The guys at NASA really are rocket scientists. just imagine you have this spacecraft floating out there going in circles around Saturn which in turn is going in circles around the Sun. THen you have the earth going in circles around the sun. Most of the time the sun is behind the earth so you can't take a good picture. So they calculated the times when the body of Saturn would be between the sun and the spacecraft. THen they calculated the orbit of the earth and when it would be visible and not blocked by Saturn and or its rings. They did this months in advance and then programmed the spacecraft beforehand to take a picture at the right time. I imagine they also timed it so as to get the maximum separation of the earth and moon so it would be clearly standing out.
They hav so much confidence that they tall everyone that its going to take place and symbolically stand outside and wave.
These guys are good. They probably had a summer intern do it for an excercise.
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