My assumption is that any body in the solar system would have it's own specific geo-synchronous orbit height. But when I took a look at Phobos and calculated the GEO height based on the simple formula for synchronous orbits I got a height that was way above it's L1/L2 points:
GEO = 12.65km (above the surface) using the following values
ME (mass) = 1.07E+16
T-Rot (rotation period) = 27,552 seconds
R (radius) = 11.26 km
L1/L2 = 3.1km (Mars/Phobos)
Since Phobos is tidally locked to Mars I assumed that its rotation period would be equal to a single orbit around Mars (7 h 39.2 min), but perhaps this is flawed?
Is it possible to place an object into a stationary orbit around a small mass like Phobos? Does being tidally locked to Mars cancel out it's rotational force? Or perhaps it's possible to have an L1 point below the GEO height, which would be really cool. Since Phobos is already really cool being subsynchronous to Mars...