginning of the night and from then on they will point to any object in the sky. If you turn the power off or bump them then the telescope will need to be realigned by the instructor. The telescope has a hand control that lets you move the telescope up, down, left and right with the arrow keys. Above the arrow keys are: [Align] never push it, [Enter] to accept an answer, [undo] to not accept an answer or to answer no. Below the arrow keys is the number pad and each number is a command/list of objects. Use the [6=Up] & [9=down] keys to scroll through a list of objects. The [5=planet] key to scroll through the planets and the [8=list] key to see lists of named stars and named objects. The [1=M] key is for a famous list of objects compiled by Charles Messier. The [info] key will give you information about the object you are looking at. There is a list of interesting objects at the end of this lab.
Observations The Moon We will start with the Moon since it is the brightest and most easily found object in the sky. To get the moon in the telescope push [undo] a few times; then push [5=planet]; then push [6=Up] 2 VISUAL OBSERVATIONS 6 until the display says “Moon” and then push [Enter] and the telescope will move to the Moon. Then look into the small finder telescope and centre the image of the moon on the cross hairs by pushing the arrow keys. The moon should now appear in the main eyepiece. Centre the moon in the field of view by pushing on the arrow keys. DO NOT pull or push on the little FINDER telescope.
• Sketch the moon as seen with your eye. Include the time and the location of the horizon.
• Sketch the moon as seen through the telescope.
The Planets People have looked at the night sky with their unaided eye for centuries and have made some interesting observations. The most obvious is that everything in the sky other than the Sun and the Moon seems to be a tiny pin-prick of light. Also, if you measure the moon’s position relative to some stars tonight and then do the same thing tomorrow you will find that the moon has moved relative to the stars. The ancients also noticed that some of the brightest “stars” moved; these they called the “planets”, which means “wanderers”. The planets are also bright and usually easily identified. Five planets can be seen with the naked eye – Mercury, Venus, Mars, Jupiter, and Saturn. Depending on their position along their orbit and our position in our orbit around the Sun, some planets may or may not be visible, i.e. above or below the horizon, at the time you are doing this lab.
• Note also the time and date of your observation.
• Use the telescope to observe each visible planet.
– What colour is the planet? – Can you see markings on its surface? – Can you see its moons? – Is the planet crescent-shape, round, or gibbous (nearly full)?
• Sketch each planet (and its moons, if any) as seen through the telescope.
• If the moons are visible, label them on your sketch.
The Stars Even if the moon and the planets are below the horizon during the night, there are many very interesting stars to look at.
• Point your telescope at any bright star in the sky. What do you see? In the list of named stars: Vega, Deneb, Altair or Arcturus are probably good choices.
Hopefully you have seen a tiny pin-prick of light that twinkles. Stars look the same through a telescope as they do to your eye, but brighter. They are so far away that they appear to us as dots of light – no matter how many times you magnify them, you will always see them as dots. The stars are many light years from us (1 ly = 9.46 × 1012 km, the distance a photon of light travels during one year). For comparison, the Moon is about 2 light seconds from us, and the planets are about 20 light minutes from us, the bright stars are about 20 light years from us and the nearby galaxies are about 20 million light years from us. 2 VISUAL OBSERVATIONS 7
Some stars have close companions which orbit them, similar to the way our Earth orbits the Sun. These stars are called double stars or binary stars. The star named Albireo (β Cygni) in the constellation Cygnus is a beautiful double star.
• Point your telescope at Albireo.
• Sketch Albireo A and B.
• What is the colour of each star?
• Based on your observations, which star is the hottest of the two? Explain.
The Constellations When you look at the night sky you will probably notice that the stars seem to form lines or simple geometrical shapes. These asterisms are the basis for the constellations. While the origin of our names of the stars and constellations is for most part lost, generally we use names derived from the Arabic names for the stars and the Latinized Greek names for the constellations. Your instructor will point out the more obvious constellations and bright stars.
• Sketch at least three (3) new Constellations that you learnt tonight.
• What is the mythology associated with them.
• Note their approximate positions in the sky, and the time and date of the observations.
• Learn the names of at least three stars and mark them on your constellation sketch.
Extrasolar Planets Presently there have been approximately 373 planets discovered orbiting other stars. Most of these planets have been discovered around relatively bright stars, which you can see with your naked eye. Three of the brightest stars, which have planets orbiting them, are listed in the table at the end of the lab. Since the planets are a billion times fainter than the star and separated from the star’s image by much less than the apparent size of the star, you can not see the planet, even with the Hubble Space Telescope. Still it might be fun to take a look.
• Find 3 stars with extrasolar planets and sketch their constellation.
• Sketch one star and the field of view of as seen through the telescope.
If you do not get a chance to see one of these objects due to clouds etc., look them up in your text book or the Internet and write a few sentences about them. Web Sites http://skyandtelescope.com/ http://www.heavens-above.com/ 2 VISUAL OBSERVATIONS 8
INTERESTING FALL OBJECTS
Objects R. A. Declination Mag. Comments Vega 18:36:56 38◦470 0.0 25 ly A0V Arcturus 14:15:40 19◦110 0.0 36 ly K2III Albireo 19:30:44 27◦570 3.1 K3II+B8V Mizar 13:24 54◦560 2.3 78 ly, Double Star NGC 869/884 02:20 57◦080 6.6 6000 ly, Double Open Cluster M57 18:53:24 33◦020 9.7 1600 ly, Ring Planetary Nebula M31 00:42:42 41◦160 3.5 2 000 000 ly, Andromeda Galaxy M13 16:41:42 36◦280 5.9 20 000 ly, Globular Cluster M15 21:30:00 12◦100 6.3 30 000 ly, Globular Cluster γ Cephei 23:39:20 +77◦370 3.2 45 ly K2V period=903days ι Drac 15:24:55 +58◦570 3.3 100 ly K2III period=511days υ And 01:36:48 +41◦240 4.1 44 ly F8V Per=4.6, 241, 1275 days 3 SPECTRA AND REMOTE SENSING 9
3 Spectra and Remote Sensing
Spectra OBJECTIVE Our objective is to observe three kinds of spectra, including continuous spectra of opaque filaments, the emission lines of transparent gases, and the solar absorption spectrum. Then in part B we will photograph some objects through red and infrared filters and measure the reflectivity of the objects.
INTRODUCTION Wave Nature of Light In many respects light exhibits a wave-like behavior. Light has an electric component which undulates up and down, and a magnetic component that oscillates side to side. The distance from one wave crest to the next wave crest is the wave length usually denoted by λ. If you stand in one place and count the wave crests as they go by, the number you count in one second is called the frequency and is denoted by ν. See Figure 1. The distance a light wave travels in one second is its velocity c. That distance will equal the number of waves passing a point in one second (ν) times the length of each wave (λ). Therefore we have a fundamental relation between these three quantities:
c = λν (1)
λ c Wavelength Velocity
Figure 1: Light Waves
Wavelengths of light waves are often measured in nanometres (1 nm = 10−9 m) or Angstroms (1 A=˚ 10−10 m). The wavelength of a light wave determines its colour. Red light has a wavelength of around 6500 A;˚ green light has a wavelength of 5000 A;˚ and blue light has a wavelength of 4500 A.˚ The human eye responds to the wavelength range of around 4000 A˚−7000 A.˚ Sometimes when it rains you can see a rainbow. The rainbow is formed from Sunlight coming over your shoulder and going into the rain drops in front of you. Inside the rain drops the light is broken up into its component colours: red, orange, yellow, green, blue, and violet. A prism can also form a rainbow, but in this case we call the rainbow a spectrum. If we have more than one spectrum then we call them spectra. A transmission grating is a piece of transparent glass or plastic ruled with many finely spaced lines. A grating will break up light into a spectrum just like a prism; only it will form many little spectra. Some light will go straight through the grating, this is the zero order image. See figure 2. The first spectrum formed beside the zero order image is the first order image, and the next is the second order image, et cetera. 3 SPECTRA AND REMOTE SENSING 10
Second Order
First Order
Zero Order
Light Bulb First Order Second Order Grating Spectra
Figure 2: Spectral Orders
EQUIPMENT We will use a diffraction grating, which is ruled with very fine lines spaced about 600 lines per millimetre. An ordinary light bulb contains a very thin wire or filament made from solid tungsten. An electric current is forced through the filament making it hot, about 2800 K (=2527 ◦C). The hotter the solid filament, the brighter it is and the more white its colour. To make light from various gases we will use gas discharge tubes. These are glass tubes filled with Helium, Hydrogen, Neon, Mercury, and Argon. A high voltage power supply is used to pass an electric current through the gas making it glow. The internal structure of the atoms of the gas make the colour of the light different for each of the different elements. The spectrum of each of the elements is composed of discrete lines of colour. The intensity and position or wavelength of the lines serve as a fingerprint to identify each element.
PROCEDURE Observe
• Hold the grating close to your eye. Look a little to the left or the right of the light source to see the spectrum, which will look like a rainbow.
• Look at the light bulb which is powered through the dimmer switch. As we turn the power to the light bulb up and down, the temperature of the filament of the bulb changes. Is the brightness of the bulb the same with the higher and lower temperature? Is the bulb’s colour the same? Is the spectrum the same with the high and low temperature? Sketch the spectrum at both high and low temperatures. How does this apply to stars?
• Look at the spectrum of a fluorescent light and make a sketch. It looks very similar to a tungsten light. The big difference is that the tungsten light puts out lots of its energy in light which is a little redder than red. This light is called infrared light. While we can not see infrared light we can photograph it with our CCD camera.
• We can also observe the spectrum of the nearest star, our Sun. One of the windows is covered with a blind which is open just a bit. If you stand across the room from that window and look at the spectrum of the slit you will see a continuous spectrum similar to the light bulb. If you look closely in the yellow part of the spectrum you will see a dark line crossing the spectrum. This line is an absorption line due to the element sodium.
– What does this tell you about the Sun’s atmosphere? 3 SPECTRA AND REMOTE SENSING 11
– Can you see other absorption lines? – Sketch the Sun’s spectrum. Using the poster of the solar spectrum identify as many lines as you can.
• Observe the gas discharge tubes. These are tubes of glass where the air has been pumped out and a sample of an element has been put in the tube before it is sealed. A high voltage current is run through the tube to excite the gas and the gas in turn emits light. Turn the box to Neon and look at the first order image. Do you see a lot of red and yellow lines? Make a sketch of the spectra that you see from the gases in the gas discharge tube box (Argon is probably too faint). Colour the lines and comment on the similarity of the different spectra. What is the unknown? Explain two observations about the unknown’s spectra, which lead you to this belief. Check your sketches with your neighbour’s. Does everyone agree? Explain.
The Vegetation Red Edge Introduction If we could obtain spectra of the surface of an extrasolar planet, what signatures would we look for to determine if life was present? Certain spectral features called ‘biomarkers’ can be used to this end. For example, the O2 (Oxygen) molecule is highly reactive and tends to bond with other chemicals very quickly. Therefore, the presence of O2 in an atmosphere requires that it be continually replen- ished faster than it is being removed from the atmosphere due to reacting with other chemicals. Earth’s atmosphere has lots of O2. What source replenishes it? Photosynthesizing organisms (like plants) metabolize CO2 and release O2, maintaining its presence in the atmosphere. So, if some alien Astronomer were to look at Earth and see the O2 in its atmosphere, they might conclude that there is life here. In this experiment, we will be looking at another potential biomarker: the Vegetation Red Edge (VRE). As illustrated in Figure 3, green vegetation reflects near-infrared (Near-IR) very well, while not reflecting as much visible light. This is an evolutionary feature that is thought to have developed to prevent plants from overheating in sunlight. This feature is distinct from most other materials that might cover the surface of a planet; for example, most rocks and soils have relatively similar reflectivity in the Near-IR as they do in the visible. So, if the surface of a planet has a large fraction covered in green vegetation, it may be possible to detect the excess Near-IR light reflected from the plants that would be absent if the surface was bare rock (or some other material).
Experimental Setup We will be using a research-grade CCD camera (Santa-Barbara Instrument Group ST-8) with a wide-angle lens attached to it to take pictures of several types of stone, soil, and your own samples of vegetation in both the Near-IR and in visible light. The CCD chip in the camera (similar to the ones in your digital cameras) is sensitive to light with wavelengths ranging from the Near-IR, through the visible spectrum, and into the Near-Ultraviolet. Filters attached to the camera allow you to select which wavelengths you wish to see in any given image. The two we will be using in 3 SPECTRA AND REMOTE SENSING 12 this lab will be the Cousin’s “R” and “I” filters. The “R” filter allows red light through, while the “I” filter lets Near-IR light through. By placing your samples in front of the camera and taking two pictures (one through the “R” filter and one through the “I” filter) and comparing the resulting images, you will measure the difference in the reflectivity of each sample in the Near-IR and in visible light.
R filter I filter
Figure 3: Reflectivity vs. wavelength for vegetation and soil/rock.
Hypothesis Green plants are more reflective in the Near-Infrared than most rocks and soils.
Prediction If this hypothesis is valid, what do you predict the (qualitative) brightness change between the “R” filter and the “I” filter will be for the plants, compared to rock and soil samples? 3 SPECTRA AND REMOTE SENSING 13
Obtaining your Images 1. Place your sample on the sample tray. Make sure to put your name label near it so you can recognize it in the final picture (several other students may also be taking their pictures simultaneously). Position it so that it is evenly illuminated by a light source (as seen from the camera’s angle), and not blocking the light or the camera’s view of any other samples on the tray.
2. NOTE: It is important that the light source be incandescent! Fluorescent lights do not produce enough NIR light to be effective for this experiment. A good lamp is the light from an overhead projector.
3. Check to see that the CCD camera is running, in focus, and that CCDOPS (the camera control software) is running on the HP laptop. If anything appears wrong at this step, your lab instructor will fix the setup.
4. Select the ”Filter” pulldown menu, and select the “I” filter. Wait for the camera to finish changing the filter (usually only a couple seconds).
5. Select the ”Camera” pulldown menu, and select ”Grab” (Figure 4). If you are prompted to save a file, select “No.” Using the pop-up window, choose a 1.2-second “Exposure Time”, and click “OK.” If the image looks too dark or too bright, you can adjust the Exposure Time accordingly.
Figure 4: “Grab” window.
6. The camera will take the image and perform a quick calibration as well (it will take a “dark” frame used to remove noise from the camera). The image will be displayed on the screen once it has been downloaded from the camera.
7. Select the “Display” pulldown menu, and select “X-hair.” Now, by clicking the cursor on a given spot of the image, some information about that spot is displayed in a pop-up window. In a digital image, the brightness of a pixel represents how much light hit that part of the camera’s sensor in the time that the shutter was open. The brightness of a pixel in software is represented by “counts” - more counts means a brighter pixel, which means that more light was hitting that part of the camera’s sensor than another part with lower counts. As long as the image isn’t overexposed, the counts linearly represent the amount of light (or number of photons) that hit each part of the camera’s sensor. In other words, if pixel A has twice the counts as pixel B, pixel A had twice as much light (twice as many photons) hit it as pixel B. 3 SPECTRA AND REMOTE SENSING 14
The “X-hair” pop-up window (Figure 5) allows you to find the counts in any given pixel that you click on. However, since we’re looking at objects that aren’t smooth, might have variations in color, etc., we want to find an average value for its brightness. The “Average” window takes a box of pixels around where you click and finds the average value of the counts in those pixels - giving you a measure of the average brightness of that area of the object in the image.
Figure 5: “X-hair” window.
8. Click on the center of each object in the “I”-filter image, and record the average counts from the pop-up window in the “Average I counts” column of the Table 3.
9. Close the open image window (do not save it).
10. Select the “Filter” pulldown menu, and select the “R” filter. Wait for the camera to finish changing the filter (usually only a couple seconds).
11. Repeat steps 4-6 above. 3 SPECTRA AND REMOTE SENSING 15
Sample Name Average “I” counts Average “R” counts Brightness ratio (“I” / “R”)
Table 1: Worksheet for the Vegetation Red Edge experiment. At the end of the lab session, we will collect all of the brightness ratios for all of the samples on the board and discuss them. Please write in your measurements on the whiteboard when you are finished with this section.
Comparing “R” and “I” For each sample recorded in your table, compare the reflectivity in the “I” and “R” filters. Since we want to know how much more (or less) reflective a given sample is in “I” compared to “R,” we will take the ratio of the counts measured for each sample in each filter. For example, if Sample A had 300 counts in “I” and 100 counts in “R”,
300 it is 100 = 3 times as bright in “I” as in “R” or if Sample B had 100 counts in “I” and 200 counts in “R”,
100 it is 200 = 0.5 times as bright in “I” as in “R” For each sample in your table, take the counts in the “I” column and divide them by the counts in the “R” column, and record the result in the Brightness ratio column. This is your measure of how many times more (or less) reflective each sample is in the Near-IR (I) as in the visible (R).
Red Edge Exercises 1. Comparing the vegetation samples in your images to the non-vegetation samples, which tend to be more reflective in the Near-IR compared to the visible? 2. How strong is the effect - is the vegetation slightly brighter/fainter or several times brighter/fainter? 3. Does this match your prediction? 4. Would you say this validates the existence of the “Vegetation Red Edge?” 5. What other device (other than filters and a camera) could be used to detect the brightening of vegetation in the Near-IR, compared to the visible? HINT: You need to measure brightness over different wavelengths - what device does this? 3 SPECTRA AND REMOTE SENSING 16
6. How would you propose an Astronomer use this technique to see if a distant planet is covered in vegetation?
7. Consider all the brightness ratios from the whole class (on the whiteboard). Do all the vegetation samples exhibit the “Red Edge” behavior? If some are stronger than others, what might make those plant samples different? What kind of vegetation exhibited the strongest “Red Edge?”
8. Do any of the non-vegetation samples appear to be bright in the Near-IR like the plants?
9. Suppose the detection of the “Vegetation Red Edge” was not convincing enough to prove that a planet was covered in vegetation - what other measurements might be made to confirm the presence of photosynthetic plants on the planet? Would the detection of multiple biomarkers convince you?
Another of Life’s Signals It turns out that all life on Earth affects polarized light. Of the 70 known amino acids, life on Earth uses only 20 of them and they are all “left handed”. Almost all the sugars used by living organisms are “right-handed”. When these sugars are produced in chemical reactions not involving life forms right and left handed sugars are produced equally. We can observe the effects of “right-handed” sugars. We will be measuring the effect of sugar molecules on polarized light. You will have a stand with an attached polarizer and several bottles of solution. Place the stand between you and a computer monitor (LCD screens produce polarized light). Rotate the polarizer until the screen goes dark - you have aligned your polarizer with the polarization direction of the monitor. Note the angle measured around the circumference of the polarizer - this is the angle of the polarization of the screen. The sugar in Corn Syrup is a molecule which will rotate the angle of polarization. Put the bottle labelled Corn Syrup in between the polarizer and the computer screen. Can you now see the light of the computer screen? Rotate the polarizer until the screen goes dark again. How much has the angle of rotation changed? Have your partner repeat the mea- surement. If we had a sample from somewhere other than the Earth (Mars for instance) and it had an excess of left-handed sugars what could we conclude? 4 MISSION TO MARS 17
4 Mission to Mars
Getting to Mars OBJECTIVE Our objective is to investigate what is involved in a mission to Mars. What we would like to know is when to launch, when will we get there, where to land, what to look for and how to look for it.
INTRODUCTION Mars is the planet in our Solar System that is the most similar to the Earth and billions of years ago it was even more similar. Let’s assume we are going to look for evidence for life on Mars — life that is similar to life on the Earth.
ORBIT Orbits of Mars and Earth In order to visualize a trip to Mars let’s make a scaled plot of the orbits of Mars and the Earth. This will help us to see the relationship between the launch of a Mars probe and the arrival of the probe at Mars. You need to launch the probe so that the probe ends up at the orbit of Mars just as Mars reaches that point in its orbit. We will supply you with some polar graph paper to make the plot. We can put the Sun in the middle of the circles and have the planets orbit along the circles. Earth can be at 4 big divisions (1AU) from the sun and Mars will be close to 6 divisions (1.5AU) from the Sun. It has the Heliocentric Longitude marked around the outside. Least Energy Transfer Orbit We want to burn the least amount of fuel possible when we send our probe to Mars so to go the least distance from the sun we want to encounter Mars when the probe is at aphelion. See figure 1. The probe will launch from the Earth, so its perihelion will be 1AU (Astronomical Unit). Since its aphelion will be at Mars at Mars’s orbit, its aphelion will be 1.52 AU. The total distance across the orbit will be the sum of its aphelion and perihelion distances (=Major Axis). The probe will move 180◦ from Earth launch to Mars encounter and for a few Earth positions these encounter positions are labelled “Encounter” in Table 1. Kepler discovered that for all objects orbiting the sun there is a relationship between the size of the orbit (Semi-major axis) and the period of the orbit. The relationship is: P 2 = A3 Where the orbital Period P is in years and the semi-major axis A is in Astronomical Units. We know the size of our probe’s orbit (the Major Axis) so we can divide by 2.0 to get the Semi-major Axis. We can put the semi-major axis into the above relationship or read it off the graph to find the orbital period. Did you get more than Earth’s orbital period (1 year) and less than the orbital period of Mars (1.88 years) for the period of the probe to make a whole orbit of the sun? If not, check with your instructor. Divide the probe’s period P by 2 to get the transit time T from Earth launch to Mars encounter. Then multiply by 365 days to convert transit time T to days.
• Transit time to Mars in days: T = 4 MISSION TO MARS 18
Table 1. Heliocentric Longitudes from XEphem 3.5.2
Date Earth Encounter Mars Mars’ Distance AU 2009-Sep-22 00 180 68 1.51 2009-Oct-23 30 210 84 1.55 2009-Nov-21 60 240 98 1.59 2009-Dec-21 90 270 112 1.62 2010-Jan-20 120 300 126 1.64 2010-Feb-18 150 138 1.66 2010-Mar-20 180 152 1.67 2010-Apr-20 210 165 1.66 2010-May-21 240 179 1.65 2010-Jun-20 270 193 1.63 2010-Jul-22 300 207 1.61 2010-Aug-23 330 222 1.57 2010-Sep-23 00 238 1.53 2010-Oct-23 30 254 1.49 2010-Nov-22 60 271 1.45 2010-Dec-21 90 287 1.42 2011-Jan-20 120 306 1.40 2011-Feb-18 150 324 1.39 2011-Mar-20 180 343 1.38 2011-Apr-20 210 003 1.39 2011-May-21 240 022 1.42 2011-Jun-21 270 040 1.45 2011-Jul-23 300 058 1.49 2011-Aug-23 330 074 1.53 2011-Sep-23 00 090 1.57 2011-Oct-23 30 104 1.60 2011-Nov-22 60 118 1.63 2011-Dec-21 90 132 1.65 2012-Jan-20 120 145 1.66 2012-Feb-18 150 158 1.67 2012-Mar-20 180 171 1.66 2012-Apr-20 210 184 1.65 2012-May-21 240 198 1.62 2012-Jun-21 270 213 1.59 2012-Jul-23 300 028 1.55 2012-Aug-23 330 244 1.51 2012-Sep-23 00 261 1.47 4 MISSION TO MARS 19
Encounter
MDE Probe
Sun
Earth Mars
ME
Figure 6: Minimum Energy Orbit
If Mars makes a complete orbit of 360◦ around the sun in 1.88 years = 687 days, how many degrees around the Sun will it travel while the probe is in transit? Let’s call this angle MDE.
• Angle around the Sun that Mars travels in T days: MDE =
So while the probe is coasting 180◦ from the Earth to Mars orbit, Mars will move MDE, to the same location. So we need to find a launch time when Mars will be MDE away from Mars encounter which is 180◦ from Earth at launch. The difference between 180 and MDE is ME so we need to find a time when Mars leads the Earth by ME.
• Angle between Earth and Mars at time of launch: ME = 180 - MDE =
Take a look at Table 1 and see if you can find a time(s) when the Earth leads Mars by ME. Pick a date from Table 1. where Mars leads the Earth by ME and plot the Earth and Mars at Launch and Encounter and sketch in the orbit of the probe. Remember the probes perihelion is at the Earth’s orbit so the probe should never be closer to the sun than the Earth’s orbit. Label it with the dates of launch and encounter. You may notice that there is a slight error between the predicted launch and encounter dates. You can understand this by understanding the assumptions we made in our analysis. We as- sumed that the planets are one circular orbits. For Earth, this is a good approximation. Mars however varies in distance from the Sun. Its orbit is elliptical. The place in its orbit where Mars is closest to the Sun is called the perihelion (peri=close; Helios=Sun) and the place in the orbit where Mars is most distant from the Sun is called the aphelion. Mark on table 1 the dates of aphelion and perihelion of Mars and define them in the lab report. 4 MISSION TO MARS 20
10
7
5
3
1.5 Period in Years 1
.7
.5
.3
.3 .5 .7 1 1.5 3 5 7 10 Semimajor Axis in AU
LANDING SITE Criteria We want to land in a spot that does not have too many hazards, but does have some interesting things to observe. If you land on the side of a steep mountain or gully your lander could turn over on its side. If there are too many big rocks, the landing strut could break. If there are too many sand dunes and you have a rover, your rover could get stuck in the sand. Below are some of the considerations for the Mars Science Laboratory (MSL).
Elevation The heat shield and parachute must slow the Mars Science Lander down from inter- planetary velocities, and these systems require Mars’ atmosphere in order to function. Therefore, high-altitude landing sites are not accessible, because there is less atmosphere to travel through before landing. Landing sites must be at lower than 1 km above Mars’ “Sea Level,” the mean elevation of Mars measured by the Mars Orbiter Laser Altimeter (MOLA). The lower the elevation, the safer the site is for landing. Landing ellipse Because we are landing on a distant world, there is some uncertainty on exactly where the probe will land — some error around “bullseye.” The direction and speeds of the winds can have significant effect during the parachute phase of the descent. A “safe” landing ellipse needs to be roughly 20×25 km. Boulders in the landing ellipse With high-resolution cameras in orbit (like HiRise) we can search for boulders in the region where we wish the probe to land. If the ground is peppered with large rocks, the chances of the landing going awry due to coming down on top of a boulder can be significant. It is therefore important to make sure that the landing ellipse is relatively devoid of large boulders or other potentially dangerous obstacles. 4 MISSION TO MARS 21
Trafficability After a successful landing, the rover must be able to move around. Sand dunes have mired the Spirit rover on Mars, and could do the same to the Mars Science Labora- tory. Make sure that the region around the landing site is navigable, relatively free of treacherous sand dunes or other obstacles.
Google Mars Google earth can be started on the computers with “Googleearth” and then you need to do is click on the button with Saturn’s image and choose Mars. You can rotate the Mars image with the hand and zoom with the + and - buttons on the slider on the right side of the screen. On the lower left of the window is the “Layers” panel. You probably want to select “Featured Satellite Images, ” and under Global Maps “Visible Imagery.” Clicking on the image icons that are overlain on the map will bring up information about a particular high-resolution image, often with links to more information about the image and its significance. Play with the controls and see what you can find that you think is an interesting place on Mars. Some suggested landing sites you might want to look at are: • Eberswalde Crater (24.0S, 327.0E)
• Holden Crater (26.4S, 325.3E)
• Gale Crater (4.6S, 137.2E)
• Mawrth Vallis (24.0N, 341.0E). Write a couple of paragraphs on the pros and cons of one of the landing sites, considering the combination of interest and safety.
Viking Lander Experiment: Detecting Metabolic Byproducts In the late 1970s, NASA sent the Viking spacecraft to Mars. Each spacecraft was composed of a lander and an orbiter. The landers carried miniature robotic laboratories, and several of the on-board experiments were designed to detect microbial life if it was present in the Martian soil. Two of these experiments (Gas EXchange or GEX, and Labeled Release or LR) were designed to detect similar things: the molecular byproducts of the metabolic processes of any microbes in the soil. They placed soil samples in special nutrient solutions and monitored the production of gasses from the soil. If there was significant production of CO2 or other metabolic byproducts, they might surmise that life produced it. However, chemical reactions can produce similar byproducts. How were the Viking scientists to tell them apart? The Labeled Release experiment used nutrient solutions with special, rare radioactive isotopes of Carbon (14C) in them, in place of the more common kinds of Carbon (12C) found in the soil, living things, etc. Metabolic processes cannot tell the difference between 14C and 12C, so if it released CO2 as a byproduct, this CO2 would contain radioactive 14C. However, any chemical reactions would release only the Carbon stored in the soil sample, which would be mostly 12C. So CO2 produced by a chemical reaction would not contain the radioactive 14C. The Gas EXchange experiment was simpler. The way biological processes produce byproducts over time has a different behavior than the way chemical reactions do. Chemical reactions usually proceed steadily until the reactants are depleted, and then the reaction slows and stops. Microbes, 4 MISSION TO MARS 22 however, reproduce and therefore produce more byproducts as time goes on - so the rate increases with time and only stops if the microbes are killed or the nutrient feeding them is depleted. So the scientists monitored the production of possible metabolic byproducts (Oxygen, CO2, Nitrogen, Hydrogen, Methane, etc) over time, and if they saw an accelerating rate of production of one of these gasses (instead of a rapid release and eventual stop), they could infer that microbes existed in the soil sample. The qualitative difference is illustrated in Figure 7. We will re-create this experiment in the lab. Chemical Biological 50 Reactants Depleted 2 37.5
25
Total CO Chemical 12.5 Biological
0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time Ramping Production Fast Initial Production
Figure 7: Qualitative illustration of chemical vs. biological production of metabolic byproducts (CO2) vs. time. 4 MISSION TO MARS 23
Figure 8: Illustration of meter stick water trap
Materials:
1. Graduated water trap (flexible tube and meter stick)
2. Sample bottle
3. Stopper with feed for water trap
4. Two unlabeled soil samples: One Soil sample with microbes (activated yeast), one Soil sample with chemical reactants (sodium bicarbonate + acid salts) NOTE: these samples must be fresh out of their packages.
5. Nutrient solution (sugar dissolved in water)
6. Clock or timer
Experiment You will place the nutrient solution in the beaker, then stir in one of your soil samples. Quickly put the stopper (attached to the water trap) in the beaker. As time passes, record the level of water in the water trap and the elapsed time in a table. It may be convenient to mark the time as the water in the trap passes every 5-cm interval. The level of the water in the water trap at any given time is proportional to the amount of gas that has been produced by the interaction of your “soil sample” with the nutrient solution. One sample should generate gas quickly, the other somewhat slowly. Record the slower one until the water trap reaches its limit (∼ 10 minutes), and the faster one until it appears to have stopped (should be less than a few minutes). After you have monitored your samples for their respective amount of time, plot the level of the water trap vs. time on graph paper. 4 MISSION TO MARS 24
Questions 1. Which reaction looks like a chemical reaction? Why? Explain.
2. Which looks like biological behavior? Why? Explain.
3. What other differences did you note between the two samples and reactions, and what other measurements could the Viking lander have made to verify biological activity? 5 EXTRASOLAR PLANETS: DETECTION AND HABITABILITY 25
5 Extrasolar planets: Detection and Habitability
Extrasolar Planets OBJECTIVE One of the most exciting fields of astronomy today is the search for and characterization of planets orbiting other stars.
Background The first extrasolar planet was discovered in 1995, when Mayor et al. announced the discovery of a planet orbiting the star 51 Peg. Mayor very precisely measured the spectra of 51 Peg and found that the star moved towards us and then away from us. He found that its movement was very predictable and varied in a sinusoidal shape with a period of 4.2293 days. The fact that the period was constant and the shape of the variations was a sine curve led him to conclude that something was orbiting 51 Peg. The amplitude of the star’s motion gave him an estimate of the mass of the orbiting body, which was so small that he concluded that the orbiting body was a planet.
Discovering Planets Planets have been discovered by four methods, namely radial velocity variations of the star, transits of the star by the planet, gravitational lensing and direct imaging.
Investigating the Planet Orbiting the Star HD209458 A spectrum of the star HD209458 shows that it is slightly bigger in radius and slightly more massive than our sun. The Hipparcos satellite has measured its parallax and found the distance to HD209458 to be 47 parsecs. Geoff Marcy discovered a planet orbiting HD209458 with an orbit which is tilted just right for the planet to pass in front of the star. When the planet blocks part of the light from the star we see the star become a bit fainter. A modeling program has been written by J. Clem to help us visualize the situation and find the mass and radius of the planet orbiting the star HD209458. The modeling program allows us to simulate the planet orbiting the star, the eclipse of the star by the planet, and also the variations in the radial velocity of the star. We can change the planet’s mass, period, radius and the orbital inclination by clicking on the buttons in the button panel seen in Figure 1. The second panel shows the blue planet orbiting the red star. The ellipse is the path of the planet around the star. Click on the [Orbital Inclination] button to change how much the orbit is inclined to the line of sight. If the inclination is just right, the planet will pass in front of the star and block out part of the star’s light making the star appear fainter. The third panel shows a plot of how the brightness of HD209458 changes as a function of time. Every 3.525 days the star becomes very slightly fainter. We watched the dimming of HD209458 one summer with our 20 inch telescope and our observations are the points plotted in the third panel. The depth of the eclipse depends on the size of the planet; the bigger the planet, the more light it blocks and the deeper the eclipse. We can find the radius of the planet from the depth of the eclipse. Change the radius of the planet using the [Planet Radius] buttons so that the line agrees with the data. Change the inclination of the orbit to get the observations of the edges of the eclipse to agree with the model. 1 EXTRASOLAR PLANETS 2
the star, the eclipse of the star by the planet, and also the variations in the radial velocity of the star. We can change the planet’s mass, period, radius and the orbital inclination by clicking on the buttons in the button panel 5 EXTRASOLAR PLANETS: DETECTION AND HABITABILITY 26 seen in Figure 1.
Figure Figure1. The 9:mo Thedelling modelingprogram. program. The second panel shows the blue planet orbiting the red star. The ellipse isRecordthe path theof radiusthe planet of thearound planetthe andstar. theClic inclinationk on the [Orbital of the orbit.Inclination] buttonThe bottomto change panelho isw a plotmuch ofthe theorbit radialis velocitiesinclined ofto HD209458the line of assigh observedt. If the by Geoff Marcy withinclination the world’sis largestjust righ telescope.t, the planet A sinewill curvepass hasin beenfront drawnof the throughstar and theblo datack points, but it doesout notpart quiteof agreethe star’s withligh them.t making The morethe massivestar app theear planetfainter. the larger the reflex motion of the star and the larger the amplitude of the radial velocities. So we can measure the mass of the planet The third panel shows a plot of how the brightness of HD209458 changes by measuring the amplitude of the radial velocity variations. Change the amplitude of the radial as a function of time. Every 3.525 days the star becomes very slightly fainter. velocity curve by clicking on the [Planet Mass] button. WWee canwatc alsohed changethe dimming the positionof HD209458 of the dataone pointssummer along thewith graphour by20 changinginch tele- our guess of the periodscop ofe theand planet’sour observ orbitations aroundare thethe star.poin Changets plotted the periodin the bythird clickingpanel. on theThe [Period] buttons anddepth you willof the findeclipse that thedep observedends on pointsthe size moveof the leftplanet; or rightthe a littlebigger bit.the Fromplanet, Kepler’s Law we knowthe themore semi-majorlight it blo axiscks ofand thethe orbitdeep of theer the planeteclipse. aroundWe thecan starfind dependsthe radius on theof period of the orbit.the Changeplanet from the periodthe depth and seeof the thateclipse. the RadiusChange of thethe Orbitradius changesof the asplanet well. Changeus- the planet massing andthe the[Planet periodRadius] to bestbuttons fit the dataso that points.the line agrees with the data. Change Record your best estimate of the mass, period, and semi-major axis of the orbit of the planet. Would you be able to detect a Jupiter mass planet in a one year orbit? Click on the [Stop] animation box and then click on the Period value and change it from 3.52 to 365 days. Click [Start] twice and the animation will start again with the planet at about 1 Astronomical Unit from the star. Increase the mass of the planet until it is at 1 Jupiter mass. Increase the radius of the planet until it is at 1 Jupiter radius. Set the Inclination to 90 degrees so that eclipses must occur. m Would you be able to observe radial velocity variations (uncertainty of ±4 sec ) or eclipses for a Jupiter sized planet in an Earth like orbit? Would it be possible to detect planets like the Earth? Set the Period in the simulator to 365 days and the radius of the planet to 0.1 Jupiter and the mass of the planet to 0.01 Jupiter Masses. 5 EXTRASOLAR PLANETS: DETECTION AND HABITABILITY 27
Web Sites http://www.seti-inst.edu/ http://exoplanet.eu/ http://exoplanets.org/index.html
Greenhouse effect Introduction The temperature of the surfaces of planets plays an important part on whether or not they could be habitable. For example, most life as we know it requires liquid water to survive. So, if the surface of a planet is hotter than the boiling point of water, or colder than the freezing point, it would be uninhabitable to this kind of life. Astronomers refer to the range of distances that a planet around a given star could have liquid water on its surface as the “Habitable Zone.” Planets’ atmospheres can have significant effects on surface temperatures by altering the way incoming radiation (sunlight) is absorbed and reflected. For example, if an atmosphere freely allows visible light to pass through it, but traps infrared light (thermal radiation), the atmosphere will have a warming effect. This effect is commonly referred to as the “greenhouse effect”, because it operates on the same principle that makes greenhouses hot. This experiment compares the greenhouse effect by Earths atmosphere with a nearly pure CO2 atmosphere like Venus’ (CO2 exhibits a strong greenhouse effect).
Blackbody Temperature What governs the temperature of the surface of a planet?
• A planet orbiting a star will intercept and absorb some light and become warm.
• The warm planet must radiate this heat away or it will become hotter and hotter.
• Thus, the planet will need to radiate all the energy it receives to keep a stable temperature. Therefore:
ENERGY ABSORBED = ENERGY RADIATED or
Ein = Eout (2) An object that maintains its temperature through this sort of energy balance is called a “Black- body.” Therefore, the following derivation find the so-called “Blackbody Temperature” of the surface of a planet - the temperature it would have if it behaved like a Blackbody (without any atmosphere). 5 EXTRASOLAR PLANETS: DETECTION AND HABITABILITY 28
Derivation of Blackbody Temperature of a Planet
The ENERGY ABSORBED by the planet will depend on the distance between the planet and star D, the luminosity of the star L, and the radius of the planet r. It will also depend on how much of the sunlight is absorbed by the planet, which is determined by the planets reflectivity or albedo. We will express the fraction of light absorbed (which is defined by 1 - albedo) with the letter F, which will range from 0 (perfectly reflective, no sunlight absorbed) to 1 (perfect absorber, all sunlight absorbed).
F Lπr2 E = (3) in 4πD2 The ENERGY RADIATED by the planet will depend on the tempera- ture of the planet T and the radius of the planet r. There is an additional constant factor, called the Stefan-Boltzmann constant that is required to convert temperatures to energy radiated. We will represent it with the letter B, where B = 5.6697 × 10−8 W atts/meter2/Kelvin4
2 4 Eout = 4πBr T (4) F Lπr2 2 4 Combining Eqns. 1, 2, and 3, we find that 4πD2 = 4πBr T Since r2 appears on both sides, we can cancel it. If we solve for T we get: 1 FL 4 T = (5) 16πBD2 We can combine 16πB into one numerical term A to simplify the equa- tion: A = 16πB = 2.85 × 10−6 W atts/meter2/Kelvin4 Substituting A into Eqn. 4 we get the following simple equation for the Blackbody temperature of a planet:
1 FL 4 T = (6) BB AD2
Blackbody Temperature Exercises 1. Use Figure 10 and the D and F values in Table 2 to determine the Blackbody temperature of Venus, Earth, and Mars.
2. Compare the results of Exercise 1 with the freezing point of water ( 0 degrees C or 273.15 Kelvin). Based on their Blackbody temperatures, could any of these planets could have liquid water on their surface?
3. Using the F = 0.6 line as the temperature of Earth if we imagine moving Earth to different distances from the Sun, at what range of distances could the Earth have liquid water on 5 EXTRASOLAR PLANETS: DETECTION AND HABITABILITY 29
Constants for Eqn. 5 Term Meaning Value A 16π×Stefan-Boltzmann constant 2.85 × 10−6 W atts/meter2/Kelvin4 L Solar Luminosity 3.84 × 1026 W atts Planet-specific values Term Meaning Venus Earth Mars F Fraction of light absorbed by planet 0.4 0.6 0.8 D Planet-Sun distance 0.73 AU 1.00 AU 1.52 AU
1 AU = 1.50 × 1011 meters
Table 2: Factors for Eqn. 5 for the planets Venus, Earth, and Mars. In order to use Eqn. 5, D must be expressed in meters, so the conversion from AU to meters is included. For using Figure 10, D is given in AU.
its surface? In other words, at what inner D is the Earth’s Blackbody temperature equal to water’s boiling point (373.15 Kelvin), and at what outer D is the Earth’s Blackbody temperature equal to the freezing point of water (273.15 Kelvin)?
4. Define the “Habitable Zone” around our Sun, using Figure 10. What is the minimum distance any planet (with any of the listed F values) can be without the surface being hotter than the boiling point of water (373.15 Kelvin)? What is the maximum distance any planet can be without the surface being colder than the freezing point of water (273.15 Kelvin)? 5 EXTRASOLAR PLANETS: DETECTION AND HABITABILITY 30
500
475
450
425
400
375
350
325
300
275 Temp (Kelvin)
250
225 F = 200 1.0 175 0.8 0.6 150 0.4
125 0.2
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10
Distance from Sun (AU)
Figure 10: Blackbody temperatures vs. distance from the Sun, for different reflectivities. Based on Eqn. 5. Only valid for Sun-like stars.
Greenhouse Effect From the results of the previous exercises, it should be clear that something is causing the Earth’s surface to be warmer than it should be. This something is the Earth’s atmosphere! Consider the addition of an atmosphere that blocks infrared (thermal) radiation but allows visible light through (Figure 11, right). Since incoming radiation from the Sun is mostly in the visible part of the spectrum, the original Ein is not decreased. However, the radiation re-radiated by the surface of the Earth is mostly in the infrared portion of the spectrum. So this radiation is absorbed by the atmosphere. Now, the atmosphere has to obey Ein = Eout as well - but it can both radiate upward and downward. So half of the energy re-radiated by the atmosphere is radiated back at the surface of the planet. Therefore, the surface not only sees the original Ein from the sun, it also sees 0.5 × Eatm ! Since the atmosphere sees the Eout from the surface of the planet, and it must re-radiate exactly this amount, Eatm = Eout(surface), so: Ein(surface) = Eout(surface) = Esun + 0.5 × Eatm = Esun + 0.5 × Eout(surface) If you solve this for Ein(surface) you find:
Ein(surface) = 2 × Esun (7) So just by adding an atmosphere, the surface of the planet now sees 2 times the incoming radiation! Now, if we substitute this in our previous equations to find how this changes the surface tem- perature, we find:
1 T = (2) 4 × TBB ≈ 1.19 × TBB (8) 5 EXTRASOLAR PLANETS: DETECTION AND HABITABILITY 31
Figure 11: Illustration of the principal of the greenhouse effect. On the left, incoming solar radiation is absorbed by the ground and re-radiated to space. On the right, incoming solar radiation is absorbed by the ground and re-radiated, but then captured by the atmosphere. The atmosphere then re-radiates this energy, but both upward and back down toward the ground, increasing the incoming radiation the ground sees over the case with no atmosphere.
where TBB is the Blackbody temperature of the planet. This calculation only considers a single layer, perfect greenhouse gas atmosphere - the simplest possible case. In reality, the effect depends on other factors, like the efficiency of the greenhouse gas and the number of atmosphere layers you consider. 5 EXTRASOLAR PLANETS: DETECTION AND HABITABILITY 32
Greenhouse Effect Exercises 1. Use Eqn. 7 to find the temperature of the Earth with this simple single-layer estimate of the greenhouse effect, using the Blackbody temperature you calculated in Exercise 1.2.1.1 .
2. With this simple estimate, would the Earth be able to sustain liquid water on its surface?
3. How does this agree with the yearly-averaged value of the temperature of the Earth, which ranges from 288 to 293 K?
Testing the Greenhouse Gas Hypothesis We have shown that if an atmosphere can cause a greenhouse effect, it will cause the surface of the planet to be warmer than its blackbody temperature. Now we must devise a test to see whether or not atmospheric gasses can cause a greenhouse effect. A frequently discussed greenhouse gas is Carbon Dioxide (CO2). To test whether or not it can cause a greenhouse effect, we will have two sealed, clear-topped containers (see the figure below) - one we will fill with pure CO2 and the other we will fill with normal air (0.035% of which is CO2). We will expose both to simulated sunlight, and monitor their internal temperature over time. Based off the above description of the experimental setup, the Hypothesis below, and the diagram of the experimental setup, make your prediction for the outcome of the experiment.
Hypothesis
CO2 is a greenhouse gas, and will absorb infrared radiation while allowing visible light to pass.
Prediction
If this hypothesis is valid, what do you predict will happen to the temperature in the CO2 filled chamber compared to the temperature in the air-filled container illustrated in Figure 12? 5 EXTRASOLAR PLANETS: DETECTION AND HABITABILITY 33
100% CO2 AIR (most thermal radiation captured by CO2) (most thermal radiation escapes)
thermal radiation thermal radiation thermometer
visible light visible light thermometer
Light source
Light absorbers (black paper)
Figure 12: Experimental setup for testing the greenhouse effect hypothesis.
Experimental Setup Experimental Materials:
• 2 2-liter plastic bottles with labels removed, half-wrapped in black paper.
• 1 filled with CO2
• 1 filled with normal air
• 2 bottle caps with thermometer probes attached.
• 1 high-power light bulb in stand.
Procedure:
1. Check to make sure both your bottles are clean and dry, and have black backing paper attached to one side of them.
2. Make sure that your temperature probes are sealed in tightly, such that your CO2 has not leaked out. 5 EXTRASOLAR PLANETS: DETECTION AND HABITABILITY 34
Time Temp (A) Temp (B) Difference (A-B) 0 min:
First stabilization:
Second stabilization:
Table 3: Worksheet for Greenhouse Effect Experiment. Please write the difference between your final temperatures on the whiteboard with your group number (indicate whether the CO2 or AIR bottle was hotter)
3. Place both bottles on opposite sides of the light source, exactly equidistant from the light source, with un-papered sides facing the bulb.
4. Note the starting temperatures in each bottle in the “0 min” row in Table 3, and turn on light bulb.
5. Watch the temperature in the bottles until they stabilize (∼ 10 − 15 minutes). Note temper- ature of each bottle in the table, and the time.
6. Now switch the sides of the lights each bottle is on (swap the bottles). This will ensure that any difference in the orientation of the lightbulb cancels out.
7. Wait for the temperature of the bottles to re-stabilize. Note the temperature of each bottle in the table, and the time.
Greenhouse Effect Experiment Exercises 1. Calculate the difference in temperature (Temp A - Temp B) for the first stabilized temp and the second stabilized temp. Now take the average of these two differences: Avg Difference = (Difference 1 + Difference 2) / 2. Make sure you include the proper signs for each difference value!
• If the Average difference is positive, then Bottle A was on average hotter than Bottle B. • If the Average difference is negative, then Bottle B was on average hotter than Bottle A.
2. Based on your hypothesis and observations, which bottle likely contains CO2? Check with your TA.
3. Does this suggest that CO2 is a greenhouse gas?
4. What other tests would you like to do to make certain that your results were accurate? 5 EXTRASOLAR PLANETS: DETECTION AND HABITABILITY 35
5. In a column of Earths atmosphere with the same diameter as your bottle, there is roughly 0.036 kg of CO2. If the density of pure CO2 is 0.0018 kg/liter (at room temperature and pressure), how does the amount of CO2 in the bottle compare to the amount in the atmospheric column? Would you expect a stronger or weaker greenhouse effect from this atmospheric column of CO2?
6. Compare the temperature differences on the whiteboard. Did every group see a similar trend? What was the average temperature difference? 6 SEARCH FOR EXTRA-TERRESTRIAL INTELLIGENCE 36
6 Search for Extra-Terrestrial Intelligence
Communicating with Extraterrestrials OBJECTIVE Assuming that there are extraterrestrial civilizations how could we possibly communicate with them? The Drake equation lists the parameters which predict the number of extraterrestrial civiliza- tions. The astronomical parameters are known to better than an order of magnitude, the biological parameters can be estimated to a few orders of magnitude but the socioeconomic parameter is not well understood. Given the most optimistic values for each of the parameters there will be lots of extraterrestrial civilizations BUT the distance to the next civilization will still be enormous. Much farther than we can travel in our lifetime. Therefore communication will be limited to messages sent by radio or optical transmissions. That is the topic for this lab.
Speed of Light The messages (Part B) that we sent to the extraterrestrial civilizations by radio and laser will travel at the speed of light. How fast is it? Galileo tried to measure the speed of light by covering and uncovering a lantern and having his assistant respond the same way. It did not work. Light is much too fast. There is a very complicated third year physics lab done with lasers and high speed rotating mirrors, but it is not much fun. You can actually measure the speed of light by remembering that it is a wave. Waves have a wavelength λ which is the distance between successive crests and a frequency f or ν which is the number of waves that go past a certain point in one second. Imagine a train of waves passing a certain point. If we know how long each wave is and how many waves go past a certain point we know how far the first wave will go during one second. This tells us the speed of the waves. Mathematically speed = frequency × wavelength If you look on the back of an ordinary microwave oven you will find the frequency of the microwaves generated inside the oven. The microwave oven we have has a frequency of 2.45 gigahertz which means that the oven will emit 2.45 billions waves in one second out of the little hole in the top of the oven. We can find the wavelength by thinking about the waves in the microwave oven. We have billions of waves per second shot into the oven and they will bouncing off the walls. The waves will interfere with each other and where the peaks of the different waves are coincident they will reinforce; it will be hotter; and the food will cook faster. The hot spots are spaced at one-half the wavelength of the microwaves. Microwave oven manufacturers try to minimize this effect but it is still observable. To measure the wavelength of the microwaves we need to grate about half a bar of chocolate onto a paper plate. Put the plate in the microwave on top of another paper plate on top of the glass turntable which is turned upside down so that it will not turn. Turn the microwave on high for about 10 seconds. Take the plate out and dump the chocolate shavings onto another plate. Hopefully some of the chocolate shavings will have melted and stuck to the paper plate. Measure 6 SEARCH FOR EXTRA-TERRESTRIAL INTELLIGENCE 37 the distance between the patches of melted chocolate and you will have approximately the one half the wavelength of the microwaves. Multiply the wavelength (2 times your measured spacing) and the frequency to find the speed of light. We have been broadcasting our presence to the universe for more than 50 years. Every radio, TV, RADAR and cell phone signal has leaked a little radio noise into space. Given the speed of light you measured, how far into space (in km) have these signals traveled?
Encoding of the Message The microwaves and visible light and radio waves all travel at the speed of light. These waves however have different frequencies and different wavelengths. To communicate with intelligent terrestrials (you and me) we use radio waves. Sometimes we encode our message by modifying the amplitude of the radio waves and call it AM radio. Sometimes we modify the frequency slightly and we call it FM radio.
Figure 13: AM and FM
The third method, which we do not usually use, but would be fun to demonstrate, is polarization. Generally the waves can jiggle up and down or side to side or anywhere in between. But when we wear “polarized” sunglasses, only the waves jiggling up and down are allowed through the glass and we can eliminate light reflected off the water for instance. We have polarizers mounted on stands for you to use. LCD computer displays are a good source of polarized light. Look through the polarizer at the computer display. Rotate the polarizer until 6 SEARCH FOR EXTRA-TERRESTRIAL INTELLIGENCE 38
it makes the screen go black. Read the protractor to find out the angle of the polarizer. Get your partner to repeat the experiment. Are the angles the same? So we could send a message by having the waves polarized first one way and then the other. Web Sites http://www.seti-inst.edu/ http://exoplanet.eu/ http://exoplanets.org/index.html http://www.hellofromearth.net/
Decoding the Arecibo Message In 1974, the Arecebo radio telescope was used to send a message into space. The message was directed at the globular cluster M13, which is an assembly of hundreds of thousands of stars roughly 25,000 light-years away. The message was sent at a frequency of 2380 MHz, with roughly 1 million Watts of power, and used frequency-modulation (FM) to encode information. Roughly 10 bits of information were sent every second, and the total message contained 1679 bits. The message was largely ceremonial, but some thought went into encoding a short message that extraterrestrial radio astronomers may have been able to detect and decode. We will be decoding the message in this lab. The message consisted of 1679 bits of information. Each bit represented either a “0” or a “1” in binary. The number 1679 is significant, because it is a “semiprime” or the product of two prime numbers. Since the bits were meant to be viewed as an image, it was hoped that the alien astronomers would realize that the two primes that make up the length of the signal would be the obvious choice for the length and width of the array that needed to be made of the data in order to see the image. This is the string of bits [1]: 0000001010101000000000000101000001010000000100100010001000100101100101010 1010101010100100100000000000000000000000000000000000001100000000000000000 0011010000000000000000000110100000000000000000010101000000000000000000111 1100000000000000000000000000000000110000111000110000110001000000000000011 0010000110100011000110000110101111101111101111101111100000000000000000000 0000001000000000000000001000000000000000000000000000010000000000000000011 1111000000000000011111000000000000000000000001100001100001110001100010000 0001000000000100001101000011000111001101011111011111011111011111000000000 0000000000000000010000001100000000010000000000011000000000000000100000110 0000000001111110000011000000111110000000000110000000000000100000000100000 0001000001000000110000000100000001100001100000010000000000110001000011000 0000000000001100110000000000000110001000011000000000110000110000001000000 0100000010000000010000010000000110000000010001000000001100000000100010000 0000010000000100000100000001000000010000000100000000000011000000000110000 0000110000000001000111010110000000000010000000100000000000000100000111110 0000000000010000101110100101101100000010011100100111111101110000111000001 1011100000000010100000111011001000000101000001111110010000001010000011000 0001000001101100000000000000000000000000000000000111000001000000000000001 1101010001010101010100111000000000101010100000000000000001010000000000000 0111110000000000000000111111111000000000000111000000011100000000011000000 0000011000000011010000000001011000001100110000000110011000010001010000010 1000100001000100100010010001000000001000101000100000000000010000100001000 0000000001000000000100000000000000100101000000000001111001111101001111000
• Question 1: What two prime numbers, when multiplied, equal 1679?
Displaying the message On the lab computers there is a file called “arecibo.dat”. It contains the string of bits from the Arecibo message. Using the “SuperMongo” plotting software, you will open this file and display it. 6 SEARCH FOR EXTRA-TERRESTRIAL INTELLIGENCE 39
The message is meant to be viewed as a grid of bright (0) and dark (1) points. The grid size must be determined by you. Since you have determined the two prime numbers that are the factors of 1679, try each of these in turn as the “width” of your grid. To display the file as a grid:
1. Open an xterm window.
2. Type sm on the command line and press return.
3. Type macro read arecibo.sm on the command line and press return.
4. You have now loaded a macro file that has the tools to decode the message.
5. Type message [width] [your name], where [width] is the grid width you wish to try, and [your name] is your name (for labeling the plot).
6. A gv window will open with your plot. Does this look like a message to you?
7. If not, try another width.
8. If so, type print message to print a paper copy of the plot.
• Question 2: What was the appropriate width for the grid?
• Question 3: Do you think that an alien looking at this grid would immediately see it as a message, or might they just think that it is strange looking noise?
• Question 4: Identify three features on the message and what you think they signify. Is the interpretation of the symbols obvious to you?
References 1. “The Arecibo Message” Retrieved from http://www.physics.utah.edu/∼cassiday/p1080/lec06.html
Giant impacts: How long do civilizations survive? Introduction There are a lot of ways that a civilization could be wiped out. We will consider one of these that has played out many times in Hollywood films: destruction by massive impact. In the Solar System, there are several reservoirs of small objects that are occasionally nudged into orbits that encounter the Earth. Small impacts occur frequently, with events like the one in 1908 that flattened a huge area of forest near Tunguska, Siberia happening about once every 100 years. Larger impacts occur less frequently, but with far greater effects. The reason larger impacts occur less frequently is that for every large asteroid or comet, there are many more that are smaller than it. The “size distributions” of asteroids and comets have been measured, and this allows us to estimate how frequently larger impacts occur, given the frequency 6 SEARCH FOR EXTRA-TERRESTRIAL INTELLIGENCE 40
of smaller ones. Also, the cratering record on the Moon gives us another handle on the frequency of large impacts. Here we will estimate how frequently two kinds of events occur. These events, “ comet showers” and the formation of asteroid families, lead to a large influx of comets and asteroids into the inner Solar System and may therefore lead to large extinction events. We will also use an online “impact calculator” to learn about the effects of different kinds of impacts. If civilizations are destroyed by these kinds of events, we can estimate the upper limit for the length of time a civilization can survive before being destroyed by natural processes (as long as they don’t invent a way to stop asteroids). We can use this number in the last term of the Drake Equation, the lifetime of technological civilizations. With our calculated timescales, we will estimate the number of civilization-hosting planets that we might discover with the Kepler space telescope.
Stellar Close Encounters and Comet Showers The sun is encircled by a vast, distant reservoir of comets called the Oort cloud. These comets have orbits that stretch out nearly halfway to the nearest star. Sometimes, if another star passes close by the Solar System, a number of these comets can be dislodged and come raining down on the planets in what is called a “comet shower.” These comet showers may be linked to extinction events on the planet Earth. In order to calculate how often a comet shower occurs, we need to know how often other stars pass close by the Sun. We will estimate how frequently this occurs. If the stars in the neighborhood of the Sun have some random distribution of velocities, then we can estimate the “Mean Free Time” between close encounters with other stars. We will use the following equation: √ Time Between Close Encounters = T = 1/( 2 × v × A × n) (9) where v is the random velocity (in parsecs / year), A is the cross-sectional area (in square parsecs) around the Solar System that counts as a “close encounter,” and n is the number of stars per cubic parsec in the Galaxy.
• The random velocity of stars in the solar neighborhood is on the order of v ' 1 × 10−5 parsec/year.
• There are ∼ 400 billion stars in the galaxy.
• The galaxy is shaped like a thin disk. So we can estimate the total volume of the galaxy by Volume= π × R2 × H. The radius of the galaxy is R ' 20, 000 parsecs, and the thickness is H ' 300 parsecs.
• A star passing within ∼ 0.1 parsec of the Sun will dislodge a large number of comets from the Oort cloud. The cross-sectional area is then A = π × (0.1)2 ' 0.03 square parsecs.
• n Number The number of stars per cubic parsec is therefore = Volume • Question 1: Using the above equations and values, estimate the Time Between Close En- counters and therefore between comet showers for a Sun-like star in the Milky Way. 6 SEARCH FOR EXTRA-TERRESTRIAL INTELLIGENCE 41
Asteroid Showers from Family Formation Another event that can cause a large influx of objects into the inner Solar System is the breakup of a large asteroid. When a large “parent” asteroid is destroyed by a collision in the asteroid belt, it creates a group of smaller objects on similar orbits, called an “asteroid family.” If this group forms near an unstable orbit (like a resonance with Jupiter), some of the newly-created objects can get injected into the inner Solar System, potentially colliding with the inner planets. In fact, it is thought that the formation of the Baptistina family created the asteroid that wiped out the dinosaurs 65 million years ago [1]. There are roughly 40 large asteroid families in the main asteroid belt [2]. Since the families have formed over the age of the Solar System (4.6 billion years), we can estimate how often an asteroid family forms by: Age of Solar System One asteroid family forms every T years, where T = (10) Number of Families • Question 2: Using the above equations and values, estimate the time between asteroid family formation events.
Caveats You should find that by these estimates, comet showers should occur much more frequently than asteroid showers. This is not exactly correct, since we used the average density of stars in the galaxy to estimate the frequency of comet showers, whereas the Sun is not in a very dense region of the galaxy (so the comet shower timescale should be greater for the Solar System). However, for the average star in the Milky Way, this might be the case. We are somewhat protected from comet showers by the presence of Jupiter, which acts like a gravitational shield against comets for the inner planets. Also, it is thought that the size distribution of comets is steeper than for asteroids, so there are fewer large comets for every small one. Therefore, asteroid showers are probably more dangerous than comet showers.
Impact Calculator There are online tools to estimate the effects of various kinds of asteroid or comet impacts. We will be using one to explore these effects and the frequency at which various kinds of impacts occur.
• Open Firefox on a lab computer. • Go to the web address http://simulator.down2earth.eu/index.html • Select English for your language, and then select Start • You are presented with a control panel to set up your impact type.
We will explore two kinds of impacts. First, we will simulate the impact of a 1-km Iron object from the Asteroid belt. We will then simulate the impact of a 1-km Ice object from the Oort cloud. Since most of the planet is covered in water, we will simulate all of our impacts as though they occur 100 km off the coast of Vancouver Island, in deep water (1000 m). The angle of impact matters for these calculations, but for consistency we will set the angle to the most probable value of 45◦. So, for all impacts, the following parameters will always be the same: 6 SEARCH FOR EXTRA-TERRESTRIAL INTELLIGENCE 42
Impactor type Material Type Typical Velocity Diameter Asteroid Iron 17 km/s 1000 m Comet Ice 51 km/s 1000 m Table 6: Table of values for impact calculator.
• Trajectory Angle = 45◦.
• Target Density = Water, with a depth of 1000m.
• Distance from crash site = 100 km.
Note that the lowest velocity any impact can have on Earth is 11 km/s (escape velocity).
Procedure For each impact type in Table 6, set up the conditions in the impact calculator, select Submit, and answer the following questions:
• Question 3: From the Crater Size panel: How wide is the resulting crater? How deep?
• Question 4: From the Data View panel: How much Kinetic Energy is released? How frequently does this calculator estimate this kind of collision occurs? Note down the damage that would occur in Victoria (100 km from the crash site).
As of 1996, the total destructive power of all (known) tested nuclear devices summed up to roughly 510.3 Megatons of TNT, or 2.1 × 1018 joules [3]. Thats over 42,000 times more destructive energy than the single bomb that was dropped on Hiroshima.
• Question 5: Set up the same impact parameters as for the “Asteroid” case. Reduce the Asteroid Diameter until the Impact Energy is roughly equal to the sum of the energy released by all nuclear tests. How small is the impactor that will generate this much energy? How frequently do these kinds of impacts occur? Note that the 8-km wide Iturralde Crater in Bolivia is thought to be the youngest “large” impact crater on Earth. It is estimated to be between 11,000-30,000 years old [4]. Are we due for another impact of this size?
Number of civilizations in the Kepler field The Kepler mission is surveying 100,000 stars for Earth-like planets. The project scientists estimate that it might discover up to 650 planets with masses less than 2.2 times the mass of the Earth [5]. What are the chances that one of those planets might currently be home to a technological civilization? We will make a rough estimate based on some of the terms of the Drake Equation. The form that we will be using is below:
Nc = 100% × N∗ × FP × FL × FT (11) 6 SEARCH FOR EXTRA-TERRESTRIAL INTELLIGENCE 43
where Nc is the number of civilizations currently detectable in the survey, N∗ is the number of stars under consideration, FP is the fraction of those stars that have Earth-like planets, FL is the fraction of those planets that produce intelligent life, and FT is the fraction of the age of the galaxy that those civilizations exist for. The Kepler scientists have already created an estimate for the combination of the terms N∗ × FP based off of their observing method and the fraction of stars currently known to have planets - this is how they arrived at their estimate of 650 Earth-like planets. So we now have:
Nc = 100% × 650 × FL × FT (12) So how can we estimate the other terms? In our own planetary system, there are three “Earth- like” planets. Only one of them (that we know of) has ever given rise to intelligent life. So, for this 1 Solar System, FL ' 3 . What about FT ? In your previous exercises, you have determined upper limits for the lifetimes of civilizations based on extinction from 1) comet showers, and 2) asteroid showers. If the galaxy is roughly 13 billion years old, you can calculate the fraction of the age of the galaxy any civilization can reach before it is destroyed by either a comet shower or an asteroid shower by the following: T F = (13) T Age of Galaxy 6 SEARCH FOR EXTRA-TERRESTRIAL INTELLIGENCE 44
Drake Equation Exercises
• Question 3: Based on the timescale T you estimated for comet showers, calculate FT and use that to calculate Nc for the Kepler survey. What are the chances that a civilization-hosting planet will be discovered based on these estimates?
• Question 4: Based on the timescale T you estimated for asteroid showers, calculate FT and use that to calculate Nc for the Kepler survey. What are the chances that a civilization-hosting planet will be discovered based on these estimates?
References 1. Bottke, W. F., Vokrouhlick´yD., & Nesvorn´y,D. (2007) “An asteroid breakup 160Myr ago as the probable source of the K/T impactor” Nature Vol. 449, pp. 48-53.
2. Parker, A. H., Ivezic, Z., Juric, M., Lupton, R., Sekora, M. D., & Kowalski, A. (2008) “Size Distributions of Asteroid Families in the Sloan Digital Sky Survey Moving Object Catalog” Icarus Vol. 198, pp. 138-155.
3. Norris, R. S., & Arkin, W. M. (May 1996) “Known Nuclear Tests Worldwide, 1945-1995.” Bulletin of the Atomic Scientists Vol. 52, No. 3., pp. 61-63.
4. Baxter, K., & Taliaferro B. “NASA Educational Brief on the Iturralde Structure” http://education.gsfc.nasa.gov/experimental/all98invProject.Site/Pages/science-briefs/ed-taliaferro/iturralde.html
5. “Overview of the Kepler Mission” (2009): http://kepler.nasa.gov/about/