Cannot unmount a time machine external disk using Disk Utility?

I cannot believe all of the ridiculous answers to this, even by Apple experts. The external disk must remain in communication with Time Machine in order to automatically backup...obviously. THAT is the mysterious hidden program that is interfering with the abillity to unmount the disc using Disk Utility. The solution is to merely go to Time Machine Preferences. On the left side of that, there is a check box to "back up automatically." SIMPLY UNCHECK THAT BOX. Thats it! If you wan't to back up automatically, that external disk must remain mounted. To unmount the disk, simply uncheck that automatic backup option. Personally, I would rather just do backups manually at the intervals I choose myself, anyway. Force ejecting the disk will merely introduce errors eventually. The repair disc function doesn't work for time machine discs because of the way multiple snapshots work. Merely ignore that. The backups will be fine.