There is a collection of satellites whose orbital characteristics roughly match those of the Earth relative to the sun. These objects while typically quite small are regularly captured as they pass through L1 and can thus insert themselves into orbit about the Earth and hence at least temporarily orbit the Earth. These orbits are temporary because the Moon's orbit in the Earth-Moon-Sun system tends to accelerate such objects.
The objects are Natural Earth Satellites (NES) and the history of them as well as modeled in a paper arXiv:1112.3781v1 by Granvik, Vaubaillon & Jedicke which presents this interesting phenomena. Sky & Telescope [http://www.skyandtelescope.com/communit ... 35308.html] also discusses the subject and points to a neat simulation of the interaction between the moon and these NES asteroids.
Bactame