Using Rocket Science to Study Rock Science



GPS

The GPS (Global Positioning System) consists of a system of at least 24 satellites that continuously broadcast information so that a passive receiver can locate its position on the surface of the earth.

Satellites are in half sidereal-day orbits that are roughly circular (altitude is approximately 20,200 km) with four satellites in each of six orbital planes inclined at 55°. The satellites are distributed so that generally a sufficient number are well above the horizon at any one time.

They broadcast on two carrier frequencies, 1575.42 MHz (≈ 19 cm) and 1227.60 MHz (≈ 24 cm). Each satellite contains an "atomic clock" and broadcasts an encoded digital message that includes data such as a satellite identification, ephemeris of the satellite orbit, satellite clock error correction, approximate data for all other satellites, and a pseudo-random sequence ranging code.

The code used by non-military receiver is modulated at 1.023 MHz rate with a period of 1 ms. The use of a spread spectrum decreases problems of interference. Data for each satellite is computed by central ground stations and uploaded periodically to keep the system accurate.

The passive nature of the system ensures that many users can simultaneously use the system, and no user need betray his or her position with an active signal.

Big Brother cannot track the individual GPS user unless a transmitter (such as a cell phone) is incorporated with a GPS receiver.


GPS receiver units

A GPS receiver unit determines the distance to each of the satellites and calculates its position by 3-dimensional triangulation. Distance is determined by measuring the time for the radio signal to propagate from the satellite to the receiver.

With a precise (expensive and large) clock in the receiver three satellites should be sufficient. In practice, a receiver contains an inexpensive and not so precise clock. The use of four satellites can compensate for any clock error in the receiver and provide the necessary data to pinpoint the receiver's position.

Modern GPS units are capable of acquiring and locking onto the signals from up to twelve satellites simultaneously.

Of course, the GPS units must also know where the satellite is located. This can be readily calculated from the orbital parameters of each satellite which are part of the broadcasted information. The GPS units are programmed to perform all the calculations necessary to obtain a final best position relative to the center of earth as well as transforming this point into one of a variety of coordinate systems used in surveying.

Minimal functioning requires the use of Einstein's General Relativity to account for varying rates of the clocks on the satellites as their elliptical orbits move them in a varying gravitaional field.

Newton was sufficient to get to the moon in 1969. Einstein is necessary to get home in the 2000's!

Inexpensive handheld units utilizing one frequency and the unencrypted code available for non-military units are capable of 5 m resolution—good enough to find a quarry or isolated fossil, but not good enough for quarry use.

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