I agree with @LPH, that these kinds of sentences should be broken down. In my case I tend to break them into phrases, or operative words, rather than full sentences. This is how I would break it down:
This meant communications had to be relayed by a satellite
This is the root of the sentence, and contains the most essential aspects of it. It could certainly function as a standalone sentence, but is not necessarily all that the writer needs to portray.
In this instance "which" is being used as relative clause meaning the satellite will be assuming certain qualities.
had been cunningly located
Both "had been" and "located" are in the past tense, so we are speaking of events which have already occurred. The word "Cunningly" is strictly the writer's opinion and is an adjective attached to the word located.
for the purpose
The inclusion of an indefinite phrase like "the purpose" is meant to refer to a subject which was discussed in a previous sentence without fully explaining the idea again. The reader should at this point already understand what the purpose is which the satellite is attempting to achieve.
at a place where
describes the location of the object of this sentence, the satellite, with a conditional statement indicated by the word "where". This conditional follows as:
the interaction of the gravitational fields of Earth and Moon meant it could orbit a point in empty space.
This could be a standalone sentence if the writer had structured this differently. It indicates that the place where the object of the sentence will preside is determined by the relationship between the Earth and Moon. The relationship of which being through their gravitational field's interaction.