Could a single CubeSat provide location services on another celestial body such as Mars? Could a constellation do it?

Question

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.

Answer 1

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.