Can you mine through the world?
Solution 1:
If you dig down, you will reach bottom. Your screen will stop scrolling.
Source: reddit.com
Solution 2:
No, you can't. You can walk around a planet though, so when you walk to the west or east for long enough, you'll once again arrive at your starting point. As far as I know you'll hit an unpenetrable border, so the planets are essentially rings; at least when considering the accessible parts.