If a clock on Earth runs more slowly than a clock in outer space (because it is in a higher gravity environment), how long will it take for the two clocks to diverge by a significant amount?
With every second that passes in outer space, the clock on Earth experiences
one second plus an extra 2 × 10
seconds. How much time must elapse before those extra 2 × 10
seconds add up to a full extra second?
Because there are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day, it will take 60 × 60 × 24 times longer for the difference to sum to a full day.
Once we have computed the amount of time that must pass for the two clocks to experience a difference of a full day, we need only to convert our answer from units of seconds to units of years.