Scientists, seekers of truth by definition, would approach the subject from the null point of view, attempting to prove, in this case, that NASA DID go to the moon. Because the hoax theorists are taking the opposite tack, and because they stretch their case based solely on the photographic evidence, one must suspect both their academic pedigree and their intentions.
This cycle has been appropriately named the 'dark moon'. The cycle from one dark moon to the next is called a lunation and an average lunation calculates at about 29 days, 12 hours, 44 minutes and 3 seconds (roughly) To be fair, it does deviate in relation to the moons erratic orbit patterns and is affected by the gravity conflict between the sun and the moon.
Cassini's successful mission of exploration to the Saturn system is over, but planetary scientists are left with a cornucopia filled with important new information that Cassini/Huygens sent back to Earth before its mission ended. A collaborative NASA/European Space Agency/Italian Space Agency mission, the robotic spacecraft was made up of two components. The first was the European Space Agency's (ESA's) Huygens Probe, that had been named in honor of the Dutch mathematician and astronomer Christiaan Huygens (1629-1695), who discovered Titan. The Huygens Probe also closely observed Saturn's lovely system of gossamer rings. The second component, the NASA-designed Cassini Orbiter, was named after the Italian-French astronomer Giovanni Dominico Cassini (1625-1712), who discovered four of Saturn's other intriguing, numerous, and icy moons.