Duct Tape will probably be better than trying to glue it. There are people who can repair it by changing the hinge but the cost is probably more than the laptop is worth. A good cloth duct tape will hold it together for a long time as long as you don't stress the hinge too much.
If it's going into your observatory, you could consider mounting the screen (lid) against the wall with the laptop bottom section on your desk. Duct tape the top edge of the screen to the wall and it should be good for years.
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