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From my understanding, by having two satellites emit a signal simultaneously (carrying atomic clocks to achieve it), a ground device could measure the difference in times of arrival to determine its own position on the axis parallel to the line between the two satellites. With three or more satellites, the ground device would determine its own position on two axes.

Firstly: Is there a way to achieve something similar with a single satellite (even if less accurate), and has it been done? Could a single satellite send the same signal from opposite ends of its own structure and achieve a similar effect (one axis localization), or does the tiny distance between two sides of a satellite mean that the difference in arrival time would be too small to measure?

Secondly: Would a CubeSat GPS network make sense, or is the size constraint a dealbreaker for the required energy/weight constraint? Could a simpler version be created that would make sense? I haven't found previous implementations of such networks :/

I hope these questions are not too dumb, I appreciate any knowledge or pointers to learning resources if the questions cannot really be answered without more background.

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If you have a lot of time, then a single satellite in Low Earth Orbit (LEO) is enough to narrow your position down to one axis. This can be done by staying still, and taking two (or more readings) from different points in its orbit (which is functionally the same as readings from two satellites with synced clocks at the same time). So yes, it's possible, but as we will see in the next section, a constellation can not only do better than that, but it can (in theory) do better than our current navigation system.

The paper "Constellation Design for Mars Navigation using Small Satellites" proposes using 15 CubeSats to provide continuous coverage of the Martian surface for navigational purposes.

The principle of using a constellation for navigation (albeit in LEO) is backed up by this paper too: "Single-Satellite Integrated Navigation Algorithm Based on Broadband LEO Constellation Communication Links" so it is definitely feasible.

As more constellations go up, and more research is done, we are likely to see this idea refined.

SpaceX's Gwynne Shotwell said in an interview:

"Once we take people to Mars, they’re going to need a capability to communicate . . . In fact I think it will be even more critical to have a constellation like Starlink around Mars."

As such, it may well be that this communication network is expanded for navigation. While the current Starlink satellites are somewhat beyond the typical size of CubeSats (260 kg vs 8 kg), it is substantially smaller than existing GPS satellites (1,630 kg), and with technological advances, they well come down in both size and weight.

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    $\begingroup$ Thank you so much for this info, I read the first paper and it's extremely understandable! It does not however mention the power requirements that an orbit so far away from the surface would entail. Isn't that a big limitation in CubeSats, or do I have a wrong concept of radio communications in terms of orbit distance vs power requirements? $\endgroup$
    – Bensas
    May 11 at 13:06
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    $\begingroup$ Looking at it there have in fact already been two 6U CubeSats put around Mars as part of the InSight mission. Details can be found here: en.wikipedia.org/wiki/Mars_Cube_One. It seems like they deployed solar panels, but due to power generation issues, the communication radio was limited to 5 watts. We have since lost contact with them, so it is unknown how sustainable this power generation was. $\endgroup$
    – Freddie R
    May 11 at 13:40
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    $\begingroup$ This (position fix with ONE satellite), or in other terms navigation using Doppler, is the principle of the US TRANSIT. "Having a lot of time" = 15mn using TRANSIT for ~30 meter precision. $\endgroup$
    – Ng Ph
    Jun 30 at 11:54

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