“Fly Me to the Moon” is a sharp, stylish comedy-drama set against the high-stakes backdrop of NASA’s historic Apollo 11 moon landing. Sparks fly in all directions as marketing maven Kelly Jones (Johansson), brought in to fix NASA’s public image, wreaks havoc on launch director Cole Davis’ (Tatum) already difficult task. When the White House deems the mission too important to fail, Jones is directed to stage a fake moon landing as backup, and the countdown truly begins.