Is anyone aware of a device/tool that one could use to check the sweetness of oranges while they are still on the tree?
Thanks in advance,
Sure, John. A refractometer. You can purchase one at any wine making store, or on amazon.com. I would want to spend at least $80.0 or so, to get a good one. Brix (sugar content of an aqueous solution) will vary per cultivar obviously, but not sure you really need to go to this extent. You will get to know when your trees are ripe simply by picking the first fruit when your cultivar should be ripening and testing it. If it's not quite sweet enough, leave the fruit hanging for another week or two, and re-check. You can find out when different citrus cultivars are ripe (as well as the brix of some cultivars) by going to the UCR Citrus Variety Collection's web site. It is an excellent source of information about various citrus cultivars.
Here is a link that might be useful: UC Riverside Citrus Variety Collection