Back to pencil and paper. Try again.
I'll try this again:
Vo = orbital-circumference/16 hours.
Vo = 13,800 meters/16 hours.
Vo = 767 meters/3600 seconds
Vo = 0.213meters/sec
Vo^2 = 0.445 meters^2/sec^2.
Vo^2 = GM/r.
M = (0.445)2200/6.67 x 10^-11.
M = 1.01x 10^12kg.
d(ro) = 1.01 x 10^12kg/[(4/3)pi{600m}^3]
d(ro) = 1.01 x 10^12kg/4.56(2.16 x 10^8m^3)
d(ro) = 1.01 x 10^12kg/9.87 x 10^9m^3)
d(ro) = 1024kg/m^3
[Now that's a rubble-pile! Maybe mixed in with some ice.]
Jake