The title of this post is incorrect. We have to wait a few hours to know if the rocket man has made it to Mars orbit. EDIT: It's not a Mars orbit, its a solar orbit that puts it close to Mars at times. From the linked article: "If all phases of the flight are successful - and that will not be known until at least 6.5 hours after lift-off - the Tesla and its passenger will be despatched into an elliptical orbit around…
Actually, no, once the 2nd stage cuts off the trajectory is mostly fixed and we know what orbit it is in. There are, I believe, two more small burns that will be done to adjust the trajectory, but these are more of an adjustment to what kind of Martian transfer orbit it is in. It already has the hyperbolic velocity to leave Earth's orbit, and enter solar orbit with an apogee at the same distance as Mars. In 6.5 hours…
It is in a parking orbit, where it will sit for a few hours and then will reignite and will be set on a trajectory toward "martian orbit".
IIRC currently they are testing (or proving depending on how confident they are) that they can have the second stage sit for several hours in space before reignighting.