[The Might]

Especially in the Hobbit, time seems to be measured just like in our world.
Clearly the same system exists as Bilbo only received the message of the Dwarves at 10.45. Of course, this probably is only one of the many differences that exist between the Hobbit and other works by Tolkien.

But what about LotR?
I know the moon seems to play an important role there in the determination of time, perhaps the sun and stars as well.
But does he ever explain how clocks (such as the one owned by Bilbo) were invented or how they worked?
Perhaps you know of some quotes I didn't find so far.