To be quite honest, that looks like cracks between 2 sheets of plasterboard. If you look at the photo of the plaster close up, you'll see the old undercoat plaster from years ago. Those cracks are far too straight for it to be a structural problem. This is what I would do.
Re-screw the plasterboard to the joists along the cracks, checking other areas too. Always push the boards upwards when adding screws, it gives a tighter fit.. Check for, and remove any loose areas of plaster along the cracks and then tape "ACROSS THE CRACKED JOINTS", all the way across the room,, from one side of the room to the other. Each piece of tape should be around 6 inches in length. Make sure that each piece of tape sits close, side by side, and all the way ACROSS the ceiling cracks. This may seem overkill, but it works, I do it all the time using mesh tape. By taping ACROSS the cracked joint/s, it's a far stronger job than a single length of tape, plus the ADDITIONAL/ EXTRA screws added earlier, will pull the plasterboard tighter to the joists. To hold the bits of tape in place if required , mix a small amount of Bonding with PVA added, and spread a little across the tapes. This will all be hidden when plastered.
When this is all prepped, PVA the ceiling, adding a red food dye to the white pva, turning it pink, so you can see exactly where you've been. Put on a coat of Bonding Coat plaster, maybe 2 coats, over the whole ceiling, onto the WET/TACKY pva, ( never plaster onto dry pva). Better to PVA the ceiling in sections, then put on the Bonding coat. When the whole ceiling has been coated with PVA and Bonding Coat, let it set, then put on 2 coats of Multi Finish, work at it until it sets, then job done, ready to paint, . This is exactly what I do all the time.
