Volume/Displacement

After much searching, top-secret astronomers discovered where the future government's time machine ended up.

Turns out that a time machine is a timespace machine, placing the traveler(s) and the machine in the exact location of space where that time occurred, taking into account the expansion of space, the natural movement of galaxies, stars, planets, etc., as well as a previously undiscovered change in subatomic makeup (you know, that whole dark matter/energy thing).

Top-secret medical advisors think this might be a way to cure diseases, by sending people to a different place in timespace (as opposed to the conventional spacetime, a minor difference but significant), rearranging their subatomic structures such that "modern" diseases can't form.

Now, how do we communicate with the timespace travelers and figure out how to tow them back to our spacetime location?