In this modern era . we (NASA and other organizations) can very easily know the relative position of moon through modern setups. http://www.moongiant.com/
Like scientists predicts the solar and lunar eclipse and other planetary incidences almost accurately. They also knows the position of moon and from which place of earth it can be sighted at any given time.
Then my question is why we still depends on the head of local moon sighting committee to know if moon is seen or not. The funny thing is they mullah use binoculars to see the moon, which is also a scientific invention. Then why they don't take their help in knowing the new moon.