Cannot click Update Vault path

Question

I want to relocate my vault to another HD. I follow the directs (ejecting HD tghat houses vault, disconnecting computer, reconnecting computer, selecting the vault), but "update vault path" is grayed out. Running OS 10.8.5, Aperture 3.4.5

Answer 1

I'm a little uncomfortable with your mixing of terms like vault and library, and then talking about deleting libraries.
It is essential you grasp the concept of a Library and Vault, and the relationship between two before deleting anything.
Your phrases:
1) "I opened Aperture, opened Show Vaults and there is my libarary called Academics on the new HD."
and
2) "If I open the new HD, the library is listed, but it is not listed under show HD"
suggest to me you are having problems writing the words you mean, nothing wrong with that, we all do it. But if you write the wrong words and then get bad advice that you then act on, that's very bad!! So I just want to be extra careful on what you are really saying here.
1) When you choose 'Show Vaults' you see Vaults not Libraries
2) "Show HD" makes no sense, so I assume you mean "Show Vaults" again.
Previously you spoke of having a library called 'academics' and now you have found a vault called 'academics' on your old HD. Is this the same thing, did you just call it a library before or did you create a new vault for academics?
So let's start again and keep everything simple.
Forget what you have for a second, and lets just go through some basic concepts.
You buy Aperture and run it. You get a default library in your Pictures folder on your internal drive called 'Aperture Library'
You decide to create a second library called 'Documents' for storing your documents in (I do this).
You now have two libraries 'Aperture Library' and 'Documents'
Aperture can only work on one library at a time. While working on 'Documents' that's all you see. You don't see your images from 'Aperture Library', just 'Documents'. When you switch to from 'Documents' to 'Aperture Library' you now only see your photos in the 'Aperture Library', you don't see your 'Documents'. They are both completely seperate.
You decide your 'Aperture Library' is getting too big for your internal drive so you buy a large external drive. You use Finder to copy the 'Aperture Library' from your Pictures folder to you external drive.
To open your copied 'Aperture Library' from the external drive you can either use Finder to go to your external drive and double click on the copy of 'Aperture Library'. Alternatively, within Aperture you can use the menu item 'File' the sub menu item 'Switch to Library' and then the further sub menu item 'Other/New...' which will ask you to navigate to the library you want to open.
Now you have three libraries. 'Aperture Library' on your internal drive, 'Documents' on your internal drive and the copy of 'Aperture Library' on your external drive. If you are happy the copy is complete and intact you can then delete the 'Aperture Library' on your internal drive.
If required, you could then repeat for your 'Documents' library.
That's how Aperture works with libraries. There is no updating of paths, you just tell it which library you want to open, either by double clicking in Finder, or by using the 'File->Switch to Library->Other/New...'
Once you have opened a library in Aperture, it will remember it as a shortcut on the 'File->Switch to Library' menu, but while you have multiple copies of the library available this is unsafe to use as you wont know which copy of the library it has opened. Wait until you have deleted the old copies of the Library before relying on these shortcuts. Until then, use 'File->Switch to Library->Other/New...' (or Finder) to be certain you are opening the right copy of the library.
So now lets talk about Vaults.
As noted above, Aperture can only open one Library at a time. Regrdless of how many libraries you have, Aperture will only open one at a time.
Lets call this Library your current library.
When you create a Vault, you are creating it for your current library only. The vault you create and your current library get married. They are joined. When you update the vault it will copy the current library to that vault.
If we now switch to a different library, my 'Documents' library, when I 'Show Vaults' I will have no Vaults. This is because the Vault I created was for my 'Aperture Library' not my 'Documents' library. If I switch back to my 'Aperture Library' I will once again see the Vault I created for my 'Aperture Library'. Switch back to my 'Documents' library, and again I have no Vaults to show.
If, while still in my 'Documents' library, I now create a new Vault, this Vault gets married to the current library, my 'Documents' library.
So if I now switch back to my 'Aperture Library', I will see one vault, the vault for the 'Aperture Library' and if I then switch back to my 'Documents' library, I will also see one vault, the vault for the 'Documents' library.
The Vaults panel in Aperture is not a navigator, I will never see these two vaults in there at the same time. The Vaults panels only shows you the Vault that is married to the Library you currently have open.
This is (most probably) why you wont see your 'academic' Vault and 'Aperture Library' Vault in Aperture at the same time. They are Vaults for different libraries so you will only see the Vault for the current library.
For completeness I should mention that a Library can have muliple vaults (multiple backups). But all of these are married to the same library. So when you 'Show Vaults' you only ever see the vaults for the current library.
If you decide to move your Vaults from the old HD to the new HD, when Aperture shows you the Vault, it shows as 'Disconnected'. This means Aperture knows it has a Vault for the current library, but it now doesn't know where the Vault is located. This is when you now use the 'Update Vault Path' so you can tell Aperture where the Vault is now located.
(really) hope this helps!
Andy