Can anyone tell me why my oranges are splitting open before they are ripe on the tree?
Well, if we had a foto or three, we could give you a better guess. Could be lack of water, over watering, lack of Calcium... a common cause... could be a fruit sucking critter... like a mite, a scale, a mold.
The answer is... there are lots of answers; if we knew more, like where you live, what is the weather, is the plant in a container or inground, how do you take care of it, what is the variety, what kind of rootstock do you have, stuff like that.
For you, based on where you are and your recent weather, I would say it has to do with uneven watering. Certain varieties are much more prone to splitting, like navel oranges, for example. I had some issues with my Page mandarin doing this, when our temps zoomed up for a week. Just a few, but it's frustrating to see. The best I can tell you, especially living in Texas, where you can have some really blistering temps, followed by really significant rainfall with your thunderstorms that can roll through, is to be sure to water well during your high temps, to even out those highs and lows with precipitation. I think this summer it was almost unavoidable to some extent for those of us in the southwest.
Here is a link that might be useful: split citrus