Abstract
In the present work, we develop an analytical theory of Low Earth Orbits (in brief "LEO") of artificial satellites moving in the Earth's gravity field. The relativistic corrections arising from the Schwarzschild solution and Earth's oblateness to the Earth's gravity field are considered and are expanded in a series form. The theory was developed on the basis of the Hori-Lie canonical transformations method. Secular and periodic perturbations in the orbital elements due to the geopotential (zonal and tesseral harmonics) of an arbitrary degree and order, and the relativistic corrections are computed up to third and second order respectively. Numerical applications to a LEO are introduced. The theory was tested for different satellite orbits and compared with results of numerical integrations.