The modified Everhart method up to order 33 and algorithms for the Adams methods up to order 16 inclusive were developed. A software package for calculating the Solar System small bodies' orbital evolution and automating the processes of database development were created. Research of the orbital evolution of 6163 asteroids belonging to Apollo, Amor, Aten groups and 197 short-period comets was performed for the time period from 1800 to 2206. 815 objects have been identified among asteroids approaching closely to inner planets, in particular 612 objects passing through the Earth's sphere of action. On the basis of performed research the website SmallBodies.Ru was created. The information offered in the website can be used by specialists when studying the orbital evolution of asteroids and short-period comets, investigating problems of the orbits stability and revealing objects presenting potential hazard to the Earth.