Einstein's theory of relativity, how GPS works, prove it with experiments

 Abstract:

        Trilateration is the method currently used in gps for locating a person's exact position. In this experiment, the objective is to learn how gps works and to prove it with experiments and precise data. A few cue questions will be considered: 

  • How to create transverse waves?
  • How to locate in the most efficient way?
  • How to prove the positions are located accurately?

       The experiment includes two parts: simulation design and model translation of the simulation as a battery operated car. Time is measure for both parts, and the distance is calculated with the time measured. The percent error is calculated by comparing the actual distance to the calculated distance. 

Introduction:

       Trilateration is to locate the position by using the distance from the three or more signal senders to the position. All signals are moving in the constant velocity. With measured time, displacement is calculated by using displacement formula.  A circle is drawn with the result of the calculation is used as a radius, and satellites are the center of the circle. The intersection of the circles is the location.

       In Einstein's theory of relativity, time dilation is the difference in time measured by different observers. It explains why two clocks will report different time after different acceleration. For example, refer to clocks on the earth, clocks on the satellites are moving a bit faster. 

Materials:

  • Computer for coding program
  • Constant speed car
  • Timer on phone
  • Strings
  • Tape
  • Meter stick

Procedure and Observation:

       Trilateration is the major method used in this experiment. In this case, the signal senders will be the satellites. There are two parts in the experiment: coding part and practical(car) part.

       In simulation part, a html file is created in text software(by Zhicheng Shen). Javascript is used in the coding. Time that the signal spent moving from satellites to the locations are measured. The displacement is calculated using the displacement formula. Three circles are drawn, using satellites as the center of the circle, and the displacement as the radius. Observing through the experiment, trilateration always works because multiple circles always intersect at one point. However, if there are only two satellites, the location will not be determined. Two circles may intersect at one point or two points. In this way, the precise location cannot be found.

     To make the coding part of the experiment more realistic, a real life experiment is also designed. A constant speed car is used to present the signal. Using the same method as coding experiment, an equilateral triangle is made. Three points is the location of each satellite. Before starting this part of the experiment, the speed of the car is measured. Time is measured when the car goes one meter. Using the speed formula: speed = distance/time, speed is calculated. A random position is chosen to be the unknown position. While the car goes from the satellite to the unknown position, the travelling time is measured. The displacement between the satellite and the unknown position is calculated by displacement formula. Using the displacement as a radius, the circle is drawn. Three circles are drawn, and the intersection is the precise location. 

     Time dilation is calculated by using time dilation formula for both parts of the experiment. As a result, time difference is so small that does not affect the result of the experiment. However, with the same data but with much higher velocity, time dilation becomes much bigger. It proves that with a high velocity, the time dilation will affect the result. 

Conclusion:

    In conclusion, transverse waves is created by moving from each satellite to the given point. The most efficient way to locate the point is by using the coding program as opposed to actually carrying out the experiment on foot. The code can be improved by making it easier for the user to use. Both parts have a low percent error. The experiments proves that using trilateration for locating the position is accurate and precise. The GPS is able to find the user by using trilateration. the overall objective for this experiment succeeds. Einstein's time dilation is proven, even though it does not affect the result much in this experiment. To improve the experiment, four satellites could be used to make the location more accurate.

Misconception: 

  • Triangulation vs. Trilaterition 
  • Time being constant vs. time dilation
  • Three satellites accuracy vs. Four satellites minimum accuracy

Extra Information

The GPS Powerpoint includes more data and information

This Code is used for the coding part of the experiment. When using the Code, make sure the button is clicked in order. For example: if position1 is tested, click position1, signal1, result1, and reset1. 

  • The powerpoint is done by the group: Madison Colin, Anthony Ronodos, Marley Scala, Madison Sullivan, Zhicheng Shen
  • The experiment is done by the group: Madison Colin, Anthony Ronodos, Marley Scala, Madison Sullivan, Zhicheng Shen
  • The coding is created by Zhicheng Shen
  • The assignment is guided by Anjali Shah
  • The coding publishment is guided by Joseph Gyulay

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