Geosynchronous orbit

[Sam_Stone]

Carnivorous Plant asks:

So they have a clock? Worthy of my physics prof touching the bowling ball pendulum to his nose and releasing it.

Each GPS satellite has an atomic clock on it, I believe. And when a GPS receiver handshakes with the satellite, it receives the satellite’s time. So one advantage of GPS is that every receiver out there has a time/date with atomic clock accuracy. The satellite doesn’t need the clock, but the GPS receiver does so it can do an accurate orbital calculation from its almanac.

[bonzer]

The figure-8 ground track in the more general case is a result of the orbit being elliptical rather than circular.

Not necessarily … The speed of the satellite will be constant, but the azimuthal component of the speed won’t be, due to the inclination … The eccentricity of the orbit would have the effect of distorting the shape of the figure 8, such as perhaps making one lobe larger than the other.

Agreed. In practice, the eccentricities used are typically such that, while still best described as a figure-8, the shape is very distorted from the symmetrical case produced by the inclined circular orbit.

[Popup]

*Originally posted by Sam Stone *
You need four GPS satellites in order to resolve a position in three dimensions. If you can only lock on to three of them, you lose altitude tracking. If you can only lock on to two of them, you can determine your position but not very accurately. With just one satellite, you can determine your position within a circle determined by all the possible solutions for the fixed distance measured to the satellite. Imagine a cone from the satellite to the ground - with one satellite, your position can be determined to be anywhere inside the cone. With two satellites, the intersection of two cones determines your position, which will be a much smaller ellipse. With three, you get the intersection of three cones. With four, you can add altitude information, and you also get maximum resolution because the intersection area is where all four cones overlap.

I have often heard the explanation that the GPS receiver calculates the distance from the satelites, in order to find the position. This is achieved by using the timing signals from the satelites, and calculating the delay. That is wrong. (Or at least overly simplified.) (even Howstuffworks gets this wrong! But they have a nice explanation nevertheless, with cool graphics. Worth a look!)
The problem is that there is no internal time referencs. So, instead what is calculated is the difference in distance from the satelites. For example, if the signal from satelite B arrives 10[sup]-5[/sup] seconds after the signal from satelite A, we know that satelite B is 3km further away. This is enough to put us on the surface of a parabola (hyperbel?). An additional satelite gives us another surface, and the intersection of the two is a line. Normally this line would only intersect the surface of the earth in one point, and that’s why three satelites is enough for position if altitude is known/fixed. In order to accurately determine altitude a fourth satelite is needed.
Basically it’s a system of four equations with four unknown (x,y,z and time).

*Originally posted by Sam Stone *
I don’t know the exact protocol used in GPS transmission, but I’d guess that the initial handshake consists of the satellite transmitting its ident, and the receiver returning the date of its almanac section for that satellite. If the almanac is out of date, the satellite will transmit a new one to the receiver, just for its own positions. That’s my guess, anyway.

Good guess, but I’d be surprised if there’s a bidirectional protocol. The satelites transmit this information all the time anyway, just not very frequently. That’s why a GPS that’s been switced off for a longer time takes much longer to get a position - It has to wait for all the satelites to send out their latest almanac.