APS 1010 Astronomy Lab 97 Planetary Temperatures PLANETARY TEMPERATURES Mars is essentially in the same orbit. Mars is somewhat the same distance from the Sun, which is very important. We have seen pictures where there are canals, we believe, and water. If there is water, that means there is oxygen. If oxygen, that means we can breathe. -D. Quayle SYNOPSIS: In the next two lab sessions we will explore the factors that contribute to the average temperature of a planet using the EARTH/VENUS/MARS module of the Solar System Collaboratory. EQUIPMENT: Computer with internet connection to the Solar System Collaboratory, photometer with light shade, soil/rock samples, calculator. Part I. Temperature of a Planet The module provides the tools you need to attack one of the grand questions of planetary science. In this case, the grand question of the EARTH/VENUS/MARS module can be phrased in two different but related ways: Why can Earth support abundant life but Venus and Mars cannot? - or - What determines the habitable region around a star? Although both questions are truly grand (meaning that it would probably take a number of major research projects to answer them in detail) they can be broken down into a number of component parts, each one of which is quite accessible. The module concentrates on one of these parts, planetary temperature. Why temperature? Of all the factors that affect the presence of abundant life on a planet (chemistry, radiation, biology, etc.) the presence of liquid water is of paramount importance, and liquid water can only exist in a narrow temperature range. I.1 Why do you think liquid water is thought to be so critical for life? (Of course, nobody really knows for sure.) I.2 Over what approximate range of temperatures do you think you could find liquid water? I.3 Over what approximate range of temperatures would you expect to find life? We will now explore the factors that determine the temperature of a planet, and to find the range of parameters that would result in an average planetary temperature that allows liquid water. In the Computer Lab, make sure your computer is on the PC side. Click on the Internet folder, and launch Netscape (be sure that the window is not maximized). Now go to the website http://solarsystem.colorado.edu. Click on "Enter Website - Low Resolution (1024x768)", click on the Modules option, and finally, select the Earth/Venus/Mars module.
APS 1010 Astronomy Lab 98 Planetary Temperatures There are five parts to the module. In this lab we will concentrate on the first one (PLANET TEMPERATURE - click on the words and you should bring up an applet - short for little application ) and use it to explore the way the temperature of a planet depends on 1) its distance from the Sun. 2) its albedo. We will explore the effect of the atmosphere on a planet's temperature in the next lab session. Part II. Distance from the Sun This is the simplest and most obvious way to determine a planet's temperature. Like hikers who build a fire and huddle around it at night, the inner planets huddle around the central fire in the solar system. The closer you get to the fire, the warmer you get. Notice that the model used to calculate the temperature of a planet in this applet is displayed at the bottom of the applet. It should be set on fast-rotating, dark planet. The fast-rotating part of this just ensures that the planet rotates fast enough that day-vs.- night temperatures are not too terribly different. The dark just means that the planet absorbs (rather than reflects) all the sunlight that hits it. The PHYSICS PAGE link provides background information on the physical processes that go into the model. SHOW ME THE MATH provides the mathematical formulation that is programmed into the computer. Select the "Fast rotating dark planet" model from the menu at the bottom of the applet. Let s explore how the distance of a planetary orbit from the Sun affects the planet s temperature. II.1 Move Planet X to the orbit of the Earth (1 AU). What is the temperature of Planet X? II.2 II.3 We know that if we move the planet to a larger orbit, its temperature will go down. But by how much? Make a prediction: what do you think will happen if you double the size of the Earth s orbit? Think about it before you move Planet X! Here are come possibilities: (a) If the temperature follows an inverse law, doubling the radius should cause the temperature to drop by a factor of 2. (b) If the temperature follows an inverse square law, doubling the radius should cause the temperature to go down by a factor of 4. (c) If the temperature follows an inverse square-root law, doubling the radius should cause the temperature to drop by a factor of square root of 2 which is about 1.414. Your prediction: Now go ahead and move Planet X to 2 AU (twice Earth s orbital distance) - what is the temperature? Which of the above laws does temperature follow? (To check, look at SHOW ME THE MATH.)
APS 1010 Astronomy Lab 99 Planetary Temperatures II.4 Do you think the temperature of a planet depends on the size of the planet in this model? Have a look at the PHYSICS PAGE and/or SHOW ME THE MATH, and explain why (or why not). II.5 II.6 How good is this model? Bring up the FACT SHEET from the quick navigation frame (the gray frame on the left). How does the temperature calculated by the model compare to the measured average temperature of Mars? What about Earth? Venus? So - is this model any good? Does it do what it claims to do (calculate the average temperature of a dark body)? How can you tell? HINT: Of all the bodies mentioned in the FACT SHEET, which is best described by the dark planet model? Is the temperature of that body calculated accurately by the model? So, what do you conclude about how well the model works? Part III. Adding Albedo to the Model Albedo (represented by the symbol A) is the fraction of sunlight falling on a surface that is reflected back into space. (The word albedo comes from the Latin word for "white" - albus.) The albedo represents the average reflectivity over the entire visible surface; hence it differs slightly from the reflectivity of different portions of it. For example, the surface of the Moon has an albedo of 0.07 (on average, 7% of the incident sunlight is reflected, 93% is absorbed), even though there are bright and dark regions that have reflectivities different from the average. Now let's consider how the planet's albedo affects its temperature. If you haven't done this already, you may want to get more background information on the physics behind this applet. Click on the PHYSICS PAGE link in the quick navigation frame (the gray strip on the left) and look up albedo. Select the "Fast rotating dark planet with adjustable albedo" model from the menu at the bottom of the applet. III.1 What value of albedo does the previous model ("Fast rotating dark planet") assume? III.2 What is the present day albedo of Mars? III.3 What happens to the temperature of Mars if you increase its present day albedo by 0.05? The temperature goes from to.
APS 1010 Astronomy Lab 100 Planetary Temperatures III.4 III.5 What happens to the temperature of Mars if you increase its albedo from 0.999 to 0.9999? The temperature goes from to. In general, if you increase the albedo, you the temperature. Explain why this is the case. III.6 If you put in the correct albedo for Mars, does the model give the correct temperature? How about for the Earth? And for Venus? III.7 So does this model do what it claims to do (calculate the average temperature of a planet with a non-zero albedo)? How can you tell? Part IV. Measuring Albedos of Samples The albedo of a planet or moon provides valuable information about its composition and temperature. You will measure the albedos of various soil and rock specimens; this information will be used to provide clues as to the nature of the surfaces of the planets and moons in our Solar System. A photometer (light meter) with a sunshade can be used to measure the reflectivity of different materials, as shown below. The measurements are made as follows: Measure the brightness of white paper illuminated by sunlight. The paper has a reflectivity of approximately 100%, corresponding to an albedo of 1.00, and thus gives you a convenient standard against which to compare the reflectivity of other surfaces. Be sure that nothing (including you or the photometer) is casting shadows onto the area under observation! Incident Sunlight Detector Light Shade Photometer Meter Measure the brightness of the sample. Be sure to hold the photometer close enough to the sample so that its detector only "sees" the sample, not the surrounding area. Reflected Sunlight Divide your sample reading by the value you obtained for the white paper. The resulting fraction is the reflectivity of the material. Specimen
APS 1010 Astronomy Lab 101 Planetary Temperatures IV.1 Measure the reflectivities of the various specimens provided by your lab instructor: rocks (vesicular basalt, dark basalt, marble, limestone, breccia), charcoal, wet and dry sand, crushed ice or snow (if available). Enter your data in the table below. Also note the color of the specimen. These samples have been chosen because they are likely to be found in other objects in the Solar System. IV.2 In addition, measure the reflectivity of some materials commonly found on the Earth's surface which you think might significantly contribute to the Earth's albedo: e.g., water, snow, grass and other plant life, etc. Add these data in the table below as well. Specimen Identification Sample Reading Paper Reference Reflectivity (albedo) Color (A) (B) (A) / (B)
APS 1010 Astronomy Lab 102 Planetary Temperatures Part V. Comparing Solar System Albedos We can measure the albedo of a planet or moon by comparing its brightness to how much sunlight it receives. We know how much sunlight it receives because we know its distance from the Sun (remember the 1/ R 2 rule!); and we can measure how much light is coming from the object with a photometer on a telescope. If the object has an albedo of 100% it will reflect all the sunlight incident upon it. Note: We are assuming that all of the light coming from the object is reflected sunlight; i.e. the object is not producing its own light. Planetary scientists are interested in knowing the albedo of a planet or moon because it provides information on the composition of the object. By comparing the albedo of a planet or moon to the albedos of substances found here on Earth we can learn what substances may or may not be on that object. V.1 What assumption are we making when we compare the albedos of substances on the Earth to other objects in space? The table below contains information regarding the measured albedo of various planets and their moons. Use the table and information in the textbook to answer the following questions. Object Albedo MERCURY 0.06 VENUS 0.76 EARTH 0.40 Moon 0.07 MARS 0.16 JUPITER 0.51 Io 0.60 Europa 0.60 Ganymede 0.40 Callisto 0.20 SATURN 0.50 Mimas 0.70 Iapetus 0.05, 0.50 URANUS 0.66 NEPTUNE 0.62 PLUTO 0.50 V.2 Why do you think the albedos of Mercury and the Moon are so close? Look at photos of these two; do the pictures confirm your hypothesis?
APS 1010 Astronomy Lab 103 Planetary Temperatures V.3 What material that you measured is closest to the albedo of Mercury and the Moon? Does it have the same color as well? Do you think the Moon's surface contains this material? V.4 The Moon has a very low albedo, meaning that it is very dark. Why then do you suppose the Moon appear to be so bright? V.5 Compare the albedos of the terrestrial planets: why do Venus and the Earth have much higher albedos than Mercury and Mars? What, if any, of the substances you measured in IV.2 might cause the Earth to have a higher albedo than Mars? Why does Venus have a higher albedo than the Earth? V.6 The albedos of Earth and Mars are averages over the planet's disk as well as averages over time. Average the albedos you measured of substances on the Earth s surface in IV.2 and compare it to the Earth s average albedo. Why might they be different? How does the Earth's reflectivity vary over the surface? And Mars? What is the likely reflectivity of the polar regions? How do their reflectivities change with time? On Earth we see basalt in several forms. When it is first created (i.e. when it comes out of the Earth in the form of lava) it is very dark; however, over time it gets weathered; exposure to oxygen oxidizes basalt and turns it reddish.
APS 1010 Astronomy Lab 104 Planetary Temperatures V.7 What planet do you think might have oxidized basalt based upon its color? What can you say about that planet s atmosphere? V.8 The Moon contains basalt in its lunar maria which is very old. Why hasn't it turned red? V.9 Compare the Jovian planets to the terrestrial planets: on average, why do the Jovian planets have a higher albedo? From this and your answer for question V.5 what can you conclude is the most important factor in determining a planet's albedo?