Why doesn't this closure have access to the 'this' keyword? - jQuery

I'm a beginner to closures (and Javscript in general), and I can't find a satisfactory explanation as to what's going on in this code:

function myObject(){
    this.myHello = "hello";
    this.myMethod = do_stuff;
}

function do_stuff(){
    var myThis = this;
    $.get('http://example.com', function(){
        alert(this.myHello);
        alert(myThis.myHello);
    });
}

var obj = new myObject;
obj.myMethod();

It will alert 'undefined' and then 'hello'. Obviously this should not be jQuery specific, but this is the simplest form of my original code I could come up with. The closure in do_stuff() has access to the variables in that scope, but apparently this rule does not apply to the this keyword.

Questions:

What happens to this when the closure is passed outside the scope of do_stuff() (in this case $.get())? Does myThis contain a copy of this or a reference to it? Is it generally not a good idea to use this in closures?

Any response much appreciated.