Sherry, I don't have a definate answer, and hope someone chimes in, but if you pick fruit when unripe, especially since oranges are green, they won't ever ripen, 'off the tree.'
On average, citrus are picked around Nov-Dec. I'm sorry I couldn't be more help. Good luck, Toni

Thanks, Toni!
Louisiana oranges and satsumas show up in the grocery stores around Christmas, but last year I left two oranges on the tree, picked them around Christmas, and they were bitter. We had had a light freeze, so I wondered if maybe the cold temps ruined the juice. If we have a freeze before mid-December, I think I'll pick some before it occurs and leave the rest to see what happens. Hopefully, there won't be any freezes before December, giving them plenty of time to ripen.
Sherry

I've heard that where the stem meets the orange, that when that turns brown the orange is ripe. Have 4 orange trees and the oranges are either orange or almost orange so I would like some advice on when to start picking.