Oklahawg,

Jonathan should be ripe between August 20th or so and mid-September and Golden Delicious should begin ripening a week or so after Jonathan.

I've linked some apple-growing info from Texas A&M. If you look at question #8, it will give a few things to watch for to help you determine when to harvest. I think somewhere in that set of questions that give the days from bloom to harvest for some apples, so if you can remember when your apples bloomed, that info might come in handy too.

Dawn

Here is a link that might be useful: How To Know When Apples Are Ripe