Hint 1: Hmm, if I remember my Latin correctly, "Ad Astra" means "to the stars".
Hint 2: Hey, wait a minute! I'm seeing "STARS" again in 51-Down51DCelestial bodies that are kinda cool (and in this puzzle n=7)[------], and the clue says there are seven of them.
Hint 3: 67-Across67A___ in the right direction[-----] is a hint regarding the symmetrical positioning of the seven interconnected STAR words. (Kinda looks like they are boldly walking or hiking across the grid, as if on a mission.)
Hint 4: Asta and Lassie were cool, but I think my favorite DOG STAR is TOTO.
Hint 5: Don't forget those first letters of grid entries in grid order! They're usually important!