Study of physical effects in the vicinity of a black hole as the basis for understanding general relativity, astrophysics, and elements of cosmology. Extension to current developments in theory and observation. Energy and momentum in flat spacetime; the metric; curvature or spacetime near rotating and nonrotating centers of attraction; the Global Positioning System and its dependence on general relativity; trajectories and orbits of particles. Subject has online component and classroom lectures are replaced with online interactions: manipulation of visualization software, access to websites describing current research, electronic submission of homework, and structured online discussions between undergraduates and alumni and with instructors and graduate specialists in the topics covered.

This OLogy activity challenges students to find nine inventions that Einstein's ideas helped to create. The activity begins with an illustration of Al's Junk Shop. Mixed in with his junk are a Global Positioning System, CD player, computer, calculator, scanner, laser pointer, TV, and representations of both laser surgery and nuclear energy. After making a mental list of their nine choices, students can click to a second page to check their answers. Each invention has a rollover note about how Einstein's ideas helped pave the way for its creation. Alternately, the first page could be printed and used as a handout for an offline activity.

Students design their own logo or picture and use a handheld GPS receiver to map it out. They write out a word or graphic on a field or playground, walk the path, and log GPS data. The results display their "art" on their GPS receiver screen.

This is a freshman advising seminar. The professor of a FAS is the first year advisor to the (no more than 8) students in the seminar. The use of Global Positioning System (GPS) in a wide variety of applications has exploded in the last few years. In this seminar we will explore how GPS works, the range of applications, and the conflict between civilian users and military planners. This seminar is followed by a UROP research project in the spring semester where results from precise GPS measurements will be analyzed and displayed on the web.

Students familiarize themselves through trial and error with the basics of GPS receiver operation. They view a receiver's satellite visibility screen as they walk in various directions and monitor their progress on the receiver's map. Students may enter waypoints and use the GPS information to guide them back to specific locations.

Students go on a GPS scavenger hunt. They use GPS receivers to find designated waypoints and report back on what they found. They compute distances between waypoints based on the latitude and longitude, and compare with the distance the receiver finds.

" This is a freshman advising seminar. The professor of a FAS is the first year advisor to the (no more than 8) students in the seminar. The use of Global Positioning System (GPS) in a wide variety of applications has exploded in the last few years. In this seminar we explore how positions on the Earth were determined before GPS; how GPS itself works and the range of applications in which GPS is now a critical element. This seminar is followed by a UROP research project in the spring semester where results from precise GPS measurements will be analyzed and displayed on the Web."

During a scavenger hunt and an art project, students learn how to use a handheld GPS receiver for personal navigation. Teachers can request assistance from the Institute of Navigation to find nearby members with experience in using GPS and in locating receivers to use.

In past times, ocean navigators tossed a piece of wood over the side of their ships and noted how long until the ship passed the wood. They used this time measurement and the length of the ship to calculate their speed and estimate how far they had traveled. In this activity, students act the part of a GPS signal traveling to the receiver to learn how travel time is converted to distance.

Introduces the concepts and applications of navigation techniques using celestial bodies and satellite positioning systems such as the Global Positioning System (GPS). Topics include astronomical observations, radio navigation systems, the relationship between conventional navigation results and those obtained from GPS, and the effects of the security systems, Selective Availability, and anti-spoofing on GPS results. Laboratory sessions cover the use of sextants, astronomical telescopes, and field use of GPS. Application areas covered include ship, automobile, and aircraft navigation and positioning, including very precise positioning applications.

Introduces the concepts and applications of navigation techniques using celestial bodies and satellite positioning systems such as the Global Positioning System (GPS). Topics include astronomical observations, radio navigation systems, the relationship between conventional navigation results and those obtained from GPS, and the effects of the security systems, Selective Availability, and anti-spoofing on GPS results. Laboratory sessions cover the use of sextants, astronomical telescopes, and field use of GPS. Application areas covered include ship, automobile, and aircraft navigation and positioning, including very precise positioning applications.

For thousands of years, navigators have looked to the sky for direction. Today, celestial navigation has simply switched from using natural objects to human-created satellites. A constellation of satellites, called the Global Positioning System, and hand-held receivers allow for very accurate navigation. In this lesson, students investigate the fundamental concepts of GPS technology trilateration and using the speed of light to calculate distances.

The aim of this course is to introduce the principles of the Global Positioning System and to demonstrate its application to various aspects of Earth Sciences. The specific content of the course depends each year on the interests of the students in the class. In some cases, the class interests are towards the geophysical applications of GPS and we concentrate on high precision (millimeter level) positioning on regional and global scales. In other cases, the interests have been more toward engineering applications of kinematic positioning with GPS in which case the concentration is on positioning with slightly less accuracy but being able to do so for a moving object. In all cases, we concentrate on the fundamental issues so that students should gain an understanding of the basic limitations of the system and how to extend its application to areas not yet fully explored.

To navigate, you must know roughly where you stand relative to your designation, so you can head in the right direction. In locations where landmarks are not available to help navigate (in deserts, on seas), objects in the sky are the only reference points. While celestial objects move fairly predictably, and rough longitude is not too difficult to find, it is not a simple matter to determine latitude and precise positions. In this activity, students investigate the uses and advantages of modern GPS for navigation.