How you would demonstrate the basics of satellites and/or gps systems?

One Response to “How you would demonstrate the basics of satellites and/or gps systems?”

1. Comment by eyeonthescreen

   Put out a large area shallow pan. Mark three separated spots on the bottom of the pan to indicate the location of your satellites. Ideally, each satellite spot would be located on one of the points of an isoceles triangle. Mark a fourth spot among the three satellite spots as your target spot, the place locating the position you want to fix via your simulated GPS.

   Fill the pan with water so as to cover its entire area with, say, 1 inch of water. Put a device to sit on the bottom of the pan where the target spot is marked so that the device sticks out of the water.

   Stick a finger in the water over the first “satellite” spot to create a ripple. The ripples represent the GPS signals from that satellite. Time the time t1 it takes for the ripple to travel from the first spot to the target. Repeat this with the other two satellite spots to get t2 and t3.

   To calibrate the velocity V of a ripple, measure the distance between one of the satellite spots and the target, using a meter or yard stick. Then V = S/t; where S is the measured distance and t is the time it took the ripple to get to the target. In a real GPS V = c, the speed of light, so this step isn’t necessary for a real GPS case.

   Given the wave velocity is the same V for all the ripples, you can calculate the distance between the target device and each of the spots where you dipped your finger to create the ripples. Thus, you’ll have s1 = Vt1, s2 = Vt2, and s3 = Vt3.

   Repeat these procedures until you have, say, N = 30 calculated sets for s1, s2, and s3. Let S1 = sum(s1)/N, S2 = sum(s2)/N, and S3 = sum(s3)/N be the average distances to the target from the respective dipping points representing three satellites. This is an important step to minimize measuring errors.

   Plot each of these three average distances on a piece of paper as radii around each of the corresponding three dipping points. Where the three radii intersect is the calculated position of your target device. You can sort-of prove this result by moving the target around and redoing the experiment to show your experimental results correspond with the actual position of the device on the pan.

   Check your calculated “GPS” results with the actual postion as measured with a meter rod or yard stick; it’ll be interesting to see how accurate your calculated “GPS” measures were. Speculate on where the errors might have come from. Might GPS have the same kinds of error?

   And there you have it…that’s how GPS works. By ranging off three or more satellites, you can fix a position on Earth’s surface quite accurately…down to about 1 m error using the best GPS receivers. And, if you add more satellites, the ranging error becomes less because there are more radii to intersect.