Indonesia to English

Applying Trigonometry as a Basic Trilliteration for Global Positioning System ( GPS )
Long time ago, actually our great – grandparents have a unique ways in order to they not being lost. They build the easy looking monument, draw detail maps which need many energy, learned to read star in the sky. Then now with the development of technology, use of maps and compass replaced by other navigator tool named Global Positioning System ( GPS ). This system improve since 1970 by USA military department. In its grow, GPS used for other necessary. Actually that modern tool based from mathematics science named triliteration.
Global Positioning System is navigation system which exploiting satellite. GPS receiver get signal from some satellite around world. With the special formation, GPS can give position and time with very high height. GPS satellite around the earth twice a day. This satellite will transmission signal to the world, then other GPS will be differentiating time that transmit to calculate position.
GPS Principal, GPS must has at least 3 satellite to calculate 2 dimension position. With 4 satellites, GPS can calculate 3 dimension position. GPS position based by mathematics measurement named trilliteration which is need 3 basic point.
Determination point of GPS :
• Assuming you don’t know about your position, and you only know, you have 7 km from reference point “A”. Make circle with 7 cm of radian.
• Others, you know , you have 14 km from reference point “B”. draw, and you can see, that circle proportion on 2 points.
• Impossible you on 2 points at the same time, so you must draw one circle again, assumed you know, you have 3 km from reference point “C”. So you have 3 circle which are produced 1 point, this point your position.
Delivery data process by satellite
When GPS satellite sending signal to GPS receiver, that signal containing about position information satellite and time of that delivery signal. Because of there is a distance between satellite position and GPS receiver so there is difference time at the first time of signal transmitted with the time of accepted signal by the GPS component.
Speed of signal transmitted assumed like a velocity of light in a vacuum. With a difference time equal to T, so distance obtained as :
Distance ( S ) = time ( T ) x velocity of light ( V )
( S ) is the radian which used before.
Reason for using 4 satellites
GPS satellite sending position data ( X, Y, Z ) to receiver. Assumed there are 3 satellites that can accepted by our GPS, so there are 3 variables in 3 equations which accepted by GPS . That three equations will be produced a calculation that shows where is our location.
x1 + x2 + x3 = y1 + y2 + y3 =z1 + z2 + z3
Because every point ( X, Y, Z ) in satellite difference each other so in order to can produced the same calculation, we must add 3 variable that used by all of information, named ( a, b, c ) so the formula become :
ax1+ by1 + cz1 = ax2 +by2 +cy3 =ax3 + ay3 +cz3
Variable ( a, b, c) are information about our height. If the process delivery information to the receiver GPS in prefect condition, so with three information we can know about our position and how high our position.
There is one again variable that unknown by us that is “ Time ( T )”. That means we have 4 variable which unknown there are X, Y, Z, T. For calculate that variable, needed 4 different mathematics equation, because of that we need position information from satellite. So with 4 variable from 4 different equation, mathematically we can know about our position.
When we get information from 3 GPS satellite we know our position in 2 dimension, not 3 dimension, because height variable disregarded. We calculate data of X, Y, and T. Height data disregarded because GPS device majoring 2 dimension position.
Useful of GPS to life
• Military
• Navigation
• Geography information system
• Watcher earthquake

Reference :
Epsilon Edisi21/th.XIX/Oktober 2007/ hal.12 - 13