Once it knows that, it then asks the .org server to tell it the IP address of a .linuxdoc.org nameserver. Most of the time, your nameserver doesn't actually have to work that hard. Your cached IP address for a site is also thrown out if the host is unreachable. Here's how that happens. Your packet may pass through several routers on the way to its destination.
Routers are smart.
They watch how long it takes for other routers to acknowledge having received a packet. They also use that information to direct traffic over fast links. There's an urban legend that the Internet was designed to survive nuclear war. This is not true, but the Internet's design is extremely good at getting reliable performance out of flaky hardware in an uncertain world. This means that failures tend to be well localized and the network can route around them.