Stellarium uses the VSOP87 method to calculate the variation in position of the planets over time.
As with other methods, the precision of the calculations vary according to the planet and the time for which one makes the calculation. Reasons for these inaccuracies include the fact that the motion of the planet isn't as predictable as Newtonian mechanics would have us believe.
As far as Stellarium is concerned, the user should bear in mind the following properties of the VSOP87 method. Precision values here are positional as observed from Earth.
|Mercury, Venus, Earth-Moon barycenter, Mars||VSOP87||Precision is 1 arc-second from 2000 B.C. - 6000 A.D.|
|Jupiter, Saturn||VSOP87||Precision is 1 arc-second from 0 A.D. - 4000 A.D.|
|Uranus, Neptune||VSOP87||Precision is 1 arc-second from 4000 B.C - 8000 A.D.|
|Pluto||?||Pluto's position is valid from 1885 A.D. -2099 A.D.|
|Earth's Moon||ELP2000-82B||Unsure about interval of validity or precision at time of writing. Possibly valid from 1828 A.D. to 2047 A.D.|
|Galilean satellites||L2||Valid from 500 A.D - 3500 A.D.|