Minimizing fuel consumption in space travels is becoming increasingly important for spatial development. In the present paper, the fuel consumption in orbit transfers (without gravitational assistance) is minimized, where a spacecraft performs a change from an orbit around the Earth to another one around a different celestial body. Two methods are presented: one of immediate transfer and another with wait time. Minimizing is done by solving a nonlinear system, obtained by applying Lagrange multipliers to the equation modelling the keplerian system, and using the seeds coming from the particle swarm algorithm to execute the Newton’s method. Numerical simulations with real values were made to compare these methods with the Hohmann transfer and data from the specialized literature.