Final answer:
Soon after starting at Langley Laboratory, Katherine Goble (Johnson) worked in the Flight Research Division, where she distinguished herself with her calculations of rocket flight paths, including the trajectory for the first moon landing.
Step-by-step explanation:
Katherine Goble, later known as Katherine Johnson, received an assignment soon after she began working at Langley Laboratory that involved complex calculations related to space flight. She joined the Flight Research Division, where she analyzed the flight paths of rockets. Her immense talent and precision in calculating orbital mechanics contributed immensely to the success of the first American manned spaceflight and subsequent missions. Her most notable work included calculating the trajectory for the first moon landing, closely collaborating with the team that sent astronauts to space, and ensuring their safe return.