# Can the satellites in Martian orbit be put to use providing a rudimentary GPS system on Mars?

This website conveys the impression a rover on the Martian surface necessarily navigates by dead-reckoning. Stereo images are used to determine how far a rover has travelled; an advancement over older technology which may have merely counted wheel revolution.

On Earth's surface, accurate navigation is made easier by the aid of satellite navigation systems such as GPS. A system such as GPS is apparently a bunch of satellites in orbit queried by a dedicated receiver to determine the position of the receiver itself.

Pure speculation on my part - feel free to shoot the thought down. I guess each question in the list below could be a separate question in itself ... let me know if that is a better way to go about it

• How many satellites would be needed in orbit around Mars to be used as a navigation aid? My guess is the smaller sphere may translate to a lesser number than required for Earth.

• Are the rovers on Mars capable of communicating with the satellites in orbit?

• Can the 5 satellites currently in orbit around Mars be made into a jury-rigged system to provide a satellite based navigation system for the rovers?

• If you knew their orbital period you could use that, a clock, and a sextant to determine your location... (As pointed out in The Martian, though that book's hero uses the natural satellites instead. Implicit plug intended; that's a Hugo-quality story.) – keshlam Sep 30 '14 at 3:38
• There are answers about time but do the satellites even know their own position accurately and in reference to what on the surface? – JamesRyan Sep 30 '14 at 11:40
• From the answers posted below, I get the impression a minimum of 3+1 satellites may be needed in the receiver's sky for position reporting. Does this number change as a function of the size of the planet? – Everyone Sep 30 '14 at 17:47

Not the way GPS works, no, since the Mars orbiters don't have atomic clocks. (Though future Mars orbiters may someday.)

The relay radios on the Mars orbiters provide a 2-way Doppler data type that can be used to locate surface assets to, as I recall, within about 100 meters. Even a single orbiter with Doppler data collected over a few passes can get this accuracy. (Yes, the surface assets are not only able to communicate with the orbiters -- they depend on the radio relays to return their required science data volume.)

However the cameras on the surface assets can be used to pinpoint their location on orbital maps to far greater accuracy by using topographic features. So radio navigation from the orbiters is neither needed nor beneficial.

• As an aside - perhaps I should post this as a follow-up; Given the magnitude of the distance between planets (let alone distances as large as travelled by the Voyager twins)How accurate does the clock aboard a craft have to be? Is there anything like an international standard/protocol? – Everyone Sep 30 '14 at 17:45
• The kind of "clock" we're talking about here is a frequency reference. The key parameter is the stability of the frequency reference over relevant time scales. Typical "Ultra-Stable Oscillators" on spacecraft (crystal oscillators in temperature controlled ovens) are around $10^{-12}$ to $10^{-13}$ over 100 seconds. This is to provide one-way Doppler tracking, which is important for some kinds of radio science data where a two-way Doppler track is not possible, such as limb measurements. – Mark Adler Sep 30 '14 at 21:42

Mark Adler already explained that the satellites aren't equipped anyway to provide a satellite navigation system. But even when they were technically capable of working as a GPS satellite, 5 satellites would not be enough. You need a direct line of sight to at least 4 satellites, and with only 5 satellites this will happen very rarely, because even considering the largest possible orbit and the smallest possible planet you will only ever be able to observe up to 50% of the sky from a position on the ground.

The reason you need four satellites is that a GPS satellite sends only two pieces of information:

• Its current position
• Its exact current time according to its atomic clock

Due to the signal only traveling with the speed of light, you can compare the time received by the satellite with your own time to learn your exact distance to the satellite. That way you know you are on the surface of an invisible sphere around the satellite.

When you also have a signal from a second satellite, you have two spheres. The intersection of two spheres is a circle. You now know you are on this circle which will be perpendicular to the surface of the planet. When you assume that you are on the ground (which isn't so sure in case you are in an aircraft or in a mountainous region) you have two possible locations.

A distance measurement to a third satellite is needed to know your precise position in three-dimensional space.

So why the fourth satellite? Because until now we assumed that you know your current time as accurately as the satellites know. Unless you also have an atomic clock calibrated to GPS time this is unlikely to be the case. To obtain the necessary time reference to make an accurate distance measurement to the satellites, you also need a fourth satellite.

• Though that all is only if you want to get an instantaneous solution. That is important for a car or airplane on Earth, but not so much for a Mars rover that goes a few tens of meters a day. By measuring a distance to a single satellite over a period of time you can get the same kind of solution, with the accuracy depending on how long you measure, and over how many passes. If you're willing to wait a day instead of a second to get your position update, you don't need four satellites. – Mark Adler Sep 30 '14 at 0:08
• How does a fourth satellite help time keeping? – LocalFluff Sep 30 '14 at 7:39
• @LocalFluff When you have 4 time measurements with 4 positions there is only one possible time where all 4 distances line up exactly. To accurately estimate your position in n dimensions, you always need n reference points. In this example you also need your "position" in the 4th "dimension" time, so you need a 4th reference point for your position. – Philipp Sep 30 '14 at 7:41