The planet Vulcan, the Transneptunian planets and TransPluto are not officially discovered planets, but are important in esoteric and Uranian astrology. They should be treated as experimental. Their true accuracy is therefore unascertainable at this time. However, efforts have been made to ensure that their calculated positions agree with the orbits that have been proposed and are in general use for these bodies.
The Lilith used in Solar Fire is the one popular in Europe, and it is also called the Black Moon. This is not actually a hypothetical planet, but rather the geocentric position of the empty focus of the moon’s orbital ellipse (the earth being at the other focus). Solar Fire gives the Black Moon’s mean position.
Selena, also know as the White Moon is also popular in Europe. It has a perfectly circular hypothetical orbit.