unit 3 assignment navigating the seas

Introduction to Vectors – Navigating the Seas

Early navigators used math to chart their course and stay on it when dealing with factors such as wind and ocean current that affected their journeys. The system left something to be desired regarding accuracy.

With the use of Introduction to vectors, your students can complete the activity that is linked below and gain not only some real-life use of vectors but also come to understand why Columbus did not reach his planned destination.

It gives meaning to math when students can use it in real-life and come to realize the part it played in history. Almost all branches of engineering use vectors as tools when calculating stress and force.

Vectors are used for designing with fluid dynamics concepts to describe the forces such as water and wind movement. They are used to describe the effects of electric and magnetic fields. You cannot stress the importance of vectors enough to your students.

This activity charts the course of a ship traveling west from Spain. With the use of vectors, students can calculate how long the journey will take and where the ship will land. Here is the link to the activity.

It is best to work through this on your own before presenting it to the class. Doing so enables you to help students who struggle at first.  Worksheets and answer keys are provided.

Here is the link to the Activity:  https://www.teachengineering.org/activities/view/cub_navigation_lesson02_activity1

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Ellipses and circles worksheets - pdfs.

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Radians and Degrees

Trigonometric functions on the unit circle, logarithmic functions, properties of logarithms, matrix operations, analyzing graphs of functions and relations, power and radical functions, polynomial functions, teaching functions in precalculus, teaching quadratic functions and equations, freebie pre-requisite resources for this lesson:.

Adding and Subtracting Matrices – Using Rainbows

The Nightmare of Exploring Conic Sections

The Pythagorean Theorem – Like You’ve Never Seen It Before

Transforming Parabolas – The Angry Birds Project

The Distributive Property – Cupcakes and Algebra

• Factoring to Solve Quadratic Equations – Know Your Roots

Pythagorean Theorem – NFL and Geometry

• Adding and Subtracting Fractions – Cut the Cheese

How to Teach Simplifying Radicals

The Order of Operations – Don’t ask your Calculator

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FREE K-12 standards-aligned STEM

curriculum for educators everywhere!

Find more at TeachEngineering.org .

• TeachEngineering
• Navigational Techniques by Land, Sea, Air and Space

Lesson Navigational Techniques by Land, Sea, Air and Space

Grade Level: 8 (7-9)

Time Required: 45 minutes

Lesson Dependency: None

Subject Areas: Earth and Space, Geometry, Measurement

• Print lesson and its associated curriculum

Curriculum in this Unit Units serve as guides to a particular content or subject area. Nested under units are lessons (in purple) and hands-on activities (in blue). Note that not all lessons and activities will exist under a unit, and instead may exist as "standalone" curriculum.

• Nidy-Gridy: Using Grids and Coordinates
• Northward Ho! Create and Use Simple Compasses
• Find Your Own Direction
• Vector Voyage!
• The North (Wall) Star
• Stay in Shape
• Close Enough? Angles & Accuracy of Measurement in Navigation
• Computer Accuracy
• Sextant Solutions
• Where Is Your Teacher?
• The Trouble with Topos
• Classroom Triangles
• Topo Triangulation
• Triangulate: Topos, Compasses and Triangles, Oh My!
• You've Got Triangles!
• Nautical Navigation
• State Your Position
• It's About Time
• GPS Receiver Basics
• Making GPS Art: Draw It, Walk It, Log It, Display It!
• GPS Scavenger Hunt
• A Roundabout Way to Mars

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Engineers adapt their fundamental science and math skills to different situations. Understanding the science of natural phenomena enables engineers to design and build appropriate structures and systems. By combining their expertise in inventing measurement and data gathering tools with their ability to analyze and learn from past failures, engineers continually improve designs and systems for the benefit of people. This process of gathering and analyzing data to better understand problems and formulate solutions is used in all engineering disciplines.

After this activity, students should be able to:

• Understand fundamental differences between navigation on land, water, air and in space.
• Identify major features and read the fundamental symbols and information provided on land maps, nautical charts and aeronautical charts.
• Explain the concept of dead reckoning (relationship between speed, time, distance and direction) as it applies to navigation estimation.
• Understand beacon nomenclature, symbols and information as found on nautical charts.

Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN) , a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g. , by state; within source by type; e.g. , science or mathematics; within type by subtype, then by grade, etc .

Common core state standards - math.

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With the students, brainstorm the differences between traveling in an airplane and traveling on foot. (Possible answers: You are up in the air, you are going faster.) Do the students think that using a standard city street map would help them navigate from an airplane? (Possible answer: No, because you would pass over a city in a couple minutes.) What kind of map would be useful for flying an airplane? (Possible answer: One that covers a much larger area.) Maps for pilots are called aeronautical charts, and we will take a look at them today.

Pose the same questions for traveling by sea. Does a city street map help you travel in a sailboat? (Possible answer: No, because there are no street signs on the ocean.) Street maps help you navigate by showing landmarks like street names, but there are no street signs on the ocean! What kinds of landmarks may be found when traveling on the sea? (Possible answers: Lighthouses, beacons, islands, buoys.) During the past few millennia, many nations and peoples have created landmarks that are either on land and visible from sea or floating in the water, like buoys. Lighthouses are a great example of landmarks for sailors. They are like street signs for the ocean. They have a big, bright light so sailors can easily see them day or night, in good weather or in storms. Seeing lighthouses helps sailors avoid hitting land or crashing into rocks. Nautical charts allow sailors to determine exactly where they are on a large body of water. Students can learn the major features of nautical charts by looking at a real charts and drawing their own in the associated activity Nautical Navigation .

What about traveling in space? How do astronauts have any idea about where they are? There certainly are no street signs in space. People on Earth can locate satellites by using big telescopes that look for special types of light emitted by the satellites.

Ask students if anyone has ever navigated with a map on land? What was that like? Ask the same questions for air and water. Tell students that in today's lesson we are going to be talking about the different types of maps that are used in the different environments — land, sea and air.

Lesson Background and Concepts for Teachers

Navigating in Different Environments

Most of us know about navigating on land; we do it everyday when we are walking home or driving to the store. Navigation is used in all sorts of environments, and it is, therefore, always important to know your location. Navigating on land is very different than in the water, in the air, or in space because all each type of navigating requires different types of information. For example, a topographical map would not help you navigate on the sea. There are different navigation needs depending on whether you are traveling on land, sea, air or in space.

Dead Reckoning

Even though traveling in different environments requires different types of information, like maps, some things are common to all navigation. All navigation requires use of the concept of dead reckoning. Refer to Lesson 2 of the Navigation unit for more detailed information on dead reckoning.

Dead reckoning is the process of navigation by advancing a known position using course, speed, time and distance to be traveled. In other words, it is the process of figuring out where you will be at a certain time in the future if you hold steady the speed , time and course you plan to travel. Prior to the development of celestial navigation, sailors navigated by deduced (or dead ) reckoning . Columbus and most other sailors of his era used this method. In dead reckoning, the navigator finds his position by estimating the course and distance he has sailed from some known point. Starting from a known point, such as a port or harbor, the navigator measures out his course and distance from that point on a chart, pricking the chart with a pin to mark the new position.

Speed, Time and Direction

How did they know their speed? In Columbus' day, the ship's speed was measured by throwing a log over the front side of the ship. There were two marks on the ship's rail that were a measured distance apart. When the log passed the forward mark, the pilot would start a quick chant; when the log passed the aft (last) mark, the pilot would stop chanting. (The exact words to such a chant are part of a lost history of navigation.) The pilot would then note how much of the chant he recited, which would then enable him to determine the speed of the boat based on the distance traveled. This method would not work when the ship was moving very slowly, since the chant would be over before the log actually reached the aft mark. This approach may be expressed as a simple equation:

Speed x Time = Distance

This makes sense when you look at the units:

In the equation, the hours cancel each other out, resulting in a distance in miles.

Along with the speed and distance, early sailors needed to know the direction of travel. This was accomplished using a compass. Once they knew their distance and direction, they could determine their current location based on their previous location.

So, what are the items we need to know to navigate using the dead reckoning approach?

• Speed: We have to know how fast we are traveling.
• Time: We need to know for how long we have been traveling.
• Direction: We certainly need to know in which direction we are going.
• Our previous location: It is good to know our speed, time and direction, but it is not enough unless we also know our exact last location.

We need to know all these variables to navigate.

Land Navigation

In previous lessons, we learned how to navigate on land. What types of information do you need to navigate on land?

Traveling by Car

• Road maps: The first thing you do when you plan a road trip is get out a road map. It provides you with information on the choice of roads, the distance to a certain destination, and sometimes even suggests the quickest route to get there.
• Street signs: A must for traveling in any city, they help you find your location on a city street map.
• Mileage signs: These signs indicate the distance to the next city or town, and are very helpful to find your location on a road map.

Traveling by Foot

• Topographical maps: These maps provide detailed information about the land surface.
• Compass: This device helps you determine your direction. Used with a topographical map, you can triangulate to determine your exact position.

Sea Navigation

We have all traveled by car or on foot; it is easy to understand. But, what about traveling by sea? The sea is open and barren with no distinctive features. Dead reckoning is a very important skill for knowing where you are when traveling by sea. Because environmental conditions, such as sea currents or wind, can cause errors when using dead reckoning, it is important to look for landmarks. But, there are no natural landmarks on the sea. Luckily, people have made landmarks for us.

Aids in Sea Navigation

What other types of information would be helpful to know? What if you are traveling in a bay that is very shallow? You would want to know how deep the water is so that you do not run aground and damage your vessel. There are few natural landmarks that can be used. For this reason, people have made landmarks to use for navigating on water. Examples include:

• Buoys: These floats with a bell or light are moored (anchored) in water. They are used as a landmark, a warning of danger, or a marker of a bay or channel.
• Lighthouse: A tower with a bright, rotating light, located on or near shore to inform a sailor that land is nearby. Lighthouses are especially useful at night or in bad weather, when one's sight is limited. For example, a sailor could easily run into land if s/he could only see a distance of 20 feet.
• Beacons: A generic term for some sort of sea landmark, such as a buoy or lighthouse.
• Old shipwrecks: Ships do sink, and you definitely want to avoid them so that you do not sink your vessel also.

Nautical Charts

Land maps are not very useful when you are on the sea. Special maps designed for traveling by sea are called nautical charts. Some of their features are:

• Depth: Nautical maps show depths under the water surface, just like topographical maps show elevation on the ground. Ship captains use these maps to avoid shallow areas or shipwrecks that could damage their ships.
• Shoreline: Sailors like to know where land is located.
• Landmarks: Such as shipwrecks and beacons.
• Magnetic declination: Sailors must know the difference between true north and magnetic north, so that they can navigate properly.
• Routes: Nautical maps show shipping lanes, and common and safe routes for sea vessels. Sailors use these lanes just like drivers use streets. Shipping lanes avoid shallow areas that can damage (or even sink) ships.
• Currents: Nautical maps show the general direction in which the current flows at various locations.

Figure 1 depicts a section of a nautical chart for the San Francisco Bay in California. Note the many common features of the map (items with arrows pointing towards them) such as water depths, contour lines, the magnetic declination, and landmarks and beacons.

Beacon Nomenclature

There are many types of beacons; some flash regularly, and some flash in a pattern, and some make sounds. Knowing the characteristics of a beacon helps a navigator identify the beacon, and therefore determine his/her location. On nautical charts, specific nomenclature (or naming system) is used to provide navigators with information to describe the type of beacon.

For example, the first beacon in the box in Figure 1 is marked: Fl R 4s 14ft 4M "4." The first descriptor denotes the type of beacon. In this case, F1 is a beacon with a flashing light, which helps navigators identify the beacon in inclement weather. The next descriptor indicates the color: R for red. The next descriptor shows the period of the flashes; this beacon flashes every 4 seconds. The next descriptor is the height of the beacon, 14 feet. After that is the range that the beacon can be seen from: 4 miles. And finally, the last descriptor is a beacon identifier, number 4.

As another example, in Figure 1 there is also a beacon marked: Q 12ft 6M. The Q stands for quick. This is a light that flashes about 60 times per minute, or once per second. Just like the previous example, the 12 ft. tells us that the beacon is 12 ft. high, and the 6M tells us that the beacon can be seen from 6 miles away.

Navigation in the Air

Pilots, like sea captains, must be able to navigate by dead reckoning. Sadly, this is not easy to do. What landmarks would you look for if you were a pilot? A street sign? A field? When airplanes were first invented, there were no good landmarks for pilots to use. In fact, many pilots would fly really low and slow, hoping to read the road signs to figure out which town they were near.

What kind of landmarks would be useful for pilots? Items such as railroad tracks, buildings, ranches, water or oil tanks, towns, lakes, rivers and highways can usually be seen from the sky. Recreational pilots in small aircraft find landmarks like these to be quite useful in determining their locations. But, a commercial airline pilot would not use these types of landmarks because commercial jetliners fly at about 35,000 ft., much too high to make out most of these landmarks. Can you imagine trying to identify landmarks that are seven miles away?

Aeronautical Charts

Pilots use aeronautical charts just like sailors use nautical charts. Anything that can help the pilot figure out where he is and help him land will be noted on the aeronautical chart. Aeronautical chart features include:

• Elevation: Pilots must know the elevation of landforms in an area. For example, if there is a mountain in your flight path, you would want to know how high it is so that you can fly above it.
• Airports: An aeronautical chart indicates the presence of airport elevation markers, runways (the road that you land on), flashing lights that show the pilot where to land, buildings and tanks. Locating these items helps pilots land safely.
• Landmarks: Such as a river, golf course or bridge.

Scale of Aeronautical Charts

Traveling by foot or boat is slow compared to airplane travel. Since so much distance is covered quickly, typical aeronautical map scales are 1:500,000, meaning that an inch on the chart represents about 10 miles.

On the aeronautical chart in Figure 2 we can see a number of distinct features. The maximum elevation for any landform on the chart is 4,800 ft.; this is the highest point on that part of the chart, including buildings and natural features such as mountains. The chart also provides elevation contour lines. Helpful landmarks, such as ranches, a golf course and a trailer park, can be identified by pilots from the flying elevation of a recreational airplane like a twin engine Cessna. Most importantly, this map shows the two airports in the area. Notice the purple circle area and the two lines crossed within it, which are the runways. The purple outline around the whole airport shows the airport's airspace, which for safety reasons — unless a pilot is landing at that airport, he should not enter.

Space Navigation

Navigating in space is very different from other forms of navigation. Usually, sea drift or wind drift cause travelers by sea or air to move off course. But in space, the sources of error are far smaller. Once a spacecraft is in a known orbit, it perpetually travels along that orbit.

What Is an Orbit?

We all know that the Earth travels around the sun. This happens because the gravity of the sun is constantly pulling on the Earth. Like tying a ball to a string and swinging it around your head, the pull of the string on the ball is like the gravity of the sun pulling on a planet or satellite. Satellites travel around the Earth just like the Earth travels around the sun. The path that the satellite travels in is called an orbit. The satellite just keeps traveling along that orbit because there are no major sources of drift in space, such as wind or sea currents. Few conditions are present that would make satellites drift, such as small changes in gravity or the impact of meteorites, and the probabilities of these events are quite small. Therefore, it is not complex for knowledgeable people to predict where that spacecraft, moon or planet will be in an hour or a day. The methods used to predict the position of objects in outer space are just like dead reckoning, but with minimal drift and a constant speed.

Key characteristics that people must know when anticipating the position of objects in space include: How fast the object is moving, in what direction the object is moving and in what orbit it travels. Spacecraft send light waves down to the Earth to determine this information. By measuring properties of the light, spacecraft and satellites can calculate where they are and how fast they are going. Once their speed and location is known, computers in the spacecraft calculate in which orbit they are traveling. Once the computers determine the spacecraft's orbital path, its future path can be predicted using methods similar to dead reckoning.

Watch this activity on YouTube

Could you use a nautical chart to get home from school or to go hiking in a park? (Answer: No, because we do not live on the ocean.) Why is a nautical chart not helpful in this situation? (Answer: It tells us information about the sea, not the land.) Can you name for me some different environments that would require different types of maps? (Answers Land, sea, air and space each require different types of maps to help people navigate in those environments.)

What types types of information do you need to know to travel on the sea? (Answers: Water depth, location of channels, paths, obstacles [such as shipwrecks or reefs], harbors, etc.) What type of information do you need to know if you are traveling in the air? (Answers: Elevation of landforms, location of airports, big landmarks that you can see, etc.) These needs are similar: sailors on the sea need to know how deep the water is, and pilots need to know how high the land is. Smaller scale land maps are also helpful for hikers who need to know about obstacles (cliffs) so that they can avoid them, and about landmarks so that they can find their locations. Everybody needs to be able to navigate no matter where they are — on land, sea or air. The navigational methods and maps just need to be specific to each environment.

aeronautical chart: A map used for traveling by airplane.

airspeed indicator: An instrument on an airplane that tells how fast the plane is traveling relative to the wind.

attitude indicator: A graphical way to see the roll, pitch and yaw of an airplane.

beacon: Similar to a floating lighthouse. Beacons have lights that flash in many different patterns and colors to help sailors navigate. A sailor can find his location by looking for a specific beacon and determining which one it is.

buoy: A float with a bell or light that is moored (anchored) in water and used as a landmark, a warning of danger, or a marker of a bay or channel.

dead reckoning: A method to calculate the location of a person, ship, or spacecraft based upon where it was some time ago. Knowing the speed, direction and how much time has passed since you last knew where it was, you can find out where the person, ship, or spacecraft is at any time in the future.

lighthouse: A tower with a bright rotating light located on or near shores to tell a sailor that land is close. Lighthouses are especially useful to sailors at night or in bad weather.

nautical chart: A map used for traveling on water.

orbit: The path that a satellite travels around the Earth.

Pre-Lesson Assessment

Brainstorming: In small groups, have students engage in open discussion. Remind students that no idea or suggestion is "silly." All ideas should be respectfully heard. Ask the students:

• What are the differences between traveling in an airplane and on foot? (Possible answers: You are up in the air, you are going faster.)

Post-Introduction Assessment

Ask the students and discuss as a class the questions below.

• Has anyone has ever navigated with a map on land? On water? In the air? What was that like? (Tell students that in today's lesson we will learn about the different maps that are used in the different environments—land, sea and air.)

Lesson Summary Assessment

Numbered Heads: Divide the class into teams of three to five. Have students on each team pick numbers (or number off) so each has a different number. Ask the students a question (give them a time frame for solving it, if desired). Use questions in the Lesson Closure section. The members of each team should work together on the question. Everyone on the team must know the answer. Call a number at random. Students with that number should raise their hands to answer the question. If not all the students with that number raise their hands, allow the teams to work a little longer.

In this lesson, students learn how great navigators of the past stayed on course — that is, the historical methods of navigation. The concepts of dead reckoning and celestial navigation are discussed.

Students learn to identify the common features of a map. Through the associated activities, students learn how to use a compass to find bearing to an object on a map and in the classroom.

In this activity, students explore the importance of charts to navigation on bodies of water. Using one worksheet, students learn to read the major map features found on a real nautical chart. Using another worksheet, students draw their own nautical chart using the symbols and identifying informati...

Students use vector analysis to understand the concept of dead reckoning. They use vectors to plot a course based on a time and speed. Then they correct the positions with vectors representing winds and currents.

Federal Aviation Administration: http://www.faa.gov/

Kid's Corner, Federal Aviation Administration: http://www.faa.gov/education/student_resources/kids_corner/

For information and photographs of aids to navigation, see the Tideland Signal Corporation manufacturer website at: http://www.tidelandsignal.com/

Contributors

Supporting program, acknowledgements.

The contents of this digital library curriculum were developed under a grant from the Satellite Division of the Institute of Navigation (www.ion.org) and National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the NSF and you should not assume endorsement by the federal government. 

Last modified: June 24, 2019

Navigating the Seas

When a modern-day ship glides across the oceans, it’s guided in large part by satellites -- the Global Positioning System. They reveal the ship’s position to within a few feet.

When early explorers began heading across the oceans, though, they were guided in large part by the stars -- a method that often led them dangerously off course.

The earliest sailors were guided by the coastline. When they began to venture out to sea, they relied on the position of the Sun, the ocean currents, and even the birds to keep them on course.

Beginning around the end of the 12th century, they were helped by technology: the magnetic compass. And they soon acquired more technology: devices that allowed them to plot the location of the Sun or the bright stars.

The North Star provided an exact plot of latitude -- the position north of the equator. If the North Star was 45 degrees above the horizon, then the ship was at 45 degrees north latitude. And as explorers ventured south of the equator, they found new stars to navigate by.

For centuries, though, even the best methods of measuring longitude -- the position east and west on the globe -- were inaccurate and hard to use.

The problem was solved in the 18th century, when Englishman James Harrison invented highly accurate clocks. A navigator could then use the Sun and stars to compare the local time to the time at a known point of longitude. The difference revealed the ship’s longitude -- keeping it on track for even the longest voyages.

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Compass Hands-on Activity

Early Maritime Navigation Inquiry Unit

Early Maritime Navigation Inquiry Unit Compass Lesson Plan – Supporting Question 3

With a towel placed over their heads and the only visual being that of a magnetized needle, set on a plastic cap in a bowl of water, students will navigate their way to a predetermined spot.

Learning Outcomes:

Students will be able to empathize with early seafarers and understand the challenges faced while traversing and navigating the seas. In addition, they will gain knowledge of how technology plays a role in global preeminence.

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Materials Needed:

• Medium sized plastic bowl(s)
• Enough water to fill ~3 – 4 inches
• Sewing needle
• Bar magnet ( Amazon )
• Small Plastic Dish (like a sour cream container lid or something similar)
• Scotch tape
• Towels (same number of towels as bowls)
• Large area (gym or field/lawn will work)
• Cones or floor markers

Instructions:

• Fill the bowl with approximately 3 – 4 inches of water
• Strike the point of the needle on the north end of the bar magnet ~20 times

• Using the scotch tape, tape the needle to the plastic dish and place it in the water A. The point of the needle should point north. If you nudge the needle, you should see it move back into position. If that does not happen, repeat steps 2-4
• Split your class into manageable groups (keep in mind that each group needs a guide/teacher/teachers’ assistant to assist students. It’s okay if you only have 1 group
• Approximately 15 yards away in a northern direction (if not directly north, instruct students to note the angle of the needle in respect to the cone), set down a cone or floor marker for each group (different colors help)
• Instruct the first student on each line to walk to their designated marker across the field and to count their steps. Have them announce their number of steps and go back to the front of their line.
• Drape a towel over the students’ heads (make sure they can’t see. This is where the guide/teacher/teachers’ assistant comes into play), spin them around to disorient them, and instruct them to get to their designated marker across the field. Have them share their experience with the class and send them back to the front of their line.

• Drape a towel over their heads in such a way that they can see the compass and the ground below them only (see picture) (this is really where the guide/teacher/teacher’s assistant will have to step up). Instruct them to use the compass to navigate to their marker.
• Cycle through all the students on each line.

Relate these activities to the challenges of navigating the Mediterranean Sea. A. Things to consider – having a fixed point (the cone), having a device that gives a sense of direction, is it accurate? What challenges can you imagine may occur without 100% accuracy? What happens to the compass when going fast and the water in the bowl moves? Imagine what this would be like on a ship in high winds and water swells. Would it help if the compass was stabilized? How so and could that help?

When engaging in the IEEE REACH hands-on activities contemplated in the IEEE REACH lesson plans please proceed with caution and use all reasonable safety measures. All IEEE REACH hands-on activities are designed for classroom use only, with supervision by a teacher or an adult educator. Please be advised that IEEE shall not be responsible for any injuries or damages related to the use of these lesson plans or any activities described herein.

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• Challenges of Sea Navigation
• Navigating Without a Clock
• The Longitude Problem
• The U.S. Goes to Sea
• Navigate at Sea! Activity
• Challenges of Air Navigation
• Early Air Navigators
• Navigation at War
• Navigate the Skies! Activity
• Challenges of Space Navigation
• Reaching for the Moon
• Navigating in Deep Space
• Navigate in Space! Activity
• Challenges of Satellite Navigation
• Reliable Global Navigation
• Global Positioning System (GPS)
• Who Uses Satellite Navigation
• Meet a Professional Navigator
• Personal Navigation Stories
• Timeline of Innovation
• Learning Resources
• Multimedia Gallery
• Visit the Exhibition

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