Okay,
I am wondering if it is possible to take a satellite constellation, say the gps satellites, and use the satellites' positions (at time $t$) as points (shown below) and use them as a lattice.
Some facts about the constellation:
- GPS Satellites lie in 6 planes.
- Each plane is inclined 55 degree.
- There are between 4 and 6 satellites in each plane. (they are not evenly spaced)
- Their orbital paths are circular (i.e. $\text{eccentricity} \approx 0$). If it helps, let's assume that that their orbits are circular.
I suppose what I am looking for is this: Given a set of points at time $t$, $GPS_t$ with specifications stated above, is there a mapping, $f$, that derives a lattice, $L_{GPS_t}$?
EDIT
what i mean by lattice is a convex polytope from $GPS_t$.
references