In this answer I mention that for very low orbits around spherical bodies, the period tends to scale only as the inverse square root of the density, and not the diameter.
For a low orbits where the semi-major axis is close to the radius of the central body, the period is related to the average density of the body and unrelated to it's size.
So a low orbit around a spherical asteroid (which there usually aren't) made of a mixture of rock and iron (which there usually aren't) will be roughly 90 minutes just like LEO (low Earth orbit), even if it's only 1 km in diameter.
I'd like to use an example, but I don't know where to find an asteroid density table, nor even a histogram, that includes something close to 5 g/cm^3.
Question: Are there any known asteroids with average density similar to that of Earth's?
Some example mean densities from Wikipedia (some rocky planets included for good measure):
body mean density (g/cm^3) Earth 5.5 Mercury 5.4 Venus 5.2 Mars 3.9 Vesta 3.4 Moon 3.3 Hygiea 2.8 Pallas 2.7 Ceres 2.1