How could two arduinos communicate, one in LEO (about 250 miles up) and one on the ground. I have heard that Lora modules could work, but the doppler shift could mess that up, I have also heard that I could use Iridium satellite phones, but I am not sure how the code would look for them communicating or how it would be done. I am aware that the arduinos could only communicate for about 2 minutes every 12 hours, that is not a problem.
Frankly, if you can put something in orbit, don't waste the money you will spend to put it there on something as basic as an Arduino. Find some money in your multi-thousand dollar budget for a decent controller.