First of all, they would need an absurdly large directional antenna to even receive GPS satellites. GPS signals are already below the noise floor on Earth's surface, and we use mathematical trickery to extract them from the background. Secondly, even that would only be possible when Earth's over the horizon at the location of the probe. Thirdly, the whole span of GPS satellites as viewed from Mars would be a small fraction of arc second, i.e. basically all coming from the one place. Lastly, there's extra light lag that you have to compensate for, that depends on relative position and orientation of Earth and Mars.
No, GPS is not suited for use in space, especially not far away from Earth. However, I read once that some Earth orbit missions did in fact look / make use of the GPS signals, as in (low) Earth orbit, they're actually easier to receive than on the ground.
The third point can be misinterpreted to make it sound like gps involves a steady tone generated from a known location like more traditional navigation aids used in aviation, rather than clocks taking advantage of our understanding relativistic effects.
While Earth is in the Martian sky, and if the signal were strong enough, a viewer could average receiving signals from over half of the constellation rather than only half a dozen. Furthermore the time signals would originate from many of the satellites moving less orthogonally to the viewer and instead moving toward and away from the viewer.
Compared to measuring the sun relative to a changing horizon, it seems plausible that an extremely precise direction and altitude relative to Earth could give even more precise location on Mars.
You mean pick up the signal from earths GPS? Off the top of my head, it would require earth to be in view, and it would be very inaccurate - GPS is already less accurate the further from equator you get, as all the visible satellites are increasingly on one side of you. You'd have this problem in the extreme, as all the satellites would be clustered in a single dot in the sky. Probably also infeasible to meaningfully correct for the fact that Mars and Earth move very quickly relative to each other.
> GPS is already less accurate the further from equator you get, as all the visible satellites are increasingly on one side of you.
Not contradicting you, but just to be clear: GPS satellites are not in geostationary orbits above the equator, or even in geosynchronous orbits. Rather, they are in medium-Earth orbits and their time-averaged density over the Earth is only a little lower over the poles as the equator. At some parts of the month, there are as many visible at the poles as at the equator. See Fig. 4 here:
Hmm, not sure I understand what you're saying. Figure 5 in that paper is the situation I'm describing: at a certain latitude (52 deg north in this case, incidentally that latitude is my 'hood) there are no satellites visible to the north. Figure 2(b) illustrates why that's bad for precision.
Sure, that's why I said I wasn't contradicting you, just clarifying. One could mistakenly read your comment and think that the coverage goes to zero at the poles ("the further from the equator you get"), but of course GPS still works pretty well there. When you get far enough north, satellites from the "other side" of the Earth come into view, so the accuracy levels off and (I think) starts increasing again with latitude.
(And I corrected my comment to refer to figure 4, not 2.)
The GPS signal is already under the noise floor on Earth there is no way with present day tech that you'd be able to get the signals on Mars and besides that the math would not work because the round-off errors regarding the timing would make all satellites appear at the same point in space when looked at from Mars. The distance is hard to appreciate in terrestrial terms without getting into 'golf balls and oranges' kind of explanations.
> round-off errors regarding the timing would make all satellites appear at the same point in space when looked at from Mars
Not just timing, also space - Earth is a fraction of an arc second on Martian sky, pretty much a very small dot. All your signals would be coming from that small dot, i.e. practically on top of one another.
The whole idea of GPS is to turn a very good time reference (an atomic clock) into a space reference, by using multiple such references with known locations at once and then to send out time stamped signals. If you can't distinguish arrival times the signal origins collapse into a point. The travel time of the signal from Earth to Mars is anywhere from 4 to 24 minutes (assuming you have line of sight, which isn't the case when Mars is on the other side of the sun), with flight times that long the difference in arrival time between the signals is meaningless.
The difference in position between the satellites is at best 40,000 km (MEO orbits and satellites in opposite positions around Earth would give you the largest baseline), the difference from Mars to Earth is > 50M kilometers. So when viewed from Mars this would be like trying to triangulate your position in the United States based on signal sources spaced a very short distance apart somewhere in Moscow.
(sorry for the strained analogy)
Another problem with the approach is that of the two possible solutions that are the result from computing your location from GPS satellites one of the solutions is deep inside the Earth, which for both radio related reasons and reasons of practicality can be safely ignored. From a location in space very far away that trick no longer works so you will end up having to pick one of several answers.
Of course you could stick a GPS like transmitter into every Mars orbiter we launch from now on so that at some point there will be enough coverage locally to allow navigation, but that's a pretty expensive trick, besides that you'd also need a bunch of base stations in order to properly compute the orbits of the satellites to the required precision so that you can tell the satellites where they are.
I'm pretty sure if you're on the Earth's surface and can pick up three GPS satellites, the other solution is out in space. If you see four or more GPS satellites, there's a unique solution.
That's probably correct. I read up on GPS years ago and I remember that one of the possible solutions is intuitively wrong for a surface of the earth measurement and filled that in mentally as 'inside the earth', but out in space sounds much more logical and likely.
We need a bunch here on Earth so we can get a fix in a reasonable time. But all the robots on Mars move extremely slowly and infrequently. i.e. it would be fine if the bot had to wait 12+ hours for a fix, they'd probably be waiting that long regularly anyways. And it probably doesn't need to be more accurate than 0.1-1 km either.
So could we deploy, say, the first three satellites that use a modified version of GPS at first that allows you to get a very slow, inaccurate fix, but a fix nonetheless?
If you have enough time, a single satellite is enough, provided it's not in a geostationary orbit. My understanding is that this is part of the initial location of landers, but that once they're located there's no point, since it's easier to just optically determine how you moved.
On Earth, similar systems were used for the TRANSIT satellites, and the Cospas-SARSat program. The latter is really cool, as it used weather satellites in low earth orbit to find a person in distress, using a cheap transmitter that's placed on a plane, boat, or very famously, Richard Branson's watch.
The way it works is that the device transmits a very stable frequency. (Perhaps modulated by the identity of the person in trouble part of the time.) As the satellite passes by, it relays the signal to the ground in a way that preserves the doppler shift. When you know the position of the satellite and the doppler shift, you can know the closest point and the distance from it.
After a few passes of your one satellite (or multiple satellites, if you have them), you can get a location that's good enough to start search and rescue.
Of course, time has passed since this was designed in the 70s and early 80s, and now GPS has fallen in price to the point where it's everywhere. So now, the devices send GPS coordinates with the identity info.
Earth's GPS satellites use earthward facing directional antennas, and even on Earth the signal is several dB below the noise floor, so our receivers have to use process gain to actually get anything useful out of them.
Mars is fifty million kilometers away. A GPS reliever on Mars looking for Earth satellites wouldn't be able to hear anything.
Mars is 140 million miles away from earth on average. Even if you could detect signals from GPS satellites on earth they would all be at a single point in the sky.
However, that does bring up an interesting idea. Maybe rovers could navigate using the position of the stars? It doesn't require you to launch 4+ GPS satellites into martian orbit.
I don't see why not - automatic celestial nagivation systems are already a thing on earth, you basically have a system that uses a camera to look at the sky and it gives you an accurate position - most military planes use it as backup in case GPS ever goes down.
The distances are literally astronomical. Mars isn't just next door. It isn't like the moon where we can talk almost in real time.
Consider it like running. How far can you run in 1 second. That's the Moon. How far can you run in 21 minutes. That's Mars. It's 1260 times the distance.
