Herein lies the difference (theoretically) between graviton detector (detecting individual gravitons) and a gravimeter. If you can actually measure the flux of gravitons through a surface, you can get the base vectors instead of the sum, and if there's a doppler signature that can be resolved for gravitons*, that would wrap up all your problems neatly. Given some of the odd bits of miscellanea that pop up, it's actually reasonable to assume that Trek sensors will actually be detecting (in some sense) individual gravitons with their strength and vector of approach.Keiran wrote:There's more to it than just that, given that each gravimeter is going to lump everything within detection range into one vector. You'll have a bunch of possible gravity well combinations that could match your readings, and the problem becomes trying to figure out which range of possibilities is close enough and which ranges to ignore.
But even with simple gravimeters measuring local g, it's actually possible to sort out quite a bit, especially over time and especially with multiple detectors.
If you have multiple detectors off-set from each other, they give you a total of two variables each in measurement - g(x1), g'(x1), g(x2), g'(x2), etc. Each is a vector quantity, so we're not concerned about the dimensionality problem.
For our problem of n bodies in detection in the general case, we have three variables each - mass, velocity, and distance. Leaving aside the effects of warp fields (presumably warp fields have a distinctive subspace field and you can sort them out), once you've resolved these three variables, you can hold mass constant and fix position in relation to velocity over the time in which you track the object.
Assuming fine resolution, therefore, you have three variables to solve for when an object initially enters a range at which you can resolve it, but you can reduce this to what amounts to one independent variable once you have successfully resolved the object if your measurements are exact enough, and at worst two variables if your tracking is fuzzy and the error for integrating velocity into position would be too high.
If you know the velocity's pattern, e.g., as with an orbiting planet, you can eliminate this to zero variables and simply correct for the known vector.
While it is true that there is a limit to the number of independently moving objects you can resolve at once, which is in general linearly related to the number of gravity measuring devices on board, it's not the case that any plurality of bodies is impossible to resolve; if the number of independent and determining variables measured exceeds the number that need to be calculated, you can find a unique solution to the problem.
(In turn, of course, the number of distinct measurements possible is limited by the sensitivity of the devices and the volume you have to place them in.)
*"Yes and no" is the reasonable assumption for that. You should, if there's anything resolvable as individual gravitons by sensors, be able to get relative speed but not relative velocity.