[melaniejs (OP)]

David has a question:

If the LHC or future accelerator created a black hole that consumes the Earth, would the Moon (and ISS) continue to orbit normally?

What does everyone think?

[Halc]

Ignoring the how of the situation, if Earth were to suddenly get compressed into a black hole, the moon would be totally unaffected.  Ditto with anything else not 'on' Earth, so even the low satellites would continue their orbits.

[Gainfast]

Your knowledge allows me to move on, no matter how much trouble.

[alancalverd]

If you've nothing better to do, read "The Krone Experiment" to see what happens when somebody …. oh never mind, I won't spoil it for you! The book is brilliant but the author made a disastrous DVD whose acting and production quality destroy what could have been developed into an oscarworthy screenplay.

[Janus]

 A bit on the "accelerator creates a black hole that consumes the Earth" scenario.
Black holes are subject to the emission of Hawking radiation.  Left by itself, a black hole will evaporate away to nothing by this process.  The only thing that would prevent this is for the black hole to be capturing new mass faster than it loses it via Hawking radiation.  This is easy for large black holes, but not for really small ones, as the less massive the black hole, the more intense the Hawking radiation is.
So how does this come into play for our "Earth consuming" black hole? 
Hawking radiation, like any other radiation, exerts pressure, in this case, outward and away from the black hole. This tends to push material trying to fall into the black hole away.  If the radiation pressure is greater than the pressure pushing stuff in toward the black hole, then none of that stuff can work its ways inwards to feed the black hole. It continues to shrink, causing the Hawking radiation intensity to increase, which raises the outward radiation pressure further.
Now imagine such a black hole sitting at the very center of the Earth.  There is an immense amount of pressure pushing in towards the center.  What would be the smallest mass the black hole could have before the radiation pressure from its Hawking radiation exceeded the inward pressure of the Earth?
It turns out that the answer is about that of a small asteroid.  Any smaller than that and it would just evaporate away over time.
And this is under the ideal situation such a black hole to consume the Earth.
Any accelerator could only produce a black hole with a mass equivalent to the energy consumption of the accelerator.
The entire world's yearly energy usage only has a mass equivalence of 7,000 kg.  It would take millions of times more than this to produce the black hole large enough to consume the Earth. 
So there is no chance that any present or future accelerator will produce an Earth consuming black hole.