Why does Hamlet follow the ghost of his father in Hamlet?

This section of the play comes in Act I scene 4. We are
told that the Ghost, when it appears before Marcellus, Horatio and Hamlet, does its best
to try and beckon Hamlet to go away with it by himself. Horatio says it is as if "some
impartment did desire / To you alone." From their perspective, it seems as if the Ghost
wants Hamlet to be with him alone so that it can tell him something. For Hamlet, the
fact that it will not speak at this stage means that he will follow it. He is obviously
incredibly curious as to why the Ghost has appeared, and in particular, what news it
wishes to share with Hamlet. We have been told by Marcellus already that "something is
rotten in the state of Denmark," and this combined with Hamlet's grief over his father
suggests that Hamlet already at some level suspects that something might not be right
with the way that his father died. Thus seeing the Ghost, with the possibility that his
father might not rest easy in his grave, would have made Hamlet desperate to know the
truth, ready to risk anything.