The accuracy of the prediction of a transit time depends on the method used to calculate it. Most planetarium programs, including Stellarium and Celestia, use a specific algorithm known as VSOP87 to calculate the positions of planets and other major bodies. It's a periodic series containing thousands of terms. (As I recall, Celestia truncates it to about a thousand terms in order to keep the calculation times reasonably short.) For details, see https://en.wikipedia.org/wiki/VSOP_%28planets%29 Its result is an approximation which gets worse and worse for times farther away from the present. Using a series approximation like this is necessary in order to minimize the amount of time used for the calculations.

A series approximation that's used by the space agencies is SPICE. It's appropriately calculated from "first principles" for each space mission and is much more accurate than VSOP. See http://naif.jpl.nasa.gov/naif/aboutspice.html Celestia can use it to position distant spacecraft within a few meters of their actual positions.

To "do it right" one would use a numeric integration of the gravitational effects of as many solar system objects as is practical, tracing their movements and gravitational interactions. This procedure is usually considered to be too "expensive", taking far longer than is reasonable for most situations.

A series approximation that's used by the space agencies is SPICE. It's appropriately calculated from "first principles" for each space mission and is much more accurate than VSOP. See http://naif.jpl.nasa.gov/naif/aboutspice.html Celestia can use it to position distant spacecraft within a few meters of their actual positions.

To "do it right" one would use a numeric integration of the gravitational effects of as many solar system objects as is practical, tracing their movements and gravitational interactions. This procedure is usually considered to be too "expensive", taking far longer than is reasonable for most situations.

Selden