Materials from the US sources on the Apollo program were considered, and the presented data were evaluated from the point of view of external ballistics equations, flights of spacecraft to the Moon and their return to the Earth. The evaluation made it possible to determine inconsistency of the data (mass characteristics) in different documents relating to one object in the Apollo 11 mission. Inconsistencies were also found in the ballistic schemes for launching into the departure trajectory to the Moon, mooning, undocking and docking in the lunar orbit, braking maneuver to enter the lunar orbit, acceleration maneuver for returning to the Earth and braking maneuver for landing on the Earth’s surface. Analysis of the lunar missions’ documents formed the basis to ask questions that were not previously raised in such a formulation, and no answers were given to them. In particular, significant discrepancies in the initial data were found in the official documents on the US lunar missions. Reference orbit altitude before the second activation of the Saturn-5 3rd stage, the first space velocity at the Florida peninsula inclination and the second space velocity seem to be strange. Significant doubts are caused by acceleration schedule, projection of the flight path to the Earth and remoteness of the first stage impact area from the launch pad. In terms of the F-1 engines of the Saturn-5 launch vehicle first stage, thrust indicators of one engine and the total thrust of the first stage are not consistent. A conclusion is made that at present it is almost impossible to put into practice some of the maneuvers demonstrated in the US documents.