The make of the modem is just NBN which is the Australian publicly-owned broadband supplier. It doesn't seem to have a model number. So the modem was not purchased from a store - it was installed by the NBN people when they fitted the satellite dish to the roof of the house.
The model number of the Airport Extreme is A1354.
On my Mac, the operating system is OS X El Capitan version 10.11.6.
I have troubleshot up hill and down dale. Spoken at length to Mac support on two occasions, likewise the satellite ISP (Skymesh). At one point I was instructed to reset the Airport and I did so and that fixed everything. But later the problem returned. There is nothing wrong with the Airport because it works fine in a non-satellite situation. In fact, it is working fine now - that is, I am receiving and sending these messages via satellite modem and Airport with no problems. On the Airport Utility I have two green lights. But the problem will return. Does it have something to do with the signal from the satellite not being continuous? I ask this because yesterday, when it did not work, I connected directly by wire to the modem and every now and then the browser would inform me that I was not connected to the internet, but a second or two later I was connected again. The problem with the Airport seems to be that once it goes down it stays down.