Magic squares can also be arranged in a planetarium array.

15. Add the numbers on each of the four concentric ellipses, and on each of the four aligned orbital paths. Describe the sums.
16. Complete this planetarium array so that the magic-square constant is 62.
17. Subtract 10 from each number in the array from exercise 16. Is the new array a planetarium array?
18. Complete this planetarium array so that the magic-square constant is 4x + 6.