Now that is an awesome button. Not a clue about the significance of the moon and stars but bet you will find out. Looks like early 1800's from the construction.
Listed on Plate 164 under heading of "MOONS an OTHER HEAVENLY BODIES" in The Big Book of Buttons, your button is called a "Man in the Moon" button, a popular theme on 19th century buttons.
I found this one 2 years ago. It was at a circa 1845 site, beside an 1822 church! I'm glad to see another! I researched until I was blue in the face, and found nothing.