The most common and most likely answer to this crossword clue is the 4 plus 6 letter word STAR SYSTEM
I've seen this crossword clue in The Sunday Telegraph
S
T
A
R
S
Y
S
T
E
M
More clues leading to the result STAR SYSTEM
Buddy explains!
The straight part
We know that "Lots of heavenly bodies/something Hollywood relied on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lots of heavenly bodies/something hollywood relied on = star system.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.