Preprint describes how was creating ballistic of support of space projects in 50 - 70 years of the twentieth century in the Keldysh IPM. 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 of building approximate and exact methods for solving boundary target problems, aimed at creating the trajectories of spacecraft.

BESM, “Strela”, Ballistic, operative calculations, numerical integration, local error, integral accuracy criteria, orbit determination, orbit correction.

Theoretical and applied problems of mechanics