Quote:
Originally Posted by kennyc
Yes! Proven by recent confirmations of General Relativity. 
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Exactly!
Our astronauts have experienced this. It's kind of a complicated balancing act. As astronauts venture further from the earth's gravitational field, their clocks speed up. But since clocks can't tell the difference between acceleration and gravity, as their speed increases, the acceleration works to counter that effect.
This Time article (no pun intended) does a pretty good job of explaining it.
"While Apollo 8 was within 4,000 miles of the earth, Alley found, the spacecraft's speed was the predominant factor; time slowed up and the astronauts actually aged more slowly than mere earthlings. But beyond that distance, as the effects of earth's gravity lessened, Apollo's time began running fast. Over the entire journey, Alley says, Apollo's time passed more quickly than earth time by the 300 microseconds."