Motion & The Global Positioning System (GPS)

Transcription

1 Grade Level: K - 8 Subject: Motion Prep Time: < 10 minutes Duration: 30 minutes Objective: To learn how to analyze GPS data in order to track an object and derive its velocity from positions and times. Description: In Spring 2013, students from the PHYS 240 course at The Catholic University of America launched a weather balloon. In this activity, students will use data collected from the GPS to study the motion of the balloon during the course of its flight. Concepts include motion, GPS operation and applications, geographic coordinate systems, and map reading. Materials: s Ruler Related Links: National Science Education Standards: Content Standard Levels K - 4 Levels 5-8 Physical Science Position and motion or objects Motion and forces Science as Inquiry Science and Technology Science in Personal and Social Perspectives Abilities necessary to do scientific inquiry Understanding about scientific inquiry Abilities to distinguish between natural objects and objects made by humans Abilities of technological design Understanding about science and technology Science and technology in local challenges Abilities necessary to do scientific inquiry Understanding about scientific inquiry Abilities of technological design Understanding about science and technology Science and technology in society Teacher Sheet Page 1 of 5

2 Background: If you have ever been lost, you might have used a civilian GPS. Navigation systems can be built into cars, bought separately to use while driving or hiking (e.g. Garmin), or utilized by an app in your Smartphone (e.g. Google Maps). Sometimes they can also speak to you and tell you how to reach your destination. These user-friendly devices are examples of GPS receivers that intercept messages from satellites to track your position on Earth. When most people talk about their GPS, they are actually talking about their GPS receiver. The role of the GPS receiver is simply to identify the user s position. Smartphone apps and other GPS devices utilize this information to show you where you are on a map or tell you where to go. The military also uses the GPS for search and rescue missions, tracking targets, and guiding missiles and projectiles. A GPS is a navigation system consisting of several satellites in space that can be used to track the position and time of an object. This information can be relayed live via some sort of receiving device to a user on the ground. A GPS can function in any weather condition as long as there is an unobstructed line of sight to four or more GPS satellites from the receiver. There are GPS satellites orbiting around Earth that were implemented by the U.S. military in 1995 and soon after made available to the public. Each satellite weighs a few tons and travels at about 14,000 km/hr, making two complete rotations around the Earth each day. To calculate your position, the GPS needs two pieces of information: the location of at least three satellites above you, and the distance between you and each of those satellites. The receiver gathers this information from radio signals sent from the satellites. Each satellite continuously transmits signals that contain the time the message was transmitted and the satellite s coordinates at that time. Radio waves travel at the speed of light (about 300,000 km per second or 186,000 miles per second). By timing how long it took the signal to arrive, the receiver can figure out how far the signal has travelled from the satellite using the simple relationship distance = rate * time, where the rate of the signal is the speed of light. These distances and satellite positions are input into navigation equations to compute the location of the receiver. Please refer to the Weather Balloon Launch Movie Activity for more information about the balloon launch used in this activity. References: Teacher Sheet Page 2 of 5

3 Answers: 1. The balloon started in Hagerstown, MD then travelled northwest across the state line (dashed) towards Dover, PA. The path of the balloon appears fairly straight based on the markers shown, but it is unclear what the shape of the path is between large distances (e.g. between 5 and 6). 2. Refer to first and last row in Table 1 for start and end time and exact coordinates. 3. The balloon has moved NW. The latitude has increased North by about half a degree. The longitude has changed by about one degree as the balloon moved eastward. 4. The motion of the balloon is strongly affected by winds. Wind speeds can differ at different altitudes and locations. Generally, wind speeds increase with altitude. Meteorologists often talk about jet streams (high wind speeds) during weather forecasts. In fact, jet stream speeds are an example of one of the things that weather balloons are sent to measure. Launching a balloon near a jet stream will strongly affect its path. The path of the balloon is fairly straight overall during this launch, so we can assume that it was not too windy from Hagerstown to Dover. However, the path is more scattered near the launch and land areas so the atmosphere was probably more turbulent near the surface of the Earth. Furthermore, the balloon seems to cover longer distances in the same ~10 minute time interval during the middle of its flight implying calmer winds (balloon had to fight less wind so it could travel further faster) 5. The markers are not missing. Data is clearly given for them in Table 1. They are hidden behind each other because their coordinates are so close to each other. For example, markers 6-8 have the same exact coordinates. The balloon is at its highest point here. It stays in the same location for about 30 min while it is rising to its maximum height, bursting, and then beginning to fall. 6. Use a ruler to measure the distance from the first to the last marker on Map 1. Total distance = 5.4 inches * 18 km/inch ~ 100 km. From #3, we can see that the balloon was displaced 100 km NW. 7. Students may want to use a ruler to measure distances on the maps. The scale on Map 1 is 18 km/in and the scale on Map 2 is 2.5 km/in. Multiply the length you measure by the scale factor to get the physical distance traveled by the balloon. Make sure to use the proper scale from Map 2 to get measurements between markers If you would like to compare to distances in miles, the conversion factor is 1km/0.62 mi. The period between each marker is about 10 min on average. Use Table 1 to get the approximate time elapsed between each point in minutes then divide by 60 to convert to hours. 8. We can calculate the average speed of the balloon between each point by dividing the total distance traveled (third column below) from point A to point B by the total time elapsed (fourth column below). If you divide the average speeds below by 2, this is a rough conversion to miles per hour. Consider measuring the average speed of the balloon given only the distance traveled and time elapsed from the launch point to the landing point. This would give us an overall speed of the balloon during its entire flight. However, this is not a Teacher Sheet Page 3 of 5

4 very good description of the speed of the balloon since the speed actually varies significantly at different periods during its flight (as you can see from the table below). Therefore, average speed is best used to describe motion that is approximately constant throughout its path. This is the case for the short 10 minute time intervals reported by the GPS, during which we can probably guess that the balloon speed is approximately constant (not speeding up or slowing down too fast). Marker Distance Distance Time Elapsed Average Speed Elapsed (in) Elapsed (km) (hr) (km/hr) 1-2 N/A N/A N/A N/A 2-3 N/A N/A N/A N/A 3-4 5/ / / N/A N/A N/A N/A 7-8 N/A N/A N/A N/A 8-9 N/A N/A N/A N/A / / N/A N/A N/A N/A / The balloon moves faster across the surface of the earth when it covers more distance in the same 10 min time period. Therefore, the balloon moves relatively fast between markers 4-6 and It appears to move slowest when landing (markers 12-13). It is important to note that the speeds we talk about here are measured parallel to the ground and are not a measurement of vertical speed (rising/falling rate). It is possible to estimate how fast the balloon was rising and falling by considering the same 10 minute time intervals and the altitudes estimated in the Balloon Launch Movie Activity. This would give us a collective analysis of the vertical and horizontal motion of the balloon. 10. It takes about the same amount of time. We know the balloon reaches its peak at marker 6. It is about the same distance to marker 6 from the start and end points. We can also see this from the time axis of Figure 3 in the Balloon Launch Movie Activity. 11. These are terrain maps. The textured areas with shadows indicate raised land. Theses could be mountains, hills, etc. There are also bodies of water colored in blue. Roads are labeled by the gray lines. Highways and freeways are labeled with the shield symbol. 12. From marker 1, take highway 70 eastward, turn left up highway 81, turn right at highway 30, turn left at highway 15 headed northwest, then exit before marker 10 and take the surface streets to marker 13. If we knew the speed at which the car was traveling (mph), then we would know the velocity of the car (since we already know the direction of the car on the Teacher Sheet Page 4 of 5

5 highways). Highway 30 seems like the quickest way through the state forest because there is a relatively large clearing between the surrounding hills. Other roads through the state forest are possible routes but there are more obstacles and those roads are not labeled as highways so they are probably narrow. 13. Use a GPS unit to locate yourself on a map and track your path. The GPS would especially be useful near the landing area, where you would need to take the proper roads to retrieve the balloon. Teacher Sheet Page 5 of 5

6 Materials: s Ruler Background: On April 21, 2013, the Catholic University of America (CUA) students enrolled in PHYS 240, a course designed for education majors entitled The Earth-Sun Connection, launched a small research balloon from The Outdoor School at Fairview, 11 miles west of Hagerstown, MD. A parachute and a payload were attached to the balloon. The payload contained a GPS unit, a digital video camera with a wide-angle lens, a simple analog refrigerator thermometer, and two biological specimens. The GPS periodically recorded the coordinates of the balloon. Vocabulary: Distance: A measure of how far apart two points are from each other. Distance has units of length (e.g. kilometers). Displacement: A measure of the distance that an object has traveled which additionally takes into account the direction it has moved in. Example: 40 km northwest. Average Speed: Speed describes how fast an object is moving. Instantaneous velocity: The speed and direction of an object at one particular instant in time. Average Velocity: The direction and average speed of a moving object. Average velocity is the ratio of the displacement of an object over some period of time. Global Positioning System (GPS): A navigation system that consists of several satellites in space that tracks the position and time of an object. This information can be relayed live via a receiving device to a user on the ground. Coordinate: A set of numbers used to identify a location. On Earth, a coordinate is defined by the intersection of latitudinal and longitudinal lines. Latitude: Lines of latitude are parallel to the equator. Latitude describes the distance of a point above or below the equator. Latitude is defined as zero degrees at the equator, positive above the Page 1 of 7

7 equator (maximum of 90 o at the north pole), and negative below the equator (minimum of -90 o at the south pole) Longitude: Lines of longitude run from the north pole to the south pole. Longitude is defined as zero degrees at the Prime Meridian, which intersects Greenwhich, England. Longitude is positive when measured eastward from the Prime Meridian and negative when measured westward from the Prime Meridian. It has a maximum of 180 o opposite the Prime Meridian. Page 2 of 7

8 The Global Positioning System If you have ever been lost, you might have used a civilian GPS. Navigation systems can be built into cars, bought separately to use while driving or hiking (e.g. Garmin), or utilized by an app in your Smartphone (e.g. Google Maps). Sometimes they can also speak to you and tell you how to reach your destination. These user-friendly devices are examples of GPS receivers that intercept messages from satellites to track your position on Earth. When most people talk about their GPS, they are actually talking about their GPS receiver. The role of the GPS receiver is simply to identify the user s position. Smartphone apps and other GPS devices utilize this information to show you where you are on a map or tell you where to go. The military also uses the GPS for search and rescue missions, tracking targets, and guiding missiles and projectiles. A GPS is a navigation system consisting of several satellites in space that can be used to track the position and time of an object. This information can be relayed live via some sort of receiving device to a user on the ground. A GPS can function in any weather condition as long as there is an unobstructed line of sight to four or more GPS satellites from the receiver. There are GPS satellites orbiting around Earth that were implemented by the U.S. military in 1995 and soon after made available to the public. Each satellite weighs a few tons and travels at about 14,000 km/hr, making two complete rotations around the Earth each day. To calculate your position, the GPS needs two pieces of information: the location of at least three satellites above you, and the distance between you and each of those satellites. The receiver gathers this information from radio signals sent from the satellites. Each satellite continuously transmits signals that contain the time the message was transmitted and the satellite s coordinates at that time. Radio waves travel at the speed of light (about 300,000 km per second or 186,000 miles per second). By timing how long it took the signal to arrive, the receiver can figure out how far the signal has travelled from the satellite using the simple relationship distance = rate * time, where the rate of the signal is the speed of light. These distances and satellite positions are input into navigation equations to compute the location of the receiver. References: Page 3 of 7

9 km Map 1: Path of Balloon The path of the balloon is marked above and numbered The balloon is launched near Hagerstown at marker 1 (hidden behind marker 3) and lands near Dover at marker Map 2: Closer View of Landing Area This map is a zoomed in view of the inset in Map1. Marked are the last two coordinates tracked by the GPS, with marker 13 being the landing spot. Page 4 of km

10 Table 1: GPS Data Marker Time Latitude Longitude 1 9:24:11 AM :34:16 AM :44:16 AM :55:06 AM :04:18 AM :17:55 AM :27:55 AM :37:55 AM :47:54 AM :57:54 AM :07:02 AM :14:23 AM :24:23 AM Questions: 1. Describe the path of the balloon. 2. Where and when was the balloon launched? Landed? 3. How have the latitude and longitude changed at the end of the flight? 4. Why do you think the balloon didn t land in the same city that it was launched from? Page 5 of 7

11 5. There are some places in Map 1 where it seems like markers are missing. Are these markers really missing? If not where are they? What is the balloon doing at these spots? (Hint: Look at the coordinates in Table 1.) 6. Approximately how far did the balloon travel? 7. Estimate the distance between each marker by using the scale on the maps. How much time has elapsed between each point? Enter your values in the second and third column of Table 2. (1 min = 1/60 hr) 8. Calculate the speed of the balloon between each point on the map. Enter your values in the last column of Table 2. Table 2: Speed Calculations Marker Distance Elapsed (km) Time Elapsed (s) Velocity (km/s) Page 6 of 7

12 9. When the balloon was moving fast and when it was moving slow? 10. Does the balloon take longer to travel across the surface of the earth when it is rising or falling? 11. What features do you see in the maps? 12. What is the best way for the recovery team to drive from the launch site to the landing point? 13. How can you make sure that you are driving in the right direction to retrieve the balloon? Page 7 of 7