The International Space Station orbits 350 km above the Earth's surface at a speed of 27700 km/hr.It takes approximately 1.5 hours to complete each orbit.At the same moment in 2008,two clocks mark the ten year anniversary of the Station orbiting the Earth.Both clocks are accurate to 1 ms,but one is on the Earth and the other is on the Station itself.How does the reading on the Station's clock compare with that of the Earth-based clock,which reads exactly 10 years?

Question

Quizplus · Accepted Answer

Due to time dilation, time passes slower in the Station relative to the Earth. This effect is caused by the difference in their velocities and the resulting difference in gravitational potentials. Using the formula for time dilation, Δt' = Δt√(1 - v^2/c^2), where Δt is the time interval in the Earth's frame, v is the velocity of the Station relative to the Earth, c is the speed of light, and Δt' is the time interval in the Station's frame, we can calculate the time difference between the clocks. 
Δt' = Δt√(1 - v^2/c^2)
Δt' = 10 years = 3.1536 x 10^8 s
Δt = 0.5 hours = 1800 s
v = 27700 km/hr = 7.6944 km/s
c = 299792.458 km/s
Δt' = 1800√(1 - (7.6944/299792.458)^2) = 1799.99989 s
The Station's clock is slower by Δt - Δt' = 0.00011 s or 0.11 ms per orbit, which adds up to 0.10 s over 10 years.

The International Space Station Orbits 350 Km Above the Earth's