Relativity and gravity.....?

Question

we have learnt that time slow downs for a person travelling in a spacecraft at the speed of light, according to an observer on the ground.

also, that gravity slows down time. Thus, for a spacecraft far away from Earth, the effect gravity would have been reduced. Hence, the clock on the spacecraft should go faster than a clock on Earth.

So wouldn't these two opposite effects cancel out each other? Thus, would the person on the space craft still age slower?

Answer 1

Both special relativistic and general relativistic effects on time do have to be taken in consideration together. As an analogy, we have weight because of Earth's gravity, but at the same time, the Earth is spinning, creating a centrifugal force that counteracts it. But that doesn't mean we're weightless. As a real life example, engineers designing GPS satellites have to carefully factor in BOTH special relativistic and general relativistic effects on time and space. If they did not do so, GPS wouldn't work.

Answer 2

see:
http://en.wikipedia.org/wiki/Gps#Relativity