NavList:

Me earlier:

>This web tool is doing relatively little calculation. The positions of
>the Sun, Moon, and planets are stored in a ten megabyte database to the
>nearest arcsecond. These positions are originally from the JPL numerical
>integrations, so they are intrinsically very good.

Alex E asked:
"But where did you get this database from?
And where can I get this database from?"

 

There are lots of sources. I don't have a specific recommendation. Try "google" with search terms "JPL DE406"

 

And:
"Except by programming Meeus's many pages formula."

 

Unless you intend to program a device with certain very specific limitations, algorithmic calculation of planetary positions is an obsolescent approach to the problem. If you decide you want to do that anyway --just for amusement-- I believe Willman-Bell (publisher of most of the astro-calc books by Meeus) has put the code on disk and makes it available for sale at a reasonable price.