As we saw last week, a basic property of planets is their size. To compare sizes, we can compare the diameter (distance from one side to the other) of one planet to another, or we can compare the radius (half the diameter) of one planet to another. MercuryVenusEarthMarsJupiterSaturnUranusNeptune487912,10412,7426779139,822116,46450,72449,244 *Data source: Size comparison is better shown graphically than with numbers. You have already done this for the terrestrial planets in last weeks lab. The image above shows an example of what you will be doing. Remember scientific notation. The numbers on the axes are 0; 20,000; 40,000; and 60,000; and refer to kilometers. In order to plot a circle representing a planet with a 70,000 km diameter, I first took the radius (35,000 which is half the diameter), moved along the x-axis to 35,000, and drew a line up from zero that was 70,000 units long. Then I repeated this for the y-axis and sketched in the circle around the + that Id drawn. Detail about drawing the circles were shown in the video last week. Table 1 gives the average diameters for the planets in our solar system in kilometers. Use this data to plot circles representing the different planets to their correct sizes on the graph paper provided ( ; ; and ). Use a different color for each circle. Clearly identify which circle corresponds to which planet (labels or keys to colors). When you have finished, upload your completed graph to the correct assignment box. UPLOAD TO FOR LAB 5 Solar-System-Planet-Sizes In addition to looking at a graphical representation, we sometimes compare objects by saying how many times larger or smaller one is relative to the other. For example: If one student is 5.5 feet tall, and another is 6 feet tall, then we can say that the taller student is 1.1 times taller than the shorter student or that the shorter student is 0.92 times shorter than the taller student. This is done by simply dividing one number into another. Lab 5: Question 1 Jupiter and Saturn are similar in size, but Jupiter is the largest planet in the solar system. Jupiter is _________ times larger than Saturn. Enter a number only. Use two significant figure [example, 2.2 or 22] Lab 5: Question 2 SHORT ESSAY: Spend a bit of time looking at the graph youve created. Describe the variation that you see for the sizes of these planets. This should be at least a paragraph, not just a sentence or two, and should be more detailed than some are bigger and some are smaller. This is worth 5 points (regular questions are worth 1 point). We determine the mass of a planet by seeing its gravitational pull on another object. As mentioned in , Galileo was the first to observe the four largest moons of Jupiter orbiting the planet; these moons (Io, Europa, Ganymede, and Callisto) are called the Galilean satellites after their discoverer. These moons orbit because of Jupiters gravitational pull on them. Kepler noticed that planets orbiting the Sun obeyed a relationship (his third law): a3 =p2{version:1.1?,math:a3 =p2} EQUATION 1 where is the semi-major axis of the planets orbit in astronomical units, and is the orbital period in years. For the Earth, both numbers are 1 (were 1 A.U. from the Sun and we orbit the Sun in one year). Newton added gravity to Keplers third law to create an expression that can be used for any object orbiting any other object: a3 = p2×(G×M4×?2){version:1.1?,math:a3 = p2×G×M4×?2} EQUATION 2 where and are the same as in Equation 1, is a gravitation constant (a constant number), and is the mass of the central object (the Suns mass for planets; Jupiter for the Galilean satellites). For the Earths orbit around the Sun, is 1 AU, is 1 year, is the mass of the Sun, and the value for was chosen to make the term in the parentheses reduce to 1, so that Equation 2 becomes Keplers third law. We can rearrange terms to solve for mass: M = a3p2×(4×?2G){version:1.1?,math:M = a3p2×4×?2G} EQUATION 3 We can use Equation 3 to calculate the mass of Jupiter by watching one of its moons orbit around it. However, astronomical units and years are not useful for satellites that are closer to Jupiter than Earths Moon is to us, and that orbit Jupiter in days, not years. So we can do conversions to adjust G to units of Jupiter diameters (a length) and days. Doing so and multiplying by 4 and PI squared gives us M = (2.27×1026)×(D3T2){version:1.1?,math:M = 2.27×1026×D3T2} EQUATION 4 where is the distance between Jupiter and one of its moons in units of Jupiter diameters, and is time in days. Figure 2 shows a sequence of 5 images of Jupiter and its four largest satellites, taken on different nights at different times. We are going to use the motion of Callisto (the moon) around Jupiter to determine the mass of Jupiter, using Equation 4. You will be making your measurements on a much larger version of this image. [ ]. You should be able to magnify this; you can also download and open with a photo viewer or paint program and magnify. In order to use Equation 4, you need to determine (the distance between Callisto and Jupiter in Jupiter Diameters-JD), and (the time in days). The figure below is an enlargement of the first (September 3) image in Figure 2. Ive measured the distance between the surface of Jupiter and the surface of Callisto as 13.8 JD, using a screen shot and small circles that are approximately the same size as Jupiter. I measured this with a millimeter ruler and got 13.6 JD. Another instructor measured this distance and got 13.1 JD. So this number will vary depending on the accuracy of your measurement. [ ] For each of the five observations (use the large version of Figure 2), determine Callistos orbital distance in JD. Write down your individual measurements for Callistos orbital distance. You will use the average of these values in subsequent calculations Lab 5: Question 3 Average the 5 measurements you made and enter that average in the box provided. Important: Use only 3 significant digits (so 13.8 rather than 13.833333). [nt: your average should be between 13.0 and 14.0). Average of 5 values: ___________ JD (Jupiter Diameters) The date and time for each image is given on the left hand side. Times are U.T. or universal time (so 21:00 UT is 9 pm in Greenwich England). The date is also given in Julian Days, which is used mainly by astronomers, assuming that the zero point is at noon U.T. on January 1, 4713 BC (or BCE). You can subtract the two numbers to get the difference in time (in UT). This has been done for you. Lab 5: Question 4 What is the average length of time between the images? Enter a number in the box provided. Use only 2 significant digits (such as 8.1). But, for Equation 4, we want the time for a complete orbit by Callisto. Each image was taken at approximately half the orbital period, so Callisto is on the left, then the right, then the left, and so on. You need to double the answer to Question 4 to get the orbital period in days. Lab 5: Question 5 What is the orbital period for Callisto in days. You need to double your answer to Question 4. Enter an answer with three significant figures (put only one digit after the decimal point). Now use Equation 4 and your answers to Question 3 (use the average) and Question 5 to calculate the mass of Jupiter. Your answer will not exactly match the true value. I came out slightly high and another instructor came out slightly low. Lab 5: Question 6 This is a short answer essay question, and is worth 5 points. In the box provided, include your calculated mass of Jupiter (answer is in kilograms) your calculations (how you used Equation 4 to get your answer) a short discussion comparing your answer to the published value (given in Table 2 below). What exactly is mass? Chemists will often define mass as the amount of matter in an object (matter is something that will have weight in a gravitational field), while physicists often talk about something with more mass having more inertia than something will less mass. Geologists and planetary scientists tend to think more about density than mass (as we learned in module 3, density is the amount of mass in a given volume). ?=MV{version:1.1?,math:?=MV} EQUATION 5 where is density, is mass, and is volume. Planets and stars are spherical (more or less), which means their volumes can be approximated by Vsphere=43×?×r3{version:1.1?,math:Vsphere=43×?×r3} EQUATION 6 where is the radius of the sphere. So, comparing sizes and masses can give us some information about the density (and therefore composition) of an object. For example, the Earth and the Moon are both terrestrial worlds containing rock and metal. The Earths diameter (twice the radius is 12,742 km, as shown in Table 1 above. The Moons diameter is 3,476 km ( ). We can say that the Earth is 3.67 times larger than the Moon (12,742 divided by 3,476), or between 3 and 4 times larger. The masses for the Earth and Moon are given in Table 2. If the Earth and Moon were made of exactly the same material, wed expect the Earth to be about 50 times more massive than the Moon ( ). If we look at the masses of the Earth and Moon (Table 2), we can see that the Earth is actually almost 82 times more massive than the Moon, which clearly indicates that the material making up the Earth has an average density greater than the material making up the Moon. So lets compare the two largest Jovian planets. Jupiter and Saturn are fairly similar in size (you calculated this is Question 1). Lab 5: Question 7 Assuming that Jupiter and Saturn are the same density, then how many times more massive do you expect Jupiter to be relative to Saturn (use your answer to Question 1 for the relative sizes)? Enter only a number. Lab 5: Question 8 Using the values in Table 2, how many times more massive is Jupiter than Saturn in reality? Enter only a number. Despite being composed of roughly the same materials, Jupiter and Saturn are not the same density. This is because gas will compress more in a stronger gravitational field. Planet/ Object Mass (times 1024 kg) Object Mass (times 1024 kg) Mercury 0.330 Sun 1,988,500 Venus 4.87 Earths Moon 0.073 Earth 5.97 All Asteroids 0.00239 Mars 0.642 All Jupiters Moons 0.39312 Jupiter 1898 All Saturns Moons 0.1406 Saturn 568 All Uranus Moons 0.008876 Uranus 86.8 All Neptunes Moons 0.021492 Neptune 102 Charon 0.001586 Pluto 0.0146 Kuiper Belt 0.13552 References for Table 2: ; ; ; ; ; ; ; ; . (All are NASA fact sheets, except for Asteroid Belt and Kuiper Belt which are based on recent research papers.) Jupiter has often been called a failed star because it is very similar in composition to the Sun, but much less massive. Table 2 gives the masses for everything in the solar system (at least for everything that currently has measured or estimated masses). Lab 5: Question 9 How many times more massive is the Sun than Jupiter? We can also think about the mass of the Sun (or Jupiter) as a percentage of the total mass. For example, if I have 5 marbles that are all identical, one marble will have 1/5th of the mass of the entire group of marbles, which is 20% of the total mass. You calculate this by taking 1 marble, dividing it by all of the marbles (1/5 = 0.2) and then multiplying by 100 to get percent. The Sun makes up approximately 99.86% of the total mass of the solar system. So the rest of the solar system is insignificant in terms of mass. The Jovian planets make up most of that remaining mass. Lab 5: Question 10 Jupiters mass makes up what percentage of the mass of the solar system that is NOT in the Sun (exclude the Sun)? Enter only a number. The larger moons of the outer planets are large enough to be considered planets if they orbited the Sun directly, instead of orbiting a planet. Both Ganymede and Titan are actually larger than Mercury (the innermost planet in our solar system). Callisto is only slightly smaller than Mercury. Io, Europa, and Triton are similar in size to Earths Moon. Io, the innermost of the four large moons of Jupiter is the only large satellite in the outer solar system that does not have an icy surface. This is because it is the most volcanically active moon in the solar system, and the surface is constantly being covered with newly erupted material (rock and sulfur deposits). The figure below shows lava flows associated with the Amirani hotspot volcano and associated plume (this image has been color-enhanced.) Image data are shown for two flybys of Io by the Galileo spacecraft, from orbit I24 (Oct. 11, 1999; Day of Year = 284) and from orbit I27 (Feb. 22, 2000; Day of Year = 53). The left color panel shows lava flows (black & dark brown), SO2-condensate deposits (white-pink) from the Amirani plume, and S-rich deposits (yellow, red-brown). The rightmost panel shows areas of new lava in two inset regions (region 1 top, region 2 bottom row). This new lava (which is colored in red on the rightmost set of images) was erupted sometime between the two observation dates. If we assume that this rate of eruption is typical, we can calculate how long it would take to resurface Io (cover the entire moon with a new surface of recent lava flows). The first step is to determine the rate of resurfacing. We can use the information for the Amirani region by looking at the amount of surface area covered between the two observations divided by the time between the two observations. The area of new lava in Regions 1 and 2 of Amirani has been estimated from the red-colored images as: Lab 5: Question 11 What is the average amount of new lava produced between the two observations (the average area)? Enter a number in the box provided. The two images were taken 135 days apart (October 11, 1999 to February 22, 2000). Were going to want to use years rather than days for our units, so we divide 135 by 365.25 to get 0.37 years between the two images. In order to calculate the time needed to resurface Io, you need to know the resurfacing rate for the Amirani region. In order to ensure that you know this, enter your answer for the resurfacing rate into Mini Quiz 1, and check the feedback for the correct answer before continuing with the main lab quiz. Calculate the rate of resurfacing by lava in km2/year for the Amirani region using your answer to Question 11 and the time between the two image. Average resurfacing rate near Amirani hotspot is ________ km2/year. Please make sure you have the correct answer (given under View Feedback after you submit your quizclick on the link to show the feedback). Use the correct value in order to answer Question 12 below. Assuming that the resurfacing rate for the Amirani region is representative for Io as a whole, we can use the answer to Mini Quiz 1 to calculate the time needed to resurface all of Io. However, we first need to know how much area needs to be covered. Ios surface area can be approximated by the surface area of a sphere: surface area of a sphere = 4×?×r2{version:1.1?,math:surface area of a sphere = 4×?×r2} EQUATION 7 where is the radius of the sphere. Ios radius is 1821 km. Calculate the surface area of Io in km2. The surface area of Io is ________ km2. Please make sure you have the correct answer (given under View Feedback after you submit your quiz). Use the correct value in order to answer Question 12 below. The time to resurface Io is equal to Ios surface area divided by the average resurfacing rate. Lab 5: Question 12 The time needed to resurface Io by volcanic flows is _______ years. Enter a number in the box provided. Scientists have good reason to believe that Jupiters moon Europa has a liquid ocean wedged between its ice shell and a rocky sea floor. Though it has a known radius of 1,561 kilometers slightly smaller than Earths moon uncertainty exists about the exact thickness of Europas ice shell and the depth of its ocean. . Estimates for Europas ice shell range from 2 to 30 kilometers thick, and estimates of the water layer beneath the surface range from 3.5 to 100 kilometers thick. How much water is on Europa? With the uncertainties on the thicknesses of the icy crust and the water layer, all we can do is estimate a maximum and minimum possible value for the volume of the ocean. How do we do this? We determine the volume of a spherical layer by subtracting the volume of a smaller sphere (the bottom of the ocean) from the volume of a larger sphere (the top of the ocean), using Equation 6 (given earlier on this page). We need to determine the radius for the top and bottom of the ocean layer. We know the radius of Io (1,561 km). The top of the ocean layer will be the bottom of the outermost ice layer. The ice layer has an estimate thickness of between 2 and 30 km. STEP 1: Find the minimum and maximum radius of the top of the water layer, which is Europa minus its ice shell. STEP 2: Find the minimum and maximum radius of the bottom of the water layer (which is also the top of Europas rocky interior) by subtracting the ice thickness and ocean depth from the radius STEP 3: Use the formula for the volume of a sphere (Equation 6) to find the minimum and maximum volume for Europas ocean layer. So the range of possible values for the volume of Europas ocean is approximately 100 million cubic kilometers to almost 2.9 billion cubic kilometers. How much water is that? Lets compare to some bodies of water on Earth. Volume of water: 12,100 cubic kilometers Data Source: Image Source: Volume of water: 3,750,000 cubic kilometers Data Source: Image Source: Volume of water: approximately 1.35 billion cubic kilometers Data Source: Image Source: Lab 5: Question13 The minimum estimated volume of water on Europa is __________. similar in size to Lake Superior approximately 1/3 the volume of the Mediterranean Sea approximately 3 times the volume of the Mediterranean Sea approximately 30 times the volume of the Mediterranean Sea approximately 1/2 the volume of the Earths oceans approximately 2 times the volume of the Earths oceans Lab 5: Question 14 The maximum estimated volume of water on Europa is __________. similar in size to Lake Superior approximately 1/3 the volume of the Mediterranean Sea approximately 3 times the volume of the Mediterranean Sea approximately 30 times the volume of the Mediterranean Sea approximately 1/2 the volume of the Earths oceans approximately 2 times the volume of the Earths oceans Lab 5: Question15 Put the four Galilean moons in order of distance from Jupiter (from closest to Jupiter to farthest from Jupiter). Callisto Europa Io Ganymede Lab 5: Question16 Examine Figure 8. Old icy surfaces are dark (from space weathering), but young craters will excavate fresh clean ice and will appear white. Put the four Galilean moons in order of age of surface (from youngest surface to oldest surface). Callisto Europa Io Ganymede Lab 5: Question 17 TRUE/FALSE: The age of the surface of a moon indicates the level of geologic activity on that moon. For the Galilean satellites, geologic activity is caused by a heating mechanism related to Jupiters gravitational pull. Saturns largest moon Titan is slightly larger than the planet Mercury (about 6%, or 1.06 times larger), and is the only moon in the solar system with a thick atmosphere (air pressure on the surface of Titan is about 1.5 times that at the surface of the Earth). As with Venus, thick clouds in Titans atmosphere prevent orbiting spacecraft from viewing the surface in visible light. The Cassini spacecraft imaged Titans surface in ultraviolet and infrared light, and used radar to map features on the surface. The Huygens lander sent back images in visible light from a small area on the surface after it got beneath Titans cloud layer. As discussed in , a uses color coding to indicate the relative elevation (highs and lows) of landforms, such as plains, volcanoes, impact craters, etc. Generally, violet and blue are used for low elevations, shades of green for average elevations, and yellow/brown/orange/red/white for high elevations. A uses different colors to represent different types of rocks and/or deposits on the surface of a planet (such as sand dune, lakes, etc.), as well as locations of tectonic structures such as faults, rift valley, volcanoes, etc. Below is a topographic map for Titan. Lab 5: Question 18 Looking at the elevation scale on Figure 9, what is the total change in elevation (in meters) on the surface of Titan (from lowest to highest elevation)? Enter a single number only. [nt: you should look at the elevation scale for this information what you can actually see depends on how large or small you make the image.] Lab 5: Question 19 Compare your answer to Question 18 with the elevation changes for the terrestrial planets which you determined in last weeks lab. Titans elevation change is more similar to _____________ than to the other terrestrial worlds. Mercury Venus Earth Earths Moon Mars Lab 5: Question 20 For the terrestrial world you chose in Question 19, compare that worlds elevation change to Titans elevation change. The elevation change on the terrestrial world from Question 19 is _______ times that of Titan. Lab 5: Question 21 Examine the distribution of high and low areas on Titan (Figure 9) and compare to the distributions of high/low areas on the terrestrial worlds in last weeks lab. The distribution of high and low areas on Titan most closely resembles the distribution of high and low areas on _____________ . Mercury Venus Earth Earths Moon Mars Below is a geologic map of Titans surface. A color coded key of features is included. An explanation of the key is given in the figure caption. Lab 5: Question 22 Examine the geologic map of Titan. Most of the sand dunes (the sand grains are composed of hydrocarbons) are located ______. near the equator in mid-latitudes, between the equator and poles near the poles Lab 5: Question 23 Examine the geologic map of Titan. Most of the bodies of liquid ethane-methane are located ______. near the equator in mid-latitudes, between the equator and poles near the poles Lab 5: Question 24 Examine the geologic map of Titan. Most of the tectonically disrupted regions are located ______. near the equator in mid-latitudes, between the equator and poles near the poles Below is a colorized radar image of Kraken Mare, which is the largest body of liquid ethane and methane on the surface of Titan. Located near Titans north pole, the sea covers 154,000 square miles (400,000 square km), making it about five times bigger than North Americas Lake Superior. ( ) The Cassini spacecraft mapped the surface of Titan using radar and included a segment designed to collect altimetry (or height) data, using the spacecrafts radar instrument along a 120-mile (200-kilometer) shore-to-shore track of Kraken Mare. For a 25-mile (40-kilometer) segment of this data along the seas eastern shoreline, Cassinis radar beam bounced off the sea bottom and back to the spacecraft, revealing the seas depth in that area. This region, which is near the mouth of a large, flooded river valley, showed depths of 66 to 115 feet (20 to 35 meters). Scientists think that, for the areas in which Cassini did not observe a radar echo from the seafloor, Kraken Mare might be too deep for the radar beam to penetrate. Alternatively, the signal over this region might simply have been absorbed by the liquid, which is mostly methane and ethane. The altimetry data for the area in and around Kraken Mare also showed relatively steep slopes leading down to the sea, which also suggests the Kraken Mare might indeed be quite deep. Lab 5: Question 25 Short answer. The Cassini spacecraft was able to determine the surface area covered by Kraken Mare, and it is about 5 times larger than the surface area covered by Lake Superior. Why cant we determine the volume of liquid in Kraken Mare? Enceladus is dissimilar from the moons examined above, as it is not comparable in size to any of the terrestrial worlds, but is much smaller. The image below compares Enceladus to the British Isles. To put this into a more local context, the state of Oregon is about 400 miles east-west and about 300 miles north-south ( ). Despite this, the Cassini spacecraft observed water erupting from fissures on Enceladus, indicating that the moon has a liquid water layer beneath its icy surface. Gravity measurements of Enceladus and the wobble in its orbital motion suggest a 10 km deep ocean beneath a layer of ice estimated to be between 30 km and 40 km thick. ( ) With this information we can estimate a possible minimum and maximum volume of liquid water beneath the icy surface on Enceladus, using the same method that is shown for Europa (section on Europa above). In order to calculate the volume of water on Enceladus, you need to know the radii to the top and bottom of the liquid water layer. In order to ensure that you know this, enter your answers for the possible radii into Mini Quiz 3, and check the feedback for the correct answers before continuing with the main lab quiz. Find the minimum and maximum radius of the top of the water layer, which is the radius for Enceladus minus its ice shell. For the minimum radius, use the thicker ice shell; for the maximum, use the thinner ice shell. Enter numbers in the boxes provided. Question 1: Minimum rtop: _______________ km Question 2: Maximum rtop: _______________ km Find the minimum and maximum radius of the bottom of the water layer (which is also the top of Enceladus rocky interior) by subtracting the ice thickness and ocean depth from the radius Question 3: Minimum rbottom: ________________ km Question 4: Maximum rbottom: ________________ km Please make sure you have the correct answers (given under View Feedback after you submit your quiz). Use the correct values in order to answer Questions 26 and 27 below. Lab 5: Question 26 Use the formula for the volume of a sphere (Equation 6) to find the minimum volume for Enceladus ocean layer. The minimum volume for Enceladus ocean layer is __________ km3. Enter only a number. Do not use scientific notation and do not include commas in the number. Lab 5: Question 27 Use the formula for the volume of a sphere (Equation 6) to find the maximum volume for Enceladus ocean layer. The maximum volume for Enceladus ocean layer is __________ km3. Enter only a number. Do not use scientific notation and do not include commas in the number. Lab 5: Question 28 The estimated volume of water on Enceladus is __________. similar in size to Lake Superior similar to, but slightly more than the volume of the Mediterranean Sea similar to, but slightly less than the volume of the Mediterranean Sea similar to, but slightly more than the volume of the Earths oceans similar to, but slightly less than the volume of the Earths oceans Of all the moons in our solar system, only Titan and Triton have atmospheres; both composed mainly of molecular nitrogen (N2). However, Titans atmosphere is thicker than that of the Earth, while Tritons atmosphere is extremely thin, with a surface pressure only about 1/7000th that of the Earth. Unlike Titan, Tritons surface is easily imaged from space. The only spacecraft to visit Triton was Voyager 2, which flew by the moon in 1989 and imaged the southern hemisphere of the moon. Below is a simplified geologic map of Triton based on the Voyager 2 images. You will want to examine a much larger version of this image to answer the questions below. [ ]. You should be able to magnify this; you can also download and open with a photo viewer or paint program and magnify. Lab 5: Question 29 Match the following descriptions to the correct terms. fractures or tectonic faults cryovolcanic lake oldest lands composed of dirty water ice plus nitrogen ice icy layer composed of nitrogen and methane with traces of ammonia Cantaloupe Terrain Subpolar land South Polar Ice Cap Patera Planitia Cryolava Plateau Sulci Cavus Maculae Geyser Lab 5: Question 30 Enlarge the image and look for impact craters. Which of the following best describes crater on Triton? there are no impact craters on the surface of Triton, so it must be constantly resurfaced (similar in age to Io) there are only a few impact craters on the surface of Triton, so it must have a young surface (similar in age to Europa) there are a fair number of impact craters on the surface of Triton, so it must have a moderately old surface (similar in age to Ganymede) there are a lot of impact craters on the surface of Triton, so is must have a very old surface (similar in age to Callisto) Lab 5: Question 31 One of the areas is described as dark spots of tholin (?). Tholins are organic molecules that can form when radiation interacts with molecules containing nitrogen, carbon, and hydrogen. These molecules can be in an atmosphere, or as ices on a surface. These areas of possible tholins are located _________. randomly over the entire moon randomly on the south polar cap only on a few areas of south polar cap ice that are at or near the edge south polar cap randomly on the cantaloupe terrain only on a few areas of the cantaloupe terrain that are very far away from the south polar cap Lab 5: Question 32 There are red arrows that are listed as direction of geyser plumes in the legend. Geysers of liquid nitrogen erupt straight upward from the surface of the south polar cap. Then, the winds in the thin atmosphere of Triton blow the liquid sideways. Based on the arrows that you can see in the image, which way is the wind blowing across the south polar cap? mainly from the south to the north mainly from the east to the west mainly from the north to the south
