The optimization problem of the planning of the survey of Earth surface by
a system of satellites that work under conditions of restricted possibiliti
es for onboard devices is considered. The method and the numerical algorith
m for the solution of this problem, which take into account the specifics o
f its technical and mathematical statements and also properties of models o
f satellite functioning, are proposed. The method is based on the directed
search for a solution in the set of values of the criterion function that c
haracterizes the efficiency of the surface survey during the planning inter
val. The method is an alternative to standard methods of exhaustive search,
linear, and dynamical programming. The method is illustrated by a model ex
ample. An example of a more complex planning problem is also considered.