If you are running Ubuntu 16.04.3 LTS either as the standard version or a flavor such as MATE, and you have Google-Earth-Stable installed, you are likely getting the error "Failed to Download Repository Information -- Check your Internet Connection." If you try to run an update from a terminal with sudo apt update you will see that the Google repository is not downloading because there is no public key available:

NO_PUBKEY 1397BC53640DB551.

Resolving this error requires downloading the new RSA key from the Ubuntu key server:

sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 1397BC53640DB551

Once you have run this command, you can then go back and either sudo apt update or run the updater through the GUI and the system will update properly.

DR