Tom, the shadow shown on the moon cannot be caused by a object orbiting the moon. The reason being, is that the shadow, once full moon occurs, cycles immediately over again. If there were such an object orbiting, we would see a much longer duration of the full moon. Such is not the case.
Also, this dark object defies the laws of physics. The only known stellar objects known to be "invisible" are black holes. The shadow object would have to be one of these objects, but it cannot be because you claim it orbits the moon. If that were the case, there would be great relativistic effects occuring near the moon and possibly here on earth as well.
And although the existence of "mini" black holes are theorized, their existence is yet to be proven, and even if the shadow object was one of these "mini" holes, they would still retain the basic characteristics of a regular black hole, and all the same effects should still apply.
Also, this shadow object is what you are claiming to be the cause of the shadow on the moon, and the cause of the lunar eclipses, both partial and full. This isn't possible.
Disregarding a lot of other logistics in this argument, take a look at this:
You'll notice that the shadow
couldn't possibly be caused from a shadow object. If you look at the very first image of the moon, that would be the exact same formation as the shadow object passed over the moon. However, it very clearly starts to change shape, turning into a "straight" line when at the half moon phase. I don't know about you, but I doubt the shadow object can change shape at will, because it would have to in order to make the following happen:
As you can see, it's a partial lunar eclipse, and the shadow maintains it's shape pretty well, exhibiting the shape of an object passing over or in front of it. However, you should also note that the moon "changes color" during this. If the shadow object was the cause of both phenomenons, then shouldn't the phases of the moon also have this coloration?
The simple fact is, there is not a shadow object, the occurances in which you are arguing for it to exist are not consistent. If it does exist, it has to be able to change shape (and there's no known solid body (planets, stars, moons) that can do this), also has to be a black hole to not reflect/shine light, and must also have "half" an orbit to create the phases of the moon, because if it was a "full" orbit, the full moon phase would be much longer.