Imagine you are a space traveler locked into a space ship without windows, or traveling through a region of invisible dark matter. Imagine that in this difficult situation, you have access to an instrument capable of recording the gravitational potential around the space ship from near to far away, an instrument or sense which we may call a Gravitational Potential Meter. Below I discuss how such an instrument might be designed.
Would that allow you to create a normal picture of the distribution of celestial objects/matter around you including your own position, which would be the picture you could see if there were windows or dark matter somehow was made visible, a standard picture/map making it possible to navigate?
Yes, it would because the mass distribution $\rho (x)$ depending on a Euclidean space coordinate $x$ at any instant of time, is related to the gravitational potential $\phi (x)$ by Poisson's equation (in normalised form):
- $\rho = \Delta\phi$, (*)
As to the design of a Gravitational Potential Meter or Gravitational Force Meter, imagine a system of little satellites in free fall distributed over the space of interest and connected to a GPS system allowing tracing of the satellites, thus giving information about the Gravitational Force and from that the Gravitational Potential. It is not unthinkable that such a system could cover any space accessible for space travel and beyond.