Energy should be conserved when the mass pick up the speed in the gravity field, regardless of the Newton equation/Orbiting. The orbiting just a case study may not exist in some cases. Do not jump to result in GR, you need to look at the basic assumption. You made the same mistakes I made before. Remember that I assumed that gravity center has zero radius, the orbiting is a case I want to study, it may not exist when it get closer to the center of the gravity. You need to read GR again, especially the basic assumptions. I read them again and again. Shrinking space is one of the important result in GR and it delivered death sentence to GR, it obviously violated energy conservation. A matter moves at higher speed will get more energy plus shrinking space means more energy (Look at relativity equations). When you compare the same matter inside the Gravity field and out side of the gravity field, the energy/mass are different and the mass energy inside the gravity field is higher. Red-shift theory is a big stretch in GR too if look at it closely.
1. A matter in a shrinked space (Gravity Field) with higher speed has more energy than the matter outside of the gravity field.
2. Closely look at the red-shift clock, the explaination makes no sense;