The End of Time: Part Two - S4-E18
Factual error: The Vinvocci ship is said to be orbiting 100,000 miles above Earth, later refined to 105,000 miles. That's one-third of the distance to the Moon, and the Earth's apparent size from the windows of the ship is far too large for them to be that distance, or even 100,000 kilometres above the Earth's surface. Judging by the Earth's apparent size, the spaceship is actually orbiting 6,000-7,000 kilometres above the planet's surface.
Chosen answer: 1) When Stephen Moffat took over he ignored a lot of what had been developed before (there is not in-universe answer). 2) It would have killed Rose, so the Doctor absorbed the energy. His body regenerated before the energy could do a significant amount of damage that would prevent regeneration.