Sharepoint AD user athenticate to another domain

Question

I have a situation where I have to autheticate SharePoint user to another website that is not part of the sharepoint domain without asking user to login again.

I have sharepoint part of domain1. I have users in domain1 that log into sharepoint using NTLM by authenticating to domain1. I don't have any control over this domain and sharepoint configuration. I am working on a ASP.net application which needs to authenticate users from domain1 without prompting users for login if they have already logged into sharepoint server.

Is it possible to do? If yes please let me know how I can do this. I may be able to install a webpart on the Sharepoint if this allows me to do single sign on between sharepoint and my application.

Thanks Irfan