The article discusses the challenges of colonizing Mars. One option to overcome much of the difficulties may be the creation of an inhabited base on Phobos in the first phase. Three different flight schemes are considered. Mathematical calculations are made for the most realistic one of them. The trajectory of flight to Phobos with starting since year 2020 for year 2030 is optimized. The attraction of the Sun, the Earth and Mars is considered on the whole trajectory. The Earth, Mars and Phobos positions correspond to ephemerides. The control is realized by impulses at the start and at the end of the trajectory. The characteristic velocity is minimized. On the basis of the Lagrange principle the problem of optimization is reduced to the boundary value problem. The boundary value problem is solved numerically with the use of the shooting method.