How long should I cook a half goose?
As @ElendilTheTall says, very correctly, cooking to time is a bad idea. However, it's good to have a working time figure for planning. In the case of goose the timeline is to cook 20-25 minutes per pound. 4.6 lb is a very small goose so I'm assuming it's 4.6kg, which is just over 10lb, so half that is 5 lb, which should take somewhere close to between 1 hour 40 minutes to 2 hours to cook. You would need to add at least 30 minutes for resting after cooking as well. 

I would aim to have the goose in the oven about 2:45 before you want to serve, and then keep a close eye on the goose's temperature. Use an oven thermometer that you can leave in the bird in the oven, it's much easier than having to pull the goose out and check it every 5 minutes. A handheld one is also useful to back up your measurements in case your leave-in probe is out of position. Do not overcook goose, keep a good eye on that temperature because goose can go from underdone to overdone in a very short time.