Aperture will not open

Does this only happen, when you select Facebook in the "Shared" section, or whenever you launch Aperture?

If it only happens, when you select Facebook, try to open the Aperture preferences and remove Facebook from your Accounts pane in the Aperture Preferences.

In any case, open the System Preferences "Accounts" pane and reenter your Facebook settings there.

If Aperture does not launch after reentering the Facebook preferences, delete the Aperture preferences as described here at this link:

Get help with Aperture 3 - Apple Support

Steps to reset preference settings

To reset your Aperture user preference settings to their original state, do the following:

1. Quit Aperture.
2. In the Finder choose "Go to folder" from the Go menu.
3. Type ~/Library/Preferences in the "Go to the folder" field. Press the Go button.
4. Remove the "com.apple.Aperture.plist" file from the Preferences folder.
5. Restart your computer if you're using OS X Mavericks.

The locations of your Aperture libraries are stored in the preference file listed above. If you have stored your library outside the default location of ~/Pictures/Aperture Library, make a note of where the library is before deleting the Aperture preferences file. If you have more than one library, you can bring up a dialog to choose which one to load by pressing Option immediately after you open Aperture.