Sorry if this comes as a nuisance at all, but I'm desperate, so here's a pop quiz. Let's pretend there's a new planet whose orbit is closer to the sun than Mercury's. We'll call it planet Tron. Tron is located 0.1 AU from the sun. How would you determine Tron's distance from EARTH (whose disatance is 1 AU from the sun) at superior conjunction, after determining Tron's orbital period around the sun (using P^2=a^3, AKA Kepler's third law)? Is there some forumla for this that I missed out on?

All I can think of to do is figure Earth's distance from the sun MINUS Tron's distance from the sun, but that calculation doesn't take superior conjunction into account. It has to be a bit more complicated than such simple subtraction....

Thanks in advance for any help!