Area: Mathematics Topic: GPS
Research Question: How does GPS rely on geometry and trigonometry now that there are satellites? Has the function of geometry and trigonometry in triangulation and navigation changed since satellites were built?
IB MATH Candidtate name: Tristan Stevenson Candidate Number: dwq773 (001366 – 016) School: Prem tinsulalonda International School November 14, 12 Word Count:2090
Abstract: This essay examines the question: How does GPS rely on geometry and trigonometry now that there are satellites? Has the function of geometry and trigonometry in triangulation and navigation changed since satellites were
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How GPS works There are 24 satellites that circle the earth every 12 hours. These satellites are split into six groups of four and each group creates an orbital plane. These six orbital planes allow the satellites to move in a way that covers the earth completely. GPS satellites transmit signals to equipment on the ground. An example is a GPS receiver (GPS receiver can only receive the signals form the satellites but they can’t transmit any signals). The receivers work best in an open outdoor area where there is a clear view to the sky. At any time there are always four visible satellites. The GPS receiver can calculate how far each satellite is based on the time it took the signal to reach the receiver. Using the distance from each satellite that the receiver calculated it could then use a process called trilateration to pinpoint the location of the receiver [1].
Problems and Improvements: Today the accuracy of GPS navigation is not questioned, however, there are still some Applications that use GPS to plot routes between two points and can be very inaccurate because it is hard to determine the difference between locations [5]. For example if you are on a trail that is not registered a GPS could give you an incorrect route. Also a GPS receiver will give inaccurate readings in a forest or a city with tall buildings because satellites have to send clear signals to GPS
Be able to list and describe the 3 main tools used to measure latitude in early navigation
| * shows evidence of information on GPS’s from a brochure and a scientific source * accesses the scientific accuracy of the brochure by identifying areas of comparison in both publications noting any relevant missing information gives supporting statements for the assessment * evaluates the validity of the information in the brochure and gives supporting statements for the assessment * presents clear relevant drawings that show how waves are used in GPS’s * identifies how the properties of waves that make them useful for this type of technology * identifies some current research into the future development of GPS’s
There is no longer a need to be a skilled map reader as GPS can provide directions anywhere to the most unskilled navigators, whether it be to a hospital for emergency treatment or a local point of interest for tourists and finds the shortest route16, making travel easier. GPS can also be used to track others16 which has made it far easier to find missing persons as with GPS becoming prevalent in phones and car, almost anyone can be tracked by one of these items. The impact of GPS on travel is unfathomable, it has made the method of navigation that was used for centuries almost obsolete and opened up the world to
In the 1500’s to 1600’s sailors made a big discovery in the line of navigation of latitude which is the art of directing vessels on the open sea. The inventor John hadley invented the Sextant which is a device that finds the angle between astronomical object and the horizon for the purpose of celestial navigation. The angle when measured can be used to calculate a position line on nautical or aeronautical chart. A common use of the sextant is the sighting of the sun or the solar moon in the northern hemisphere of the world to determine the latitude. it would be hard if the sailors did not have a sextant or if the moon was not out at that night. Or if your math was not right because if you had one little miscalculation your latitude could be
Advances were required in cartography, shipbuilding, navigation in open water, and arming a fleet with shipboard cannons. In tackling the problem with maps, the Europeans were most assisted by the Arabs, who were responsible for preserving and adding to the works of Claudius Ptolemy, a Hellenistic scholar whose work fused the astronomical and geographical knowledge of his time. By ca. 1410, sailors had revised Ptolemy’s contributions and developed portolani, practical charts designed for coastal navigation that alone, unfortunately, were still of little use once in the open ocean (Ames, 11). However, this hitch was solved by the concurrent use of the compass, astrolabe, quadrant, cross-staff, and tables of declination.
GPS software can be installed on all devices so that if they do go missing they can be found.
Lots of people around the world use GPS on their phones and in their cars. Before the Space Race and GPS’s, it would take people much longer to get to their
Air travel has been massively impacted by GPS. Flights are currently tracked by radar18 which mostly works well over well-populated areas but can be problematic over remote, mountainous areas where there are less radar stations or over the ocean. Planes must stick to established routes in these areas and remain more
From the essay, it can be noted that GSE and GPS have multiple similarities and differences, which sets them apart. More so, GSE covers the gaps, which were left out in the in GPS by giving a more detailed
Ever since man has been observing their surroundings, there has been a desire to go to the far reaches of our earth and out of our earth. Global Positioning Systems, or GPS, has allowed an easier way for people to know where the user is on our earth and to know that we put something into space.
The development of the Global Positioning System, GPS for short, was accelerated by Sputnik in more than one way. When Sputnik launched, Guier and Wieffenback were able to measure the doppler shift in the signal that was broadcast from Sputnik and successfully estimate the location of Sputnik. After telling their Laboratory’s Director about their discovery they were granted
Since the advent of humanity, nature has always proved to provide us with sustenance and opportunities for adventure. Yet, it was not only the lack of funds for urban adventure that drew millions of millennials into the woods. In May of 2000, GPS had a revolutionary improvement. This advancement of the global positioning system allowed users to engage and control selective availability, enabling them to pinpoint their exact location and other select locations. The White House stated that, anyone could use GPS to isolate, "the location of items left behind for later recovery.” Thus, sparking the origin of
On the contrary, these devices do have many advantages and conveniences to them; for example, GPS navigation. This prodigious accessory to modern cellphones have consequently deteriorated any need for other GPS devices, merely because it is a amenity. They also serve as an essential
GPS has made our lives so much easier. We don't have to print out directions before heading to an unknown address. GPS-enabled devices we carry with us daily allows us to travel freely without worrying about getting lost. There are also a number of GPS devices to help us keep track of our children. It's a dangerous world out there, and at any moment, we might need to know where our children are located.
The inertial navigation system (INS) is a highly complex device which utilises very sensitive sensors to generate movement information and a computer to develop an algorithm of motion over time. The INS can be described as very sophisticated dread reckoning. The sensors which are used in an INS are accelerometers and gyroscopes which are further linked to a computer. The main consideration is that these highly sensitive and advanced sensors used in an INS still have errors from accuracy limitations in units of basic design or original outdated concepts. The accuracy can be improved with more complex and updated integration which includes the use of the better and more advanced components. To understand the errors associated with INS, a closer look into the flow of information is essential. The north facing accelerometer is mounted to a platform which is supported by gyroscopes. Any accelerations detected are given to the first stage integrator which uses the time component to develop velocity data. The second integrator uses the velocity data and time to calculate the distance travelled which is then added to the present position to generate a new present position. The system uses a backwards feedback loop of velocity data to the gyroscopes to make accelerometer platform perpendicular to the local gravity vector. This model is used for both north facing and east facing platforms and combined with the secant multiplier. The basic system designs would carry a greater error but