If the pivot is set up correctly, simply choose your object and bring up the duplicate options box. Figure out how many copies you need and divide 360 by it. In the example I've attached, I put that I want 10 copies. So, 360/10 = 36. 36 will be the degree between each sphere so you put 36 in the rotate box of Y (again look at my screenshot). Hit apply and voila, there it is.

10 copies (yes, I'm aware the 10th copy overlaps the original...easy enough to delete or figure it out using 9 copies instead)

36 in the y column for rotate.