Creating tools for design and operational works for ballistic ensuring of space missions. Project works at the first computers

Preprint describes how it was created ballistic space projects support in 1950es–1970es in the Keldysh IAM. We discuss algorithms for solving rocket dynamics in the first digital computers. The circumstances of solving for key ballistics problems of the first flights to the moon and planets are given. The story concerns building approximate and exact methods for solving boundary target problems, aimed at creating the trajectories of spacecraft.